Big Ideas Math Answers Grade 5 Chapter 8 Add and Subtract Fractions

Big Ideas Math Answers Grade 5 Chapter 8 Add and Subtract Fractions

Big Ideas Math Answers Grade 5 Chapter 8 Add and Subtract Fractions is the best source to learn Add and Subtract Fractions concepts. Get free access to download Big Ideas Math Answers Grade 5 Chapter 8 Add and Subtract Fractions pdf. Learn how to solve a problem in different ways. We have provided a step-by-step process to solve the problems with real-time examples. Various tips and tricks are given to learn the concepts deeply. Follow the important notes for the quick learning of maths. Improve your math skills with the help of the Big Ideas Math Grade 5 Chapter 8 Add and Subtract Fractions Answers.

Big Ideas Math Book 5th Grade Chapter 8 Add and Subtract Fractions Answer Key

It is mandatory for the students to go through all the topics included in this chapter to kickstart their preparation. The list of topics is mentioned below along with the quick links. Understand each topic by referring to every link and solving every problem available below. Find the various methods to solve the questions and choose the best one to practice well for the exam. All the topics such as Simplest form, Subtract Fractions with Unlike Denominators, Find Common Denominators, Estimate Sums, and Differences of Fractions, Add Fractions with Unlike Denominators are prepared with a clear explanation in BIM Grade 5 Ch 8 Add and Subtract Fractions Solution key.

Lesson: 1 Simplest Form

Lesson: 2 Estimate Sums and Differences of Fractions

Lesson: 3 Find Common Denominators

Lesson: 4 Add Fractions with Unlike Denominators

Lesson: 5 Subtract Fractions with Unlike Denominators

Lesson: 6 Add Mixed Numbers

Lesson: 7 Subtract Mixed Numbers

Lesson: 8 Problem Solving: Fractions

Chapter 8 – Add and Subtract Fractions 

Lesson 8.1 Simplest Form

Explore and Grow

Use the model to write as many fractions as possible that are equivalent to \(\frac{36}{72}\) but have numerators less than 36 and denominators less than 72.
Big Ideas Math Answers Grade 5 Chapter 8 Add and Subtract Fractions 1
Which of your fractions has the fewest equal parts? Explain.

Construct Arguments
When might it be helpful to write \(\frac{48}{72}\) as \(\frac{2}{3}\) in a math problem?

Think and Grow: Simplest Form

Key Idea
When the numerator and denominator of a fraction have no common factors other than 1, the fraction is in simplest form. To write a fraction in simplest form, divide the numerator and the denominator by the greatest of their common factors.
Example
simplify \(\frac{6}{8}\) in the simplest form.
Big Ideas Math Answers Grade 5 Chapter 8 Add and Subtract Fractions 2
Step 1: Find the common factors of 6 and 8.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 3
The common factors of 6 and 8 are 1 and 2.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 4

Answer:
Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-4

Show and Grow

Question 1.
Use the model to write \(\frac{2}{4}\) in simplest form.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 5
Answer:
Step 1: Find the common factors of 2 and 4.
Factors of 2:   1, 2
Factors of 4:   1, 2, 4
The common factors of 2 and 4 are 1 and 2.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
                              Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 5
Because 1 and 2 have no common factors other than 1, \(\frac{2}{4}\) is in simplest form.

Question 2.
Write \(\frac{8}{12}\) in simplest form
Answer:
Step 1: Find the common factors of 8 and 12.
Factors of 8:    1, 2, 4, 8
Factors of 12:  1, 2, 3, 4, 6, 12
The common factors of 8 and 12 are 1, 2 and 4.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.

Because 2 and 3 have no common factors other than 1, \(\frac{8}{12}\) is in simplest form.

Apply and Grow: Practice

Use the model to write the fraction in simplest form.

Question 3.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 6
Answer:
Step 1: Find the common factors of 8 and 10.
Factors of 8:    1, 2, 4, 8
Factors of 10:  1, 2, 5, 10
The common factors of 8 and 10 are 1 and 2.

Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.

\small \frac{8}{10}= \frac{8 \div 2}{10 \div 2} = \frac{4}{5}

Because 4 and 5 have no common factors other than 1, \(\frac{8}{10}\) is in simplest form.

Question 4.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 7
Answer:
Step 1: Find the common factors of 5 and 15.
Factors of 5: 1, 5
Factors of 15: 1, 3, 5,15
The common factors of 5 and 15 are 1 and 5.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{5}{15}= \frac{5 \div 5}{15 \div 5} = \frac{1}{3}
Because 1 and 3 have no common factors other than 1, \(\frac{5}{15}\) is in simplest form.

Question 5.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 8

Write the fraction in simplest form.
Answer:
Step 1: Find the common factors of 10 and 12.
Factors of 10:  1, 2, 5, 10
Factors of 12:  1, 2, 3, 4, 6, 12
The common factors of 10 and 12 are 1 and 2.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{10}{12}= \frac{10 \div 2}{12 \div 2} = \frac{5}{6}
Because 5 and 6 have no common factors other than 1, \(\frac{10}{12}\) is in simplest form.

Question 6.
\(\frac{3}{6}\)
Answer:
Step 1: Find the common factors of 3 and 6.
Factors of 3:  1, 3
Factors of 6:  1, 2, 3, 6
The common factors of 3 and 6 are 1 and 3.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{3}{6}= \frac{3 \div 3}{6 \div 3} = \frac{1}{2}
Because 1 and 2 have no common factors other than 1, \(\frac{3}{6}\) is in simplest form.

Question 7.
\(\frac{2}{10}\)
Answer:
Step 1: Find the common factors of 2 and 10.
Factors of 2:  1, 2
Factors of 10:  1, 2, 5, 10
The common factors of 2 and 10 are 1 and 2.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{2}{10}= \frac{2 \div 2}{10 \div 2} = \frac{1}{5}
Because 1 and 5 have no common factors other than 1, \(\frac{2}{10}\) is in simplest form.

Question 8.
\(\frac{6}{8}\)
Answer:
Step 1: Find the common factors of 6 and 8.
Factors of 6:  1, 2, 3, 6
Factors of 8:  1, 2, 4, 8
The common factors of 6 and 8 are 1 and 2.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{6}{8}= \frac{6 \div 2}{8 \div 2} = \frac{3}{4}
Because 3 and 4 have no common factors other than 1, \(\frac{6}{8}\) is in simplest form.

Question 9.
\(\frac{7}{14}\)
Answer:
Step 1: Find the common factors of 7 and 14.
Factors of 7:  1, 7
Factors of 14:  1, 2, 7, 14
The common factors of 7 and 14 are 1 and 7.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{7}{14}= \frac{7 \div 7}{14 \div 7} = \frac{1}{2}
Because 1 and 2 have no common factors other than 1, \(\frac{7}{14}\) is in simplest form.

Question 10.
\(\frac{10}{100}\)
Answer:
Step 1: Find the common factors of 10 and 100.
Factors of 10: 1, 2, 5, 10
Factors of 100:  1, 2, 4, 5, 10, 20, 25, 50, 100
The common factors of 10 and 100 are 1, 2, 5 and 10.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{10}{100}= \frac{10 \div 10}{100 \div 10} = \frac{1}{10}
Because 1 and 10 have no common factors other than 1, \(\frac{10}{100}\) is in simplest form.

Question 11.
\(\frac{12}{4}\)
Answer:
Step 1: Find the common factors of 12 and 4.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 4:  1, 2, 4
The common factors of 12 and 4 are 1, 2 and 4.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{12}{4}= \frac{12 \div 4}{4 \div 4} = \frac{3}{1}
Because 3 and 1 have no common factors other than 1, \(\frac{12}{4}\) is in simplest form.

Question 12.
Three out of nine baseball players are in the outfield. In simplest form, what fraction of the players are in the outfield?
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 9
Answer:
Step 1: Find the common factors of 3 and 9.
Factors of 3: 1, 3
Factors of 9:  1, 3, 9
The common factors of 3 and 9 are 1 and 3
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{3}{9}= \frac{3 \div 3}{9 \div 3} = \frac{1}{3}
Because 1 and 3 have no common factors other than 1.
Therefore, players are in the outfield.

Question 13.
YOU BE THE TEACHER
Your friend writes \(\frac{2}{6}\) in simplest form. Is your friend correct? Explain
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 10

Answer: No, the answer is wrong.
The numerator and the denominator has to divide by the greatest of the common factors. You have divided only the denominator.

Explanation for \(\frac{2}{6}\) in simplest form.
Step 1: Find the common factors of 2 and 6.
Factors of 2: 1, 2
Factors of 6:  1, 2, 3, 6
The common factors of 2 and 6 are 1 and 2.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{2}{6}= \frac{2 \div 2}{6 \div 2} = \frac{1}{3}
Because 1 and 3 have no common factors other than 1, \(\frac{2}{6}\) is in simplest form.

Question 14.
Reasoning
The numerator and denominator of a fraction have 1, 2, and 4 as common factors. After you divide the numerator and denominator by 2, the fraction is still not in simplest form. Why?
Answer:
Given that, common factors are 1, 2 and 4
For the fraction to be in the simplest form, the numerator and denominator has to divide by the greatest of the common factors.
Here 4 is the greatest common factor. So, divide both the numerator and denominator by 4 to get the simplest form.
For example 4 and 8
Factors for 4: 1, 2, 4
Factors for 8: 1, 2, 4, 8
common factors: 1, 2 and 4
Simplest form:    \small \frac{4}{8}= \frac{4 \div 4}{8 \div 4} = \frac{1}{2}

Think and Grow: Modeling Real Life

Example
A quarterback passes the ball 45 times during a game. The quarterback completes 35 passes. What fraction of the passes, in simplest form, does the quarterback complete?
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 11
Find the number of passes that are not completed by subtracting the pass completions from the total number of passes.
45 – 35 = 10
Write a fraction for the passes the quarterback does not complete.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 12
Find common factors of 10 and 45. Then write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 13
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 14
The quarterback does not complete __ of the passes.

Answer:
Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-14
The quarterback does not complete 2/9 of the passes.

Show and Grow

Question 15.
There are 24 students in your class. Four of the students have blue eyes. What fraction of the class, in simplest form, do not have blue eyes?
Answer:
Given that,
Total no. of students in the class = 24
Students have blue eyes = 4
Students do not have blue eyes = 24 – 4 = 20
Step 1: Find the common factors of 24 and 20.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 20:  1, 2, 4, 5, 10, 20
The common factors of 24 and 20 are 1, 2 and 4.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.

\small \frac{20}{24}= \frac{20 \div 4}{24 \div 4} = \frac{5}{6}

Because 5 and 6 have no common factors other than 1.
Therefore, \small \frac{5}{6}th of the class do not have blue eyes.

Question 16.
DIG DEEPER!
A student answers 4 out of 12 questions on a test incorrectly. What fraction of the questions, in simplest form, does the student answer incorrectly? Interpret the fraction.
Answer:
Given that,
Total no. of questions = 12
No. of incorrect answers = 4
Step 1: Find the common factors of 12 and 4.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 4:  1, 2, 4
The common factors of 12 and 4 are 1, 2 and 4.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{4}{12} = \frac{4 \div 4}{12 \div 4} = \frac{1}{3}
Because 1 and 3 have no common factors other than 1.
Therefore, \small \frac{1}{3} of the questions student answered incorrectly.

Lesson 8.1 Simplest Form Homework & Practice 8.1

Use the model to write the fraction in simplest form.

Question 1.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 16
Answer:
Step 1: Find the common factors of 6 and 9.
Factors of 6: 1, 2, 3, 6
Factors of 9:  1, 3, 9
The common factors of 6 and 9 are 1 and 3.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.

\small \frac{6}{9} = \frac{6 \div 3}{9 \div 3} = \frac{2}{3}
Because 2 and 3 have no common factors other than 1, \small \frac{6}{9} is in simplest form.

Question 2.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 17
Answer:
Step 1: Find the common factors of 3 and 12.
Factors of 3: 1, 3
Factors of 12:  1, 3, 4, 6, 12
The common factors of 3 and 12 are 1 and 3.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{3}{12} = \frac{3 \div 3}{12 \div 3} = \frac{1}{4}
Because 1 and 4 have no common factors other than 1, \small \frac{3}{12} is in simplest form.

Question 3.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 18

Write the fraction in simplest form
Answer:
Step 1: Find the common factors of 5 and 10.
Factors of 5: 1, 5
Factors of 10:  1, 2, 5, 10
The common factors of 5 and 10 are 1 and 5.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}
Because 1 and 2 have no common factors other than 1, \small \frac{5}{10} is in the simplest form.

Question 4.
\(\frac{4}{8}\)
Answer:
Step 1: Find the common factors of 4 and 8.
Factors of 4: 1, 2, 4
Factors of 8:  1, 2, 4, 8
The common factors of 4 and 8 are 1, 2 and 4.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{4}{8} = \frac{4 \div 4}{8 \div 4} = \frac{1}{2}
Because 1 and 2 have no common factors other than 1, \(\frac{4}{8}\) is in simplest form.

Question 5.
\(\frac{5}{100}\)
Answer:
Step 1: Find the common factors of 5 and 100.
Factors of 5: 1, 5
Factors of 100:  1, 2, 4, 5, 10, 20, 25, 50, 100
The common factors of 5 and 100 are 1 and 5.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{5}{100} = \frac{5 \div 5}{100 \div 5} = \frac{1}{20}
Because 1 and 20 have no common factors other than 1, \(\frac{5}{100}\) is in simplest form.

Question 6.
\(\frac{20}{15}\)
Answer:
Step 1: Find the common factors of 20 and 15.
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 15:  1, 3, 5, 15
The common factors of 20 and 15 are 1 and 5.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{20}{15} = \frac{20 \div 5}{15 \div 5} = \frac{4}{3}
Because 4 and 3 have no common factors other than 1, \(\frac{20}{15}\) is in simplest form.

Question 7.
There are 18 students in your class. Six of the students pack their lunch. In simplest form, what fraction of the students in your class pack their lunch?
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 19
Answer:
Total students in the class = 18
No. of students pack their lunch = 6
Step 1: Find the common factors of 6 and 18.
Factors of 6: 1, 2, 3, 6
Factors of 18:  1, 2, 3, 6, 9, 18
The common factors of 6 and 18 are 1, 2, 3 and 6
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{6}{18} = \frac{6 \div 6}{18 \div 6} = \frac{1}{3}
Because 1 and 3 have no common factors other than 1.
Therefore, \small \frac{1}{3} of the students pack their lunch.

Question 8.
Reasoning
Why do you have to divide a numerator and a denominator by the greatest of their common factors to write a fraction in simplest form?
Answer:
To simplify a fraction to lowest terms, divide both the numerator and the denominator by their common factors. Repeat as needed until the only common factor is 1.

Question 9.
Writing
Explain how you know when a fraction is in simplest form.
Answer:
If the fraction has no common factors other than 1, then it is said to be the simplest form of the fraction.

Question 10.
Open-Ended
Write a fraction in which the numerator and the denominator have 1, 2, 4, and 8 as common factors. Then write the fraction in the simplest form.
Answer:
The fraction in which the numerator and the denominator is \small \frac{8}{16}.
Step 1: Find the common factors of 8 and 16.
Factors of 8: 1, 2, 4, 8
Factors of 16:  1, 2, 4, 8, 16
The common factors of 8 and 16 are 1, 2, 4 and 8.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{8}{16} = \frac{8 \div 8}{16 \div 8} = \frac{1}{2}
Because 1 and 2 have no common factors other than 1.

Question 11.
Modeling Real Life
A flight attendant has visited 30 of the 50 states. What fraction of the states, in simplest form, has he not visited?
Answer:
Given that,
No. of states = 50
A flight attendant has visited 30 states.
The no. of states he has not visited = 50 – 30 = 20
Step 1: Find the common factors of 20 and 50.
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 50: 1, 2, 5, 10, 25, 50
The common factors of 20 and 50 are 1, 2, 5 and 10.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{20}{50} = \frac{20 \div 10}{50 \div 10} = \frac{2}{5}
Because 2 and 5 have no common factors other than 1.
So the flight attendant has not visited \small \frac{2}{5} of the states.

Question 12.
DIG DEEPER!
A bin has red, orange, yellow, green, blue, and purple crayons. There are 4 of each color in the bin. In simplest form, what fraction of the crayons are red, orange, yellow, or green?
Answer:
Given that, a bin has 6 colors(red, orange, yellow, green, blue, and purple) of crayons.
There are 4 crayons in the each color = 4 x 6 = 24
If the bin having only 3 colors(red, orange, yellow or green) = 4 x 3 = 12
Step 1: Find the common factors of 12 and 24.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The common factors of 12 and 24 are 1, 2, 3, 4, 6 and 12.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{12}{24} = \frac{12 \div 12}{24 \div 12} = \frac{1}{2}
Because 1 and 2 have no common factors other than 1.
\small \frac{1}{2} of the crayons are red, orange, yellow or green.

Review & Refresh

Estimate the sum or difference.

Question 13.
598.44 – 45.61 = 
Answer: 550
The number round to 598.44 is 600.
The number round to 45.61 is 50.
600 – 50 = 550
Thus the estimated difference is 550.

Question 14.
93.8 + 4.3 =
Answer: 98
The number round to 93.8 is 94.
The number round to 4.3 is 4.
94 + 4 = 98
Thus the estimated addition is 98.

Lesson 8.2 Estimate Sums and Differences of Fractions

Explore and Grow

Plot \(\frac{7}{12}\), \(\frac{5}{6}\) and \(\frac{1}{10}\) on the number line.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 20
How can you estimate \(\frac{7}{12}\) + \(\frac{5}{6}\) ?
How can you estimate \(\frac{2}{3}\) – \(\frac{1}{10}\)?

Reasoning
Write two fractions that have a sum of about \(\frac{1}{2}\). Then write two fractions that have a difference of about \(\frac{1}{2}\). Explain your reasoning.

Think and Grow: Estimate Sums and Differences

You have used the benchmarks \(\frac{1}{2}\) and 1 to compare fractions. You can use the benchmarks 0, \(\frac{1}{2}\), and 1 to estimate sums and differences of fractions.
Example
Estimate \(\frac{1}{6}\) + \(\frac{5}{8}\)
Step 1: Use a number line to estimate each fraction.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 21
Step 2: Estimate the sum.
An estimate of \(\frac{1}{6}\) + \(\frac{5}{8}\) is __ + __ = ___
Example
Estimate \(\frac{9}{10}\) – \(\frac{2}{5}\).
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 22

Show and Grow

Estimate the sum or difference

Question 1.
\(\frac{1}{3}\) + \(\frac{11}{12}\)
Answer:
Step 1: Estimate each fraction.
\small \frac{1}{3} is between 0 and \small \frac{1}{2} , but is closer to \small \frac{1}{2}
\small \frac{11}{12} is between \small \frac{1}{2} and 1, but is closer to 1
Step 2: Estimate the sum.
An estimate of \(\frac{1}{3}\) + \(\frac{11}{12}\) is   \small \frac{1}{2} +  1 =  \small \frac{3}{2}

Question 2.
\(\frac{3}{5}\) + \(\frac{5}{6}\)
Answer:
Step 1: Estimate each fraction
\small \frac{3}{5} is between  \small \frac{1}{2} and 1 , but is closer to \small \frac{1}{2}
\small \frac{5}{6} is between \small \frac{1}{2} and 1, but is closer to 1
Step 2: Estimate the sum.
An estimate of \(\frac{3}{5}\) + \(\frac{5}{6}\) is \small \frac{1}{2} +  1 =  \small \frac{3}{2}

Question 3.
\(\frac{15}{16}\) – \(\frac{7}{8}\)
Answer:
Step 1: Use mental math to estimate each fraction.
\small \frac{15}{16} is about
Think : The numerator is about the same as the denominator.
\small \frac{7}{8} is about
Think : The numerator is about the same as the denominator.
Step 2: Estimate the difference.
An estimate of \small \frac{15}{16}\small \frac{7}{8}  is 1 – 1 = 0.

Apply and Grow: Practice

Estimate the sum or difference.

Question 4.
\(\frac{1}{6}\) + \(\frac{3}{5}\)
Answer:
Step 1: Estimate each fraction.
\small \frac{1}{6} is between 0 and \small \frac{1}{2}, but is closer to 0.
\small \frac{3}{5} is between \small \frac{1}{2} and 1, but is closer to \small \frac{1}{2}.
Step 2: Estimate the sum.
An estimate of \(\frac{1}{6}\) + \(\frac{3}{5}\) = 0 + \small \frac{1}{2} = \small \frac{1}{2}

Question 5.
\(\frac{4}{5}\) – \(\frac{5}{12}\)
Answer:
Step 1: Use mental math to estimate each fraction.
\small \frac{4}{5} is about
Think: The numerator is about the same as the denominator.
\small \frac{5}{12} is about
Think: The numerator is about half of the denominator.
Step 2: Estimate the difference.
An estimate of \small \frac{15}{16}\small \frac{7}{8}  is 1 – \small \frac{1}{2}  = \small \frac{1}{2}

Question 6.
\(\frac{13}{16}\) + \(\frac{5}{6}\)
Answer:
Step 1: Estimate each fraction.
\small \frac{13}{16} is between \small \frac{1}{2} and 1, but is closer to 1.
\small \frac{5}{6} is between \small \frac{1}{2} and 1, but is closer to 1.
Step 2: Estimate the sum.
An estimate of \(\frac{13}{16}\) + \(\frac{5}{6}\) = 1+1 = 2

Question 7.
\(\frac{3}{6}\) – \(\frac{1}{8}\)
Answer:
Step 1: Use mental math to estimate each fraction.
\small \frac{3}{6} is about
Think: The numerator is about half of the denominator.
\small \frac{1}{8} is about
Think: The numerator is near to zero.
Step 2: Estimate the difference.
An estimate of \small \frac{3}{6}\small \frac{1}{8} is  \small \frac{1}{2}  – 0 = \small \frac{1}{2} .

Question 8.
\(\frac{1}{14}\) + \(\frac{98}{100}\)
Answer:
Step 1: Estimate each fraction.
\small \frac{1}{14} is closer to 0
\small \frac{98}{100} is closer to 1.
Step 2: Estimate the sum.
An estimate of \(\frac{1}{14}\) + \(\frac{98}{100}\) = 0 +1 = 1

Question 9.
\(\frac{11}{12}\) – \(\frac{1}{8}\)
Answer:
Step 1: Use mental math to estimate each fraction.
\small \frac{11}{12} is about
Think: The numerator is about the same as the denominator.
\small \frac{1}{8} is about
Think: The numerator is near to zero.
Step 2: Estimate the difference.
An estimate of  \small \frac{11}{12} – \small \frac{1}{8} is  1  – 0 = 1.

Question 10.
You walk \(\frac{1}{10}\) mile to your friend’s house and then you both walk \(\frac{2}{5}\) mile. Estimate how much farther you walk with your friend than you walk alone.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 23
Answer:
To find how much farther I walk with my friend than I walk alone, subtract the distance that I walk alone from we both walk.
Step 1: Use mental math to estimate each fraction.
\small \frac{1}{10} is about____
Think: The numerator is near to zero.
\small \frac{2}{5} is about____
Think: The numerator is about half of the denominator.
Step 2: Estimate the difference.
An estimate of  \small \frac{2}{5}\small \frac{1}{10} = \small \frac{1}{2} – 0 = \small \frac{1}{2}
So the distance I walk with my friend than I walk alone is \small \frac{1}{2} mile.

Question 11.
A carpenter has two wooden boards. One board is \(\frac{3}{4}\) foot long and the other board is \(\frac{1}{6}\) foot long. To determine whether the total length of the boards is 1 foot, should the carpenter use an estimate, or is an exact answer required? Explain.
Answer:
Given,
A carpenter has two wooden boards. One board is \(\frac{3}{4}\) foot long and the other board is \(\frac{1}{6}\) foot long.
\(\frac{3}{4}\) + \(\frac{1}{6}\)
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCM = 12
\(\frac{3}{4}\) × \(\frac{3}{3}\) = \(\frac{9}{12}\)
\(\frac{1}{6}\) × \(\frac{2}{2}\) = \(\frac{2}{12}\)
\(\frac{9}{12}\) + \(\frac{2}{12}\) = \(\frac{11}{12}\)
\(\frac{11}{12}\) is approximately equal to 1 foot.

Question 12.
Number Sense
A fraction has a numerator of 1 and a denominator greater than 4. Is the fraction closer to 0, \(\frac{1}{2}\), or 1? Explain.
Answer:
Given,
A fraction has a numerator of 1 and a denominator greater than 4.
\(\frac{1}{4}\) = 0.25
If the denominator is greater than 4. Let’s consider 8.
\(\frac{1}{8}\) = 0.125
The fraction will be close to 0.

Think and Grow: Modeling Real Life

Example
In the human body, the small intestine is about 20\(\frac{1}{12}\) feet long. The large intestine is about 4\(\frac{5}{6}\) feet long. About how long are the intestines in the human body?
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 24
To find the total length of the intestines, estimate 20\(\frac{1}{12}\) + 4\(\frac{5}{6}\).
Step 1: Use mental math to round each mixed number to the nearest whole number.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 25

Answer:
Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-25

Show and Grow

Question 13.
A bullfrog jumps 5\(\frac{11}{12}\) feet. A leopard frog jumps 4\(\frac{1}{3}\) feet. About how much farther does the bullfrog jump than the leopard frog?
Answer:
Step 1: Use mental math to round each mixed number to the nearest whole number.
5\small \frac{11}{12} is about,  \small \frac{11}{12} is closer to 1 than 0.
4\small \frac{1}{3} is about, \small \frac{1}{3} is closer to 0 than 1.
Step 2: Estimate the difference
An estimate of 5\small \frac{11}{12}  – 4\small \frac{1}{3} = 1 – 0 = 1
So, bullfrog jumps 1 feet farther than the leopard frog.
Question 14.
DIG DEEPER!
A cell phone has 32 gigabytes of storage. The amounts of storage used by photos, songs, and apps are shown. About how many gigabytes of storage are left?
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 26
Answer:
Given that,
No. of gigabytes of storage in cellphone = 32
Step 1: Use mental math to round each mixed number to the nearest whole number.
Photos —>  8\small \frac{4}{5} is about,  \small \frac{4}{5} is closer to 1 than 0
Songs —>   2\small \frac{3}{100} is about,  \small \frac{3}{100} is closer to 0 than 1
Apps —>     6\small \frac{7}{10}  is about,  \small \frac{7}{10} is closer to 1 than 0
Step 2: Storage left in the phone = Total storage – storage(photos + songs + apps)
= 32 – (1 + 0 + 1)
Therefore, storage left = 30 gigabytes.

Question 15.
DIG DEEPER!
Use two different methods to estimate how many cups of nut medley the recipe makes. Which estimate do you think is closer to the actual answer? Explain.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 27
Answer:
1 \(\frac{3}{8}\) + \(\frac{5}{8}\) + 2 \(\frac{1}{3}\)
First add the whole numbers
1 + 2 = 3
\(\frac{3}{8}\) + \(\frac{5}{8}\) + \(\frac{1}{3}\)
1 \(\frac{1}{3}\)
3 + 1 \(\frac{1}{3}\) = 4 \(\frac{1}{3}\)
The fraction is 4 \(\frac{1}{3}\)
4 is equal to the actual answer.

Estimate Sums and Differences of Fractions Homework & Practice 8.2

Estimate the sum or difference

Question 1.
\(\frac{11}{12}\) – \(\frac{5}{6}\)
Answer:
Step 1: Use mental math to estimate each fraction.
\small \frac{11}{12} is about
Think : The numerator is about the same as the denominator.
\small \frac{5}{6} is about
Think : The numerator is about same as the denominator.
Step 2: Estimate the difference.
An estimate of  \small \frac{11}{12}\small \frac{5}{6}  is  1  – 1 = 0.

Question 2.
\(\frac{17}{20}\) + \(\frac{13}{20}\)
Answer:
Step 1: Estimate each fraction.
\small \frac{17}{20} is between \small \frac{1}{2} and 1, but is closer to 1.
\small \frac{13}{20} is between \small \frac{1}{2} and 1, but is closer to \small \frac{1}{2}.
Step 2: Estimate the sum.
An estimate of \(\frac{17}{20}\) + \(\frac{13}{20}\) = 1 + \small \frac{1}{2} = \small \frac{3}{2}.

Question 3.
\(\frac{3}{8}\) – \(\frac{1}{6}\)
Answer:
Step 1: Use mental math to estimate each fraction.
\small \frac{3}{8} is about
Think : The numerator is about half of the denominator.
\small \frac{1}{6} is about
Think : The numerator is near to zero.
Step 2: Estimate the difference.
An estimate of  \small \frac{3}{8}  – \small \frac{1}{6}   is  \small \frac{1}{2}  – 0 = \small \frac{1}{2}.

Question 4.
\(\frac{7}{12}\) + \(\frac{2}{5}\)
Answer:
Step 1: Estimate each fraction.
\small \frac{7}{12} is between \small \frac{1}{2} and 1, but is closer to \small \frac{1}{2}.
\small \frac{2}{5} is between 0 and \small \frac{1}{2}, but is closer to \small \frac{1}{2}.
Step 2: Estimate the sum.
An estimate of \(\frac{7}{12}\) + \(\frac{2}{5}\) = \small \frac{1}{2} + \small \frac{1}{2} = 1.

Question 5.
\(\frac{4}{5}\) – \(\frac{7}{12}\)
Answer:
Step 1: Use mental math to estimate each fraction.
\small \frac{4}{5} is about
Think: The numerator is about the same as the denominator.
\small \frac{7}{12} is about
Think: The numerator is about half of the denominator.
Step 2: Estimate the difference.
An estimate of  \small \frac{4}{5}  – \small \frac{7}{12}   is  1 –  \small \frac{1}{2}  = \small \frac{1}{2}

Question 6.
\(\frac{1}{5}\) + 1\(\frac{10}{21}\)
Answer:
Step 1: Use mental math to round each mixed number to the nearest whole number.
\(\frac{1}{5}\) is closer to 0
1\(\frac{10}{21}\) is close to 1.
Step 2: Estimate the sum.
An estimate of \(\frac{1}{5}\) + 1\(\frac{10}{21}\)
= 0 + 1 = 1

Question 7.
3\(\frac{5}{8}\) – \(\frac{1}{10}\)
Answer:
Step 1: Use mental math to round each mixed number to the nearest whole number.
3\small \frac{5}{8}  is about, \small \frac{5}{8} is closer to 1 than 0
\small \frac{1}{10} is near to 0
Step 2: Estimate the difference
An estimate of 3\small \frac{5}{8}  – \small \frac{1}{10} = 1 – 0 = 1.

Question 8.
6\(\frac{1}{3}\) + 2\(\frac{4}{6}\)
Answer:
Step 1: Use mental math to round each mixed number to the nearest whole number.
\(\frac{1}{3}\) is close to 0 than 1.
\(\frac{4}{6}\) is to 1 than 0.
Step 2: Estimate the sum
An estimate of 6\(\frac{1}{3}\) is 6.
An estimate of 2\(\frac{4}{6}\) is 3.
6 + 3 = 9

Question 9.
5\(\frac{7}{8}\) – 4\(\frac{49}{100}\)
Answer:
Step 1: Use mental math to round each mixed number to the nearest whole number.
5\small \frac{7}{8}  is about, \small \frac{7}{8} is closer to 1 than 0
4\small \frac{49}{100}  is about, \small \frac{49}{100} is closer to 0 than 1
Step 2: Estimate the difference
An estimate of 5\small \frac{7}{8}  – 4\small \frac{49}{100}  = 1 – 0 =  1.

Question 10.
You make a bag of trail mix with \(\frac{2}{3}\) cup of raisins and \(\frac{9}{8}\) cups of peanuts. About how much trail mix do you make?
Answer:
Raisins = \small \frac{2}{3} cups
Peanuts = \small \frac{9}{8} cups
Step 1: Estimate each fraction.
\small \frac{2}{3} is between \small \frac{1}{2} and 1, but is closer to \small \frac{1}{2}.
\small \frac{9}{8} is closer to 1.
Step 2: Estimate the sum.
An estimate of \(\frac{2}{3}\) + \(\frac{9}{8}\) = \small \frac{1}{2} + 1 = \small \frac{3}{2}.
So trail mix = \small \frac{3}{2}.

Question 11.
You have \(\frac{2}{3}\) cup of flour in a bin and \(\frac{7}{8}\) cup of flour in a bag. To determine whether you have enough flour for a recipe that needs 1\(\frac{3}{4}\) cups of flour, should you use an estimate, or is an exact answer required? Explain.
Answer:
Given,
You have \(\frac{2}{3}\) cup of flour in a bin and \(\frac{7}{8}\) cup of flour in a bag.
\(\frac{2}{3}\) + \(\frac{7}{8}\) = 1 \(\frac{13}{24}\)
Th estimated fraction of 1 \(\frac{13}{24}\) is 1\(\frac{3}{4}\)

Question 12.
Writing
Explain how you know \(\frac{9}{10}\) – \(\frac{3}{5}\) is about \(\frac{1}{2}\).
Answer:
Step 1: Use mental math to estimate each fraction.
\small \frac{9}{10} is about
Think: The numerator is about the same as the denominator.
\small \frac{3}{5} is about
Think : The numerator is about half of the denominator.
Step 2: Estimate the difference.
An estimate of \small \frac{9}{10}\small \frac{3}{5}  is 1 – \small \frac{1}{2}  = \small \frac{1}{2}.

Question 13.
Precision
Your friend says \(\frac{5}{8}\) + \(\frac{7}{12}\) is about 2. Find a closer estimate. Explain why your estimate is closer.
Answer:
\(\frac{5}{8}\) + \(\frac{7}{12}\) = 1 \(\frac{5}{24}\)
\(\frac{5}{24}\) is closer to 1 than 0.
1 \(\frac{5}{24}\) is about 2.

Question 14.
Modeling Real Life
About how much taller is Robot A than Robot B?
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 28
Answer:
Step 1: Use mental math to round each mixed number to the nearest whole number.
1 \small \frac{6}{10} is about, \small \frac{6}{10} is closer to 1 than 0.
1 \small \frac{1}{5}  is about, \small \frac{1}{5} is closer to 0 than 1.
Step 2: Estimate the difference
An estimate of 1 \small \frac{6}{10}  – 1 \small \frac{1}{5}   = 1 – 0 =  1.
Robot A is 1 meter taller than Robot B.

Question 15.
Modeling Real Life
A class makes a paper chain that is 5\(\frac{7}{12}\) feet long. The class adds another 3\(\frac{5}{6}\) feet to the chain. About how long is the chain now?
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 29
Answer:
Step 1: Use mental math to round each mixed number to the nearest whole number.
5\small \frac{7}{12} is about,  \small \frac{7}{12} is closer to 1 than 0.
3\small \frac{5}{6} is about, \small \frac{5}{6} is closer to 1 than 0.
Step 2: Estimate the sum
An estimate of 5\small \frac{7}{12}  + 3\small \frac{5}{6} = 1 + 1 = 2
Therefore, the chain is now 2 feet long.

Review & Refresh

Find the product. Check whether your answer is reasonable.

Question 16.
509 × 5 = ___
Answer:
The number 509 round to hundred is 500.
500 × 5 = 2500
509 × 5 = 2545
So the answer is reasonable.

Question 17.
7,692 × 6 = ___
Answer:
The number 7692 round to hundred is 7700.
7700 × 6 = 46200
7,692 × 6 = 46152
So the answer is reasonable.

Question 18.
31,435 × 7 = ___
Answer:
The number 31435 round to hundred is 31,400.
31,400 × 7 = 219800
31,435 × 7 = 220045
So the answer is reasonable.

Lesson 8.3 Find Common Denominators

Explore and Grow

You cut a rectangular pan of vegetable lasagna into equal-sized pieces. You serve \(\frac{1}{2}\) of the lasagna to a large table and \(\frac{1}{3}\) of the lasagna to a small table. Draw a diagram that shows how you cut the lasagna.
What fraction of the lasagna does each piece represent? How does the denominator of the fraction compare to the denominators of \(\frac{1}{2}\) and \(\frac{1}{3}\) ?

Reasoning
Is there another way you can cut the lasagna? Explain your reasoning.

Think and Grow: Find Common Denominators

Key Idea
Fractions that have the same denominator are said to have a common denominator. You can find a common denominator either by finding a common multiple of the denominators or by finding the product of the denominators.
Example
Use a common denominator to write equivalent fractions for \(\frac{1}{2}\) and \(\frac{5}{8}\).
List multiples of the denominators.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 30

Answer:
Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-30

Example
Use a common denominator to write equivalent fractions for \(\frac{2}{3}\) and \(\frac{1}{4}\). Use the product of the denominators: 3 × 4 = __.
Write equivalent fractions with denominators of 12.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 31

Answer:
Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-31

Show and Grow

Use a common denominator to write an equivalent fraction for each fraction.

Question 1.
\(\frac{2}{3}\) and \(\frac{1}{6}\)
Answer:
Use the product of the denominators : 3 \small \times 6 = 18
Write equivalent fractions with denominators of 18
\small \frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18}
\small \frac{1}{6} = \frac{1 \times 3}{6 \times 3} = \frac{3}{18}
Therefore, equivalent fractions are \small \frac{12}{18}  and \small \frac{3}{18}.

Question 2.
\(\frac{5}{6}\) and \(\frac{3}{4}\)
Answer:
Step 1: Use the product of the denominators : 6 \small \times 4 = 24
Step 2: Write equivalent fractions with denominators of 24
\small \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}
\small \frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}
Therefore, equivalent fractions are \small \frac{20}{24}  and \small \frac{18}{24}.

Apply and Grow: Practice

Use a common denominator to write an equivalent fraction for each fraction.

Question 3.
\(\frac{2}{3}\) and \(\frac{5}{6}\)
Answer:
Step 1: Use the product of the denominators : 3 \small \times 6 = 18
Step 2: Write equivalent fractions with denominators of 18

\small \frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18}

\small \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}
Therefore, equivalent fractions are \small \frac{12}{18}  and \small \frac{15}{18}.

Question 4.
\(\frac{3}{4}\) and \(\frac{1}{2}\)
Answer:
Step 1: Use the product of the denominators : 4 \small \times 2 = 8
Step 2: Write equivalent fractions with denominators of 8
\small \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
\small \frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}
Therefore, equivalent fractions are \small \frac{6}{8}  and \small \frac{4}{8}.

Question 5.
\(\frac{5}{9}\) and \(\frac{2}{3}\)
Answer:
Step 1: Use the product of the denominators: 9 \small \times 3 = 27
Step 2: Write equivalent fractions with denominators of 27
\small \frac{5}{9} = \frac{5 \times 3}{9 \times 3} = \frac{15}{27}
\small \frac{2}{3} = \frac{2 \times 9}{3 \times 9} = \frac{18}{27}
Therefore, equivalent fractions are \small \frac{15}{27}  and \small \frac{18}{27}.

Question 6.
\(\frac{8}{21}\) and \(\frac{3}{7}\)
Answer:
Step 1: Use the product of the denominators: 21 \small \times 7 = 147
Step 2: Write equivalent fractions with denominators of 147
\small \frac{8}{21} = \frac{8 \times 7}{21 \times 7} = \frac{56}{147}
\small \frac{3}{7} = \frac{3 \times 21}{7 \times 21} = \frac{63}{147}
Therefore, equivalent fractions are \small \frac{56}{147}  and \small \frac{63}{147}.

Question 7.
\(\frac{1}{5}\) and \(\frac{1}{2}\)
Answer:
Step 1: Use the product of the denominators: 5 \small \times 2 = 10
Step 2: Write equivalent fractions with denominators of 10
\small \frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}
\small \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
Therefore, equivalent fractions are \small \frac{2}{10}  and \small \frac{5}{10}.

Question 8.
\(\frac{3}{4}\) and \(\frac{1}{6}\)
Answer:
Step 1: Use the product of the denominators: 4 \small \times 6 = 24
Step 2: Write equivalent fractions with denominators of 24
\small \frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}
\small \frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24}
Therefore, equivalent fractions are \small \frac{18}{24}  and \small \frac{4}{24}.

Question 9.
\(\frac{3}{7}\) and \(\frac{2}{9}\)
Answer:
Step 1: Use the product of the denominators: 7 \small \times 9 = 63
Step 2: Write equivalent fractions with denominators of 63
\small \frac{3}{7} = \frac{3 \times 9}{7 \times 9} = \frac{27}{63}
\small \frac{2}{9} = \frac{2 \times 7}{9 \times 7} = \frac{14}{63}
Therefore, equivalent fractions are \small \frac{27}{63}  and \small \frac{14}{63}.

Question 10.
\(\frac{3}{8}\) and \(\frac{5}{11}\)
Answer:
Step 1: Use the product of the denominators: 8 \small \times 11 = 88
Step 2: Write equivalent fractions with denominators of 88
\small \frac{3}{8} = \frac{3 \times 11}{8 \times 11} = \frac{33}{88}
\small \frac{5}{11} = \frac{5 \times 8}{11 \times 8} = \frac{40}{88}
Therefore, equivalent fractions are \small \frac{33}{88} and \small \frac{40}{88}.

Question 11.
You walk your dog \(\frac{3}{4}\) mile on Saturday and \(\frac{5}{8}\) mile on Sunday. Use a common denominator to write an equivalent fraction for each fraction.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 32
Answer:
Step 1: Use the product of the denominators: 4 \small \times 8 = 32
Step 2: Write equivalent fractions with denominators of 32
\small \frac{3}{4} = \frac{3 \times 8}{4 \times 8} = \frac{24}{32}
\small \frac{5}{8} = \frac{5 \times 4}{8 \times 4} = \frac{20}{32}
Dog walk on Saturday, equivalent fraction = \small \frac{24}{32}
Dog walk on Sunday, equivalent fraction = \small \frac{20}{32}

Question 12.
Writing
Explain how to use the models to find a common denominator for \(\frac{1}{2}\) and \(\frac{3}{5}\). Then write an equivalent fraction for each fraction.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 33
Answer:
Initially find the product of the denominators and that product value is the denominator for both fractions.
Step 1: Use the product of the denominators: 2 \small \times 5 = 10
Step 2: Write equivalent fractions with denominators of 10
\small \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
\small \frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}
Therefore, equivalent fractions are \small \frac{5}{10} and \small \frac{6}{10}.

Question 13.
Number Sense
Which pairs of fractions are equivalent to \(\frac{1}{2}\) and \(\frac{2}{3}\) ?
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 34
Answer:
\small \frac{6}{12} and \small \frac{8}{12}

\small \frac{3}{6} and \small \frac{4}{6}
These two fractions are equivalent to \(\frac{1}{2}\) and \(\frac{2}{3}\).

Think and Grow: Modeling Real Life

Example
You and your friend make woven key chains. Your key chain is \(\frac{2}{4}\) foot long. Your friend’s is \(\frac{3}{6}\) foot long. Are the key chains the same length?
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 35
Use a common denominator to write equivalent fractions for the lengths of the key chains. Use the product of the denominators.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 36
Write equivalent fractions with denominators of 24.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 37
Compare the lengths of the key chains.
So, the key chains __ the same length.

Answer:
4 × 6 = 24
Write equivalent fractions with denominators of 24.
Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-37
So, the key chains has the same length.

Show and Grow

Question 14.
Your hamster weighs \(\frac{13}{16}\) ounce. Your friend’s hamster weighs \(\frac{6}{8}\) ounce. Do the hamsters weigh the same amount?
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 38
Answer:
Use a common denominator to write equivalent fractions for the hamsters weight.
Step 1: Use the product of the denominators: 16 \small \times 8 = 128
Step 2: Write equivalent fractions with denominators of 128

\small \frac{13}{16} = \frac{13 \times 8}{16 \times 8} = \frac{104}{128}

\small \frac{6}{8} = \frac{6 \times 16}{8 \times 16} = \frac{96}{128}
Hamsters weigh the different amount. One is \small \frac{104}{128} ounce and the other one is \small \frac{96}{128} ounce.

Question 15.
DIG DEEPER!
You have three vegetable pizzas of the same size. One has 4 equal slices. The second has 8 equal slices. The third has 6 equal slices. You cut the pizzas until all of them have the same number of slices. How many slices does each pizza have?
Answer:
Given,
You have three vegetable pizzas of the same size.
One has 4 equal slices. The second has 8 equal slices.
The third has 6 equal slices. You cut the pizzas until all of them have the same number of slices.
4 + 6 + 8 = 18
one has \(\frac{4}{18}\)
second has \(\frac{6}{18}\)
Third has \(\frac{8}{18}\)
Total there are 18 slices.

Find Common Denominators Homework & Practice 8.3

Use a common denominator to write an equivalent fraction for each fraction.

Question 1.
\(\frac{1}{2}\) and \(\frac{3}{8}\)
Answer:
Step 1: Use the product of the denominators: 2 \small \times 8 = 16
Step 2: Write equivalent fractions with denominators of 16

\small \frac{1}{2} = \frac{1 \times 8}{2 \times 8} = \frac{8}{16}

\small \frac{3}{8} = \frac{3 \times 2}{8 \times 2} = \frac{6}{16}
Therefore, equivalent fractions are \small \frac{8}{16}  and \small \frac{6}{16}.

Question 2.
\(\frac{7}{9}\) and \(\frac{2}{3}\)
Answer:
Step 1: Use the product of the denominators: 9 \small \times 3 = 27
Step 2: Write equivalent fractions with denominators of 27.

\small \frac{7}{9} = \frac{7 \times 3}{9 \times 3} = \frac{21}{27}

\small \frac{2}{3} = \frac{2 \times 9}{3 \times 9} = \frac{18}{27}
Therefore, equivalent fractions are \small \frac{21}{27}  and \small \frac{18}{27}.

Question 3.
\(\frac{5}{6}\) and \(\frac{1}{2}\)
Answer:
Step 1: Use the product of the denominators: 6 \small \times 2 = 12
Step 2: Write equivalent fractions with denominators of 12.

\small \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}

\small \frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}
Therefore, equivalent fractions are \small \frac{10}{12}  and \small \frac{6}{12}.

Question 4.
\(\frac{3}{4}\) and \(\frac{5}{16}\)
Answer:
Step 1: Use the product of the denominators: 4 \small \times 16 = 64
Step 2: Write equivalent fractions with denominators of 64.

\small \frac{3}{4} = \frac{3 \times 16}{4 \times 16} = \frac{48}{64}

\small \frac{5}{16} = \frac{5 \times 4}{16 \times 4} = \frac{20}{64}
Therefore, equivalent fractions are \small \frac{48}{64}  and \small \frac{20}{64}.

Question 5.
\(\frac{18}{24}\) and \(\frac{5}{6}\)
Answer:
Step 1: Use the product of the denominators: 24 \small \times 6 = 144
Step 2: Write equivalent fractions with denominators of 144.

\small \frac{18}{24} = \frac{18 \times 6}{24 \times 6} = \frac{108}{144}

\small \frac{5}{6} = \frac{5 \times 24}{6 \times 24} = \frac{120}{144}
Therefore, equivalent fractions are \small \frac{108}{144}  and \small \frac{120}{144}.

Question 6.
\(\frac{1}{3}\) and \(\frac{1}{5}\)
Answer:
Step 1: Use the product of the denominators: 3 \small \times 5 = 15
Step 2: Write equivalent fractions with denominators of 15.

\small \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}

\small \frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}
Therefore, equivalent fractions are \small \frac{5}{15}  and \small \frac{3}{15}.

Question 7.
\(\frac{3}{5}\) and \(\frac{4}{7}\)
Answer:
Step 1: Use the product of the denominators: 5 \small \times 7= 35
Step 2: Write equivalent fractions with denominators of 35.

\small \frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}

\small \frac{4}{7} = \frac{4 \times 5}{7 \times 5} = \frac{20}{35}
Therefore, equivalent fractions are \small \frac{21}{35}  and \small \frac{20}{35}.

Question 8.
\(\frac{5}{8}\) and \(\frac{2}{9}\)
Answer:
Step 1: Use the product of the denominators: 8 \small \times 9 = 72
Step 2: Write equivalent fractions with denominators of 72.

\small \frac{5}{8} = \frac{5 \times 9}{8 \times 9} = \frac{45}{72}

\small \frac{2}{9} = \frac{2 \times 8}{9 \times 8} = \frac{16}{72}
Therefore, equivalent fractions are \small \frac{45}{72}  and \small \frac{16}{72}.

Question 9.
A mint plant grows \(\frac{7}{8}\) inch in 1 week and \(\frac{13}{16}\) inch the next week. Use a common denominator to write an equivalent fraction for each fraction.
Answer:
Step 1: Use the product of the denominators : 8 \small \times 16 = 128
Step 2: Write equivalent fractions with denominators of 128.

\small \frac{7}{8} = \frac{7 \times 16}{8 \times 16} = \frac{112}{128}

\small \frac{13}{16} = \frac{13 \times 8}{16 \times 8} = \frac{104}{128}
Therefore, equivalent fractions are \small \frac{112}{128}  and \small \frac{104}{128}.

Question 10.
Which One Doesn’t Belong? Which pair of fractions is not equivalent to \(\frac{2}{5}\) and \(\frac{1}{10}\)?
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 39
Answer:
So, \small \frac{6}{15} and \small \frac{5}{15} is not equivalent to \(\frac{2}{5}\) and \(\frac{1}{10}\) and remaining all the pairs are equivalent.

Question 11.
YOU BE THE TEACHER
Your friend says she used a common denominator to find fractions equivalent to \(\frac{2}{3}\) and \(\frac{8}{9}\). Is your friend correct? Explain.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 39.1
Answer:
No, she is wrong because 9 and 12 are not common denominators.
Step 1: Use the product of the denominators : 3 \small \times 9 = 27
Step 2: Write equivalent fractions with common denominator of 27.

\small \frac{2}{3} = \frac{2 \times 9}{3 \times 9} = \frac{18}{27}

\small \frac{8}{9} = \frac{8 \times 3}{9 \times 3} = \frac{24}{27}
Therefore, equivalent fractions are \small \frac{18}{27}  and \small \frac{24}{27}.

Question 12.
Modeling Real Life
Some friends spend \(\frac{1}{3}\) hour collecting sticks and \(\frac{5}{6}\) hour building a fort. Do they spend the same amount of time on each? Explain.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 40
Answer:
No, they can not spend the same time on each because \small \frac{1}{3} is not equivalent to \small \frac{5}{6}.
\small \frac{1}{3} is equivalent to \small \frac{2}{6}.

Question 13.
DIG DEEPER!
Use a common denominator to write an equivalent fraction for each fraction. Which two students are the same distance from the school? Are they closer to or farther from the school than the other student?
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 41
Answer:
Step 1: Use the LCM of the denominators. LCM of 12, 8 and 6 = 24
Step 2: Write equivalent fractions with common denominator of 24.
Student A –>  \small \frac{10}{12} = \frac{10 \times 2}{12 \times 2} = \frac{20}{24}
Student B –>  \small \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}
Student C –>  \small \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}
Therefore, student A and student C are the same distance from the school i.e. \small \frac{20}{24} mile.
They are closer to student B.

Review & Refresh

Find the value of the expression.

Question 14.
102
Answer: 100

Question 15.
8 × 104
Answer: 80,000

Question 16.
6 × 103
Answer: 6000

Question 17.
9 × 105
Answer: 9,00,000

Lesson 8.4 Add Fractions with Unlike Denominators

Use a model to find the sum.

Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 42

Explain how you can use a model to add fifths and tenths.

Construct Arguments
How can you add two fractions with unlike denominators without using a model? Explain why your method makes sense.

Think and Grow: Add Fractions with Unlike Denominators

You can use equivalent fractions to add fractions that have unlike denominators.
Example
Find \(\frac{1}{4}\) + \(\frac{3}{8}\)
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 8 is a multiple of 4, so rewrite \(\frac{1}{4}\) with a denominator of 8.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 43

Answer:
Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-43
Example
Find \(\frac{7}{8}\) + \(\frac{1}{6}\) Estimate __
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 8 is not a multiple of 6, so rewrite each fraction with a denominator of 8 × 6 = 48.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 44

Answer:
Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-44

Show and Grow

Add.

Question 1.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 45
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 6 is a multiple of 3, so rewrite it with a denominator of 6.
Rewrite \small \frac{2}{3} as \small \frac{2 \times 2}{3 \times 2} = \small \frac{4}{6}

\small \frac{5}{6} + \small \frac{2}{3}  =  \small \frac{5}{6} + \small \frac{4}{6}

= \small \frac{9}{6} or \small \frac{3}{2}

Question 2.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 46
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 5 is not a multiple of 4, so rewrite each fraction with a denominator of 5 \small \times 4 = 20

Rewrite \small \frac{1}{5}  as \small \frac{1 \times 4}{5 \times 4} = \small \frac{4}{20}  and  \small \frac{3}{4} as \small \frac{3 \times 5}{4 \times 5} = \small \frac{15}{20}

\small \frac{1}{5} + \small \frac{3}{4} = \small \frac{4}{20} + \small \frac{15}{20}

= \small \frac{19}{20}

Question 3.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 47
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 6 is not a multiple of 4, so rewrite each fraction with a denominator of 6 \small \times 4 = 24
Rewrite \small \frac{1}{6}  as \small \frac{1 \times 4}{6 \times 4} = \small \frac{4}{24}  and  \small \frac{1}{4} as \small \frac{1 \times 6}{4 \times 6} = \small \frac{6}{24}

\small \frac{1}{6} + \small \frac{1}{4} = \small \frac{4}{24} + \small \frac{6}{24}

= \small \frac{10}{24} or \small \frac{5}{12}

Apply and Grow: Practice

Add.

Question 4.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 48
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 8 is a multiple of 4, so rewrite it with a denominator of 8.
Rewrite \small \frac{1}{4} as \small \frac{1 \times 2}{4 \times 2} = \small \frac{2}{8}

\small \frac{5}{8} + \small \frac{1}{4} = \small \frac{5}{8} + \small \frac{2}{8}

= \small \frac{7}{8}

Question 5.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 49
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 12 is a multiple of 3, so rewrite it with a denominator of 12.
Rewrite \small \frac{2}{3} as \small \frac{2 \times 4}{3 \times 4} = \small \frac{8}{12}

\small \frac{2}{3} + \small \frac{7}{12}\small \frac{8}{12} + \small \frac{7}{12}

= \small \frac{15}{12} or \small \frac{5}{4}

Question 6.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 50
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 15 is a multiple of 5 , so rewrite it with a denominator of 15.
Rewrite \small \frac{2}{5} as \small \frac{2 \times 3}{5 \times 3} = \small \frac{6}{15}

\small \frac{2}{5} + \small \frac{10}{15} = \small \frac{6}{15} + \small \frac{10}{15}

= \small \frac{16}{15}

Question 7.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 51
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 8 is not a multiple of 6, so rewrite each fraction with a denominator of 8 × 6 = 48.
Rewrite \small \frac{1}{6} as \small \frac{1 \times 8}{6 \times 8} = \small \frac{8}{48}  and  \small \frac{4}{8} as \small \frac{4 \times 6}{8 \times 6} = \small \frac{24}{48}

\small \frac{1}{6} + \small \frac{4}{8} = \small \frac{8}{48} + \small \frac{24}{48}

= \small \frac{32}{48} or \small \frac{2}{3}

Question 8.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 52
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 12 is not a multiple of 5, so rewrite each fraction with a denominator of 12 × 5 = 60.
Rewrite \small \frac{11}{12} as \small \frac{11 \times 5}{12 \times 5} = \small \frac{55}{60}  and  \small \frac{3}{5} as \small \frac{3 \times 12}{5 \times 12} = \small \frac{36}{60}

\small \frac{11}{12} + \small \frac{3}{5} = \small \frac{55}{60} + \small \frac{36}{60}

= \small \frac{91}{60}

Question 9.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 53
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 9 is a multiple of 3 , so rewrite it with a denominator of 9.
Rewrite \small \frac{4}{3} as \small \frac{4 \times 3}{3 \times 3} = \small \frac{12}{9}

\small \frac{2}{9} + \small \frac{4}{3} + \small \frac{5}{9}  =  \small \frac{2}{9} + \small \frac{12}{9} + \small \frac{5}{9}

= \small \frac{19}{9}

Question 10.
Your friend buys \(\frac{1}{8}\) pound of green lentils and \(\frac{3}{4}\) pound of brown lentils. What fraction of a pound of lentils does she buy?
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 54
Answer:
Given that,
pound of green lentils = \small \frac{1}{8}
Pound of brown lentils = \small \frac{3}{4}
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 8 is a multiple of 4, so rewrite \small \frac{3}{4} with a denominator of 8.
Rewrite \small \frac{3}{4} as \small \frac{3 \times 2}{4 \times 2} = \small \frac{6}{8}
Pound of lentils = \small \frac{1}{8} + \small \frac{3}{4}
= \small \frac{1}{8} + \small \frac{6}{8}
Fraction of pound of lentils = \small \frac{7}{8}

Question 11.
Reasoning
Newton and Descartes find \(\frac{1}{2}\) + \(\frac{1}{6}\). Newton says the sum is \(\frac{4}{6}\). Descartes says the sum is \(\frac{2}{3}\). Who is correct? Explain.
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
\small \frac{1}{2} + \small \frac{1}{6}
Think: 6 is a multiple of 2, so rewrite \small \frac{1}{2} with a denominator of 6.
Rewrite \small \frac{1}{2} as \small \frac{1 \times 3}{2 \times 3} = \small \frac{3}{6}
\small \frac{1}{2} + \small \frac{1}{6} = \small \frac{3}{6} + \small \frac{1}{6}
= \small \frac{4}{6} or \small \frac{2}{3}
Therefore, both Newton and Descartes answers are correct.

Question 12.
DIG DEEPER!
Write two fractions that have a sum of 1 and have different denominators.
Answer:
\(\frac{1}{2}\) + \(\frac{3}{6}\)
= \(\frac{1}{2}\) × \(\frac{3}{3}\) + \(\frac{3}{6}\)
= \(\frac{3}{6}\) + \(\frac{3}{6}\)
= \(\frac{6}{6}\)
= 1

Think and Grow: Modeling Real Life

Example
About \(\frac{17}{15}\) of Earth’s surface is covered by ocean water.
About \(\frac{3}{100}\) of Earth’s surface is covered by other water resources.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 55
About how much of Earth’s surface is covered by water?
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 56

Answer:
Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-56

Show and Grow

Question 13.
The George Washington Bridge links Manhattan, NY, to FortLee, NJ. The part of the bridge in New Jersey is about \(\frac{1}{2}\) mile long. The part in New York is about \(\frac{2}{5}\) mile long. About how long is the George Washington Bridge?
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 57
Answer:
Given that,
New Jersey bridge = \(\frac{1}{2}\) mile long
New York bridge = \(\frac{2}{5}\) mile long
Add \small \frac{1}{2} and \small \frac{2}{5} to find how long is the George Washington Bridge
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 5 is not a multiple of 2, so rewrite each fraction with a denominator of 5 \small \times 2 = 10
Rewrite \small \frac{1}{2} as \small \frac{1 \times 5}{2 \times 5} = \small \frac{5}{10}  and \small \frac{2}{5} as \small \frac{2 \times 2}{5 \times 2} = \small \frac{4}{10}
\small \frac{1}{2} + \small \frac{2}{5}  = \small \frac{5}{10} + \small \frac{4}{10}
= \small \frac{9}{10}
So, George Washington Bridge is about \small \frac{9}{10} mile long.

Question 14.
DIG DEEPER!
Your goal is to practice playing the saxophone for at least 2 hours in 1 week. Do you reach your goal? Explain.
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 58
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
\small \frac{3}{4} + \small \frac{1}{2} + \small \frac{2}{3}
Think: Rewrite the denominators as 4 \small \times 2 \small \times 3 = 24
Rewrite \small \frac{3}{4} as \small \frac{3 \times 6}{4 \times 6} = \small \frac{18}{24}
\small \frac{1}{2} as \small \frac{1 \times 12}{2 \times 12} = \small \frac{12}{24}
\small \frac{2}{3} as \small \frac{2 \times 8}{3 \times 8} = \small \frac{16}{24}
\small \frac{3}{4} + \small \frac{1}{2} + \small \frac{2}{3} = \small \frac{18}{24} + \small \frac{12}{24} + \small \frac{16}{24}
= \small \frac{46}{24} or \small \frac{23}{12}
Total practice time in a week = \small \frac{23}{12} = 1.91 hours
So, goal does not reached.

Add Fractions with Unlike Denominators Homework & Practice 8.4

Add

Question 1.
\(\frac{1}{9}\) + \(\frac{2}{3}\) = ___
Answer:
\small \frac{1}{9} + \small \frac{2}{3}
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 9 is a multiple of 3, so rewrite it with a denominator of 9
Rewrite \small \frac{2}{3} as \small \frac{2 \times 3}{3 \times 3} = \small \frac{6}{9}
\small \frac{1}{9} + \small \frac{2}{3} = \small \frac{1}{9} + \small \frac{6}{9}
= \small \frac{7}{9}
\(\frac{1}{9}\) + \(\frac{2}{3}\) = \small \frac{7}{9}

Question 2.
\(\frac{1}{2}\) + \(\frac{3}{4}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 4 is a multiple of 2, so rewrite it with a denominator of 4
Rewrite \small \frac{1}{2} as \small \frac{1 \times 2}{2 \times 2} = \frac{2}{4}
\small \frac{1}{2} + \small \frac{3}{4} = \small \frac{2}{4} + \small \frac{3}{4}
= \small \frac{5}{4}
\(\frac{1}{2}\) + \(\frac{3}{4}\) = \small \frac{5}{4}

Question 3.
\(\frac{4}{6}\) + \(\frac{5}{12}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 12 is a multiple of 6, so rewrite it with a denominator of 12
Rewrite \small \frac{4}{6} as \small \frac{4 \times 2}{6 \times 2} = \small \frac{8}{12}
\small \frac{4}{6} + \small \frac{5}{12} = \small \frac{8}{12} + \small \frac{5}{12}
= \small \frac{13}{12}
\(\frac{4}{6}\) + \(\frac{5}{12}\) = \small \frac{13}{12}

Question 4.
\(\frac{1}{3}\) + \(\frac{1}{4}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 4 is not a multiple of 3, so rewrite each fraction with a denominator of 4 \small \times 3 = 12
Rewrite \small \frac{1}{3} as \small \frac{1 \times 4}{3 \times 4} = \small \frac{4}{12}  and \small \frac{1}{4} as \small \frac{1 \times 3}{4 \times 3} = \small \frac{3}{12}
\small \frac{1}{3} + \small \frac{1}{4}  = \small \frac{4}{12} + \small \frac{3}{12}
= \small \frac{7}{12}
\(\frac{1}{3}\) + \(\frac{1}{4}\) = \small \frac{7}{12}

Question 5.
\(\frac{3}{2}\) + \(\frac{4}{5}\) = __
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 5 is not a multiple of 2, so rewrite each fraction with a denominator of 5 \small \times 2 = 10
Rewrite \small \frac{3}{2} as \small \frac{3 \times 5}{2 \times 5} = \small \frac{15}{10}  and \small \frac{4}{5} as \small \frac{4 \times 2}{5 \times 2} = \small \frac{8}{10}
\small \frac{3}{2} + \small \frac{4}{5}  = \small \frac{15}{10} + \small \frac{8}{10}
= \small \frac{23}{10}
\(\frac{3}{2}\) + \(\frac{4}{5}\) = \small \frac{23}{10}

Question 6.
\(\frac{6}{8}\) + \(\frac{9}{10}\) + \(\frac{1}{8}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 10 is not a multiple of 8, so rewrite each fraction with a denominator of 10 \small \times 8 = 80
Rewrite \small \frac{6}{8} as \small \frac{6 \times 10}{8 \times 10} = \small \frac{60}{80}
\small \frac{9}{10} as \small \frac{9 \times 8}{10 \times 8} = \small \frac{72}{80}
\small \frac{1}{8} as \small \frac{1 \times 10}{8 \times 10} = \small \frac{10}{80}
\small \frac{6}{8} + \small \frac{9}{10} + \small \frac{1}{8} = \small \frac{60}{80} + \small \frac{72}{80} + \small \frac{10}{80} = \small \frac{142}{80}
\(\frac{6}{8}\) + \(\frac{9}{10}\) + \(\frac{1}{8}\) = \small \frac{142}{80}

Question 7.
You use beads to make a design. Of the beads, \(\frac{1}{3}\) are red and \(\frac{1}{6}\) are blue. The rest are white.What fraction of the beads are red or blue?
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 6 is a multiple of 3, so rewrite it with a denominator of 6
Rewrite \small \frac{1}{3} as \small \frac{1 \times 2}{3 \times 2} = \small \frac{2}{6}
\small \frac{1}{3} + \small \frac{1}{6} = \small \frac{2}{6} + \small \frac{1}{6}
= \small \frac{3}{6}
The fraction of beads are red or blue = \small \frac{3}{6} = \small \frac{1}{2}
Rest are white = \small \frac{1}{2}

Question 8.
YOU BE THE TEACHER
Your friend says the sum of \(\frac{1}{5}\) and \(\frac{9}{10}\) is \(\frac{10}{15}\). Is your friend correct? Explain.
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 10 is a multiple of 5, so rewrite it with a denominator of 10
Rewrite \small \frac{1}{5} as \small \frac{1 \times 2}{5 \times 2} = \small \frac{2}{10}
\small \frac{1}{5} + \small \frac{9}{10} = \small \frac{2}{10} + \small \frac{9}{10}
= \small \frac{11}{10}
Therefore, the sum of \(\frac{1}{5}\) and \(\frac{9}{10}\) is \small \frac{11}{10}.
So, my friend answer is wrong.

Question 9.
Reasoning
Which expressions are equal to \(\frac{14}{15}\)?
Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 59
Answer:
\small \frac{3}{5} + \small \frac{1}{3} and \small \frac{1}{5} + \small \frac{11}{15} are equal to \(\frac{14}{15}\) and these two expressions only having denominator of 15.

Question 10.
Modeling Real Life
There are 100 senators in the 115th Congress. Democrats make up of the senators, and Republicans make up \(\frac{13}{25}\) of the 25 senators. The rest are Independents. What fraction of the senators are Democrat or Republican?
Answer:
Given,
There are 100 senators in the 115th Congress.
Democrats make up of the senators, and Republicans make up \(\frac{13}{25}\) of the 25 senators.
\(\frac{100}{115}\) + \(\frac{13}{25}\)
= \(\frac{100}{115}\) × \(\frac{5}{5}\) + \(\frac{13}{25}\) × \(\frac{23}{23}\)
= \(\frac{799}{575}\)
= 1 \(\frac{224}{575}\)

Question 11.
Modeling Real Life
Your friend needs 1 cup of homemade orange juice. He squeezes \(\frac{1}{2}\) cup of orange juice from one orange and \(\frac{3}{8}\) cup from another orange. Does your friend need to squeeze another orange? Explain.
Answer:
\small \frac{1}{2} + \small \frac{3}{8}
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 8 is a multiple of 2, so rewrite it with a denominator of 8
Rewrite \small \frac{1}{2} as \small \frac{1 \times 4}{2 \times 4} = \small \frac{4}{8}
\small \frac{1}{2} + \small \frac{3}{8} = \small \frac{4}{8} + \small \frac{3}{8} = \small \frac{7}{8}
Juice from 2 oranges = \small \frac{7}{8}
My friend needs 1 cup of orange juice = 1 – \small \frac{7}{8} = \small \frac{1}{8}
So, my friend needs to squeeze \small \frac{1}{8} cup from another orange.

Question 12.
DIG DEEPER!
Of all the atoms in caffeine, \(\frac{1}{12}\) are oxygen atoms, \(\frac{1}{6}\) are nitrogen atoms, and \(\frac{1}{3}\) are carbon atoms. The rest of the atoms are hydrogen. What fraction of the atoms in caffeine are oxygen, nitrogen, or hydrogen?
Answer:
From the given information, hydrogen atoms = 1- (\small \frac{1}{12} + \small \frac{1}{6} + \small \frac{1}{3}) = \small \frac{5}{12}
\small \frac{1}{12} + \small \frac{1}{6} + \small \frac{5}{12} = ?
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 12 is a multiple of 6, so rewrite it with a denominator of 12
Rewrite \small \frac{1}{6} as \small \frac{1 \times 2}{6 \times 2} = \small \frac{2}{12}
\small \frac{1}{12} + \small \frac{1}{6} + \small \frac{5}{12} = \small \frac{1}{12} + \small \frac{2}{12} + \small \frac{5}{12}
= \small \frac{8}{12}
= \small \frac{2}{3}
So \small \frac{2}{3} of the atoms in caffeine are oxygen, nitrogen, or hydrogen.

Review & Refresh

Use properties to find the sum or product.

Question 13.
5 × 84
Answer: 420

Explanation:
We can find the product by using the distributive property.
5 × 84 = 5 × (80 + 4)
= (5 × 80) + (5 × 4)
= 400 + 20
= 420

Question 14.
521 + 0 + 67
Answer: 588

Explanation:
We can find the sum of the given expression using the additive identity.
521 + 0 + 67 = 521 + 67
= 588

Question 15.
25 × 8 × 4
Answer: 800

Explanation:
25 × 8 × 4
= 25 × 32
= 800

Lesson 8.5 Subtract Fractions with Unlike Denominators

Explore and Grow

Use a model to find the difference.
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 60
Explain how you can use a model to subtract fourths from twelfths.

Construct Arguments
How can you subtract two fractions with unlike denominators without using a model? Explain why your method makes sense.

Think and Grow: Subtract Fractions with Unlike Denominators

You can use equivalent fractions to subtract fractions that have unlike denominators.
Example
Find \(\frac{9}{10}\) – \(\frac{1}{2}\).
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 10 is a multiple of 2, so rewrite \(\frac{1}{2}\) with a denominator of 10.
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 61

Answer:
Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-61

Example
Find \(\frac{4}{3}\) – \(\frac{1}{4}\). Estimate _____
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 4 is not a multiple of 3, so rewrite each fraction with a denominator of 3 × 4 = 12.

Show and Grow

Subtract.

Question 1.
\(\frac{1}{2}\) – \(\frac{1}{4}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 4 is a multiple of 2, so rewrite \(\frac{1}{2}\) with a denominator of 4.
Rewrite \small \frac{1}{2} as \small \frac{1 \times 2}{2 \times 2} = \small \frac{2}{4}
\small \frac{1}{2}\small \frac{1}{4} = \small \frac{2}{4}\small \frac{1}{4}
= \(\frac{1}{4}\)
\(\frac{1}{2}\) – \(\frac{1}{4}\) = \(\frac{1}{4}\)

Question 2.
\(\frac{7}{9}\) – \(\frac{2}{3}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 9 is a multiple of 3, so rewrite \(\frac{2}{3}\) with a denominator of 9.
Rewrite \small \frac{2}{3} as \small \frac{2 \times 3}{3 \times 3} = \small \frac{6}{9}
\small \frac{7}{9}\small \frac{2}{3} = \small \frac{7}{9}\small \frac{6}{9}
= \small \frac{1}{9}
\(\frac{7}{9}\) – \(\frac{2}{3}\) = \(\frac{1}{9}\)

Question 3.
\(\frac{6}{5}\) – \(\frac{3}{8}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 8 is not a multiple of 5, so rewrite each fraction with a denominator of 5 \small \times 8 = 40
Rewrite \small \frac{6}{5} as \small \frac{6 \times 8}{5 \times 8} = \small \frac{48}{40}
\small \frac{3}{8} as \small \frac{3 \times 5}{8 \times 5} = \small \frac{15}{40}
\small \frac{6}{5}\small \frac{3}{8} = \small \frac{48}{40} – \small \frac{15}{40}
= \small \frac{33}{40}
\(\frac{6}{5}\) – \(\frac{3}{8}\) = \small \frac{33}{40}

Apply and Grow: Practice

Subtract.

Question 4.
\(\frac{10}{12}\) – \(\frac{3}{4}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 12 is a multiple of 4, so rewrite \(\frac{3}{4}\) with a denominator of 12.
Rewrite \small \frac{3}{4} as \small \frac{3 \times 3}{4 \times 3} = \small \frac{9}{12}
\small \frac{10}{12}\small \frac{3}{4} = \small \frac{10}{12}\small \frac{9}{12}
=\small \frac{1}{12}
\(\frac{10}{12}\) – \(\frac{3}{4}\) = \(\frac{1}{12}\)

Question 5.
\(\frac{1}{3}\) – \(\frac{1}{6}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 6 is a multiple of 3, so rewrite \(\frac{1}{3}\) with a denominator of 6.
Rewrite \small \frac{1}{3} as \small \frac{1 \times 2}{3 \times 2} = \small \frac{2}{6}
\small \frac{1}{3}\small \frac{1}{6} = \small \frac{2}{6}\small \frac{1}{6}
= \small \frac{1}{6}
\(\frac{1}{3}\) – \(\frac{1}{6}\) = \(\frac{1}{6}\)

Question 6.
\(\frac{9}{10}\) – \(\frac{2}{5}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 10 is a multiple of 5, so rewrite \(\frac{2}{5}\) with a denominator of 10.
Rewrite \small \frac{2}{5} as \small \frac{2 \times 2}{5 \times 2} = \small \frac{4}{10}
\small \frac{9}{10}\small \frac{2}{5} = \small \frac{9}{10}\small \frac{4}{10}
= \small \frac{5}{10} or \small \frac{1}{2}
\(\frac{9}{10}\) – \(\frac{2}{5}\) = \(\frac{1}{2}\)

Question 7.
\(\frac{5}{4}\) – \(\frac{2}{5}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 5 is not a multiple of 4, so rewrite each fraction with a denominator of 4 \small \times 5 = 20
Rewrite \small \frac{5}{4} as \small \frac{5 \times 5}{4 \times 5} = \small \frac{25}{20}
\small \frac{2}{5} as \small \frac{2 \times 4}{5 \times 4} = \small \frac{8}{20}
\small \frac{5}{4}\small \frac{2}{5} = \small \frac{25}{20}\small \frac{8}{20}
= \small \frac{17}{20}
\(\frac{5}{4}\) – \(\frac{2}{5}\) = \(\frac{17}{20}\)

Question 8.
\(\frac{13}{16}\) – \(\frac{3}{16}\) – \(\frac{5}{8}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 16 is a multiple of 8, so rewrite \(\frac{5}{8}\) with a denominator of 16.
Rewrite \small \frac{5}{8} as \small \frac{5 \times 2}{8 \times 2} = \small \frac{10}{16}
\small \frac{13}{16}\small \frac{3}{16}\small \frac{10}{16} = 0
\(\frac{13}{16}\) – \(\frac{3}{16}\) – \(\frac{5}{8}\) = 0

Question 9.
\(\frac{8}{9}\) – (\(\frac{2}{3}\) + \(\frac{1}{6}\)) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator.
common denominator for 9, 3 and 6 = 18
Rewrite \small \frac{8}{9} as \small \frac{16}{18}
\small \frac{2}{3} = \small \frac{12}{18}
\small \frac{1}{6} = \small \frac{3}{18}
\small \frac{8}{9}\small \frac{2}{3} + \small \frac{1}{6} = \small \frac{16}{18}\small \frac{12}{18} + \small \frac{3}{18} = \small \frac{1}{18}
\(\frac{8}{9}\) – (\(\frac{2}{3}\) + \(\frac{1}{6}\)) = \(\frac{1}{18}\)

Question 10.
You have \(\frac{1}{3}\) yard of wire. You use \(\frac{1}{3}\) yard to make an electric circuit. How much wire do you have left?
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 63
Answer: Left with 0 wire
\small \frac{1}{3}\small \frac{1}{3} = 0

Question 11.
Your friend finds \(\frac{5}{8}\) – \(\frac{2}{5}\). Explain why his answer is unreasonable. What did he do wrong?
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 64
Answer: For subtracting two fractions, the denominators must be same. Here, denominators are different.
So, the answer is wrong
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 8 is not a multiple of 5, so rewrite each fraction with a denominator of 8 \small \times 5 = 40
Rewrite \small \frac{5}{8} as \small \frac{5 \times 5}{8 \times 5} = \small \frac{25}{40}
\small \frac{2}{5} as \small \frac{2 \times 8}{5 \times 8} = \small \frac{16}{40}
\small \frac{5}{8}\small \frac{2}{5} = \small \frac{25}{40}\small \frac{16}{40}
= \small \frac{9}{40}
\(\frac{5}{8}\) – \(\frac{2}{5}\) = \(\frac{9}{40}\)

Question 12.
Number Sense
Which two fractions have a difference of \(\frac{1}{8}\) ?
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 65
Answer:
\small \frac{1}{2} and \small \frac{3}{8}
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 8 is a multiple of 2, so rewrite \small \frac{1}{2} with a denominator of 8.
Rewrite \small \frac{1}{2} as \small \frac{1 \times 4}{2 \times 4} = \small \frac{4}{8}
\small \frac{1}{2}\small \frac{3}{8} = \small \frac{4}{8}\small \frac{3}{8}
= \small \frac{1}{8}
So, fractions \small \frac{1}{2} and \small \frac{3}{8} have the difference of \small \frac{1}{8}.

Think and Grow: Modeling Real Life

Example
A geologist needs \(\frac{1}{2}\) cup of volcanic sand to perform an experiment. She has \(\frac{3}{2}\) cups of quartz sand. She has \(\frac{2}{3}\) cup more quartz sand than volcanic sand. Can she perform the experiment?
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 66
Find how many cups of volcanic sand the geologist has by subtracting \(\frac{2}{3}\) from \(\frac{3}{2}\).
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 3 is not a multiple of 2, so rewrite each fraction with a denominator 2 × 3 = 6.
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 67

Answer:
Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-67

Show and Grow

Question 13.
The world record for the longest dog tail is \(\frac{77}{100}\) meter. The previous record was \(\frac{1}{20}\) meter. shorter than the current record. Was the previous record longer than \(\frac{3}{4}\) meter?
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 68
Answer:
Given that,
World record for the longest dog tail is \small \frac{77}{100} meter.
Previous record was \small \frac{1}{20} meter shorter than the current record
So subtract \small \frac{1}{20} meter from the current record to find previous record.
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Rewrite \small \frac{1}{20} as \small \frac{5}{100}
Previous record = \small \frac{77}{100}\small \frac{5}{100} = \small \frac{72}{100} = \small \frac{18}{25} meter
So the previous record is not longer than \small \frac{3}{4} meter.

Question 14.
DIG DEEPER!
A woodworker has 1 gallon of paint for a tree house. He uses \(\frac{3}{8}\) gallon to paint the walls and \(\frac{1}{5}\) gallon to paint the ladder. He needs \(\frac{1}{4}\) gallon to paint the roof. Does he have enough paint? Explain.
Answer:
Given that,
Woodworker has 1 gallon of paint
\small \frac{3}{8} gallon is used to paint the walls.
\small \frac{1}{5} gallon is used to paint the ladder.
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
\small \frac{3}{8} = \small \frac{15}{40}
\small \frac{1}{5} = \small \frac{8}{40}
1 – \small \frac{15}{40}\small \frac{8}{40} = \small \frac{17}{40}
Therefore, he has more than \small \frac{1}{4} gallon to paint the roof.

Subtract Fractions with Unlike Denominators Homework & Practice 8.5

Subtract

Question 1.
\(\frac{3}{4}\) – \(\frac{1}{8}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 8 is a multiple of 4, so rewrite \(\frac{3}{4}\) with a denominator of 8
Rewrite \small \frac{3}{4} as \small \frac{3 \times 2}{4 \times 2} = \small \frac{6}{8}
\small \frac{3}{4}\small \frac{1}{8} = \small \frac{6}{8}\small \frac{1}{8}
= \small \frac{5}{8}
\(\frac{3}{4}\) – \(\frac{1}{8}\) = \small \frac{5}{8}

Question 2.
\(\frac{4}{5}\) – \(\frac{6}{15}\) = __
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 15 is a multiple of 5, so rewrite \(\frac{4}{5}\) with a denominator of 15
Rewrite \small \frac{4}{5} as \small \frac{4 \times 3}{5 \times 3} = \small \frac{12}{15}
\small \frac{4}{5}\small \frac{6}{15} = \small \frac{12}{15}\small \frac{6}{15}
= \small \frac{6}{15}
\(\frac{4}{5}\) – \(\frac{6}{15}\) = \small \frac{6}{15}

Question 3.
\(\frac{1}{2}\) – \(\frac{1}{8}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 8 is a multiple of 2, so rewrite \(\frac{1}{2}\) with a denominator of 8
Rewrite \small \frac{1}{2} as \small \frac{1 \times 4}{2 \times 4} = \small \frac{4}{8}
\small \frac{1}{2}\small \frac{1}{8} = \small \frac{4}{8}\small \frac{1}{8}
= \small \frac{3}{8}
\(\frac{1}{2}\) – \(\frac{1}{8}\) = \small \frac{3}{8}

Question 4.
\(\frac{5}{3}\) – \(\frac{3}{4}\) = _____
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 4 is not a multiple of 3, so rewrite each fraction with a denominator of 4 x 3 =12
Rewrite \small \frac{5}{3} as \small \frac{5 \times 4}{3 \times 4} = \small \frac{20}{12}
\small \frac{3}{4} as \small \frac{3 \times 3}{4 \times 3} = \small \frac{9}{12}
\small \frac{5}{3}\small \frac{3}{4} = \small \frac{20}{12}\small \frac{9}{12}
= \small \frac{11}{12}
\(\frac{5}{3}\) – \(\frac{3}{4}\) = \small \frac{11}{12}

Question 5.
\(\frac{6}{8}\) – \(\frac{7}{10}\) = _____
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 10 is not a multiple of 8, so rewrite each fraction with a denominator of 10 x 8 =80
Rewrite \small \frac{6}{8} as \small \frac{6 \times 10}{8 \times 10} = \small \frac{60}{80}
\small \frac{7}{10} as \small \frac{7 \times 8}{10 \times 8} = \small \frac{56}{80}
\small \frac{6}{8}\small \frac{7}{10} = \small \frac{60}{80}\small \frac{56}{80}
= \small \frac{4}{80}
\(\frac{6}{8}\) – \(\frac{7}{10}\) = \small \frac{4}{80} = \small \frac{1}{20}

Question 6.
\(\frac{5}{6}\) – \(\frac{1}{4}\) – \(\frac{3}{12}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 12 is a multiple of 4 and 6, so rewrite each fraction with a denominator of 12
Rewrite \small \frac{5}{6} as \small \frac{5 \times 2}{6 \times 2} = \small \frac{10}{12}
\small \frac{1}{4} as \small \frac{1 \times 3}{4 \times 3} = \small \frac{3}{12}
\small \frac{5}{6}\small \frac{1}{4}\small \frac{3}{12} = \small \frac{10}{12}\small \frac{3}{12}\small \frac{3}{12}
= \small \frac{4}{12}
\(\frac{5}{6}\) – \(\frac{1}{4}\) – \(\frac{3}{12}\) = \small \frac{4}{12}

Question 7.
You eat \(\frac{1}{12}\) of a vegetable casserole. Your friend eats \(\frac{1}{6}\) of the same casserole. How much more does your friend eat than you?
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 69
Answer:
\small \frac{1}{6}\small \frac{1}{12}
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 12 is a multiple of 6, so rewrite \small \frac{1}{6} with a denominator of 12
Rewrite \small \frac{1}{6} as \small \frac{1 \times 2}{6 \times 2} = \small \frac{2}{12}
\small \frac{1}{6}\small \frac{1}{12} = \small \frac{2}{12}\small \frac{1}{12} = \small \frac{1}{12}
So, my friend eats \small \frac{1}{12} of a vegetable casserole than me.

Question 8.
Writing
Why do fractions need a common denominator before you can add or subtract them?
Answer:
In order to add fractions, the fractions must have a common denominator. We need the pieces of each fraction to be the same size to combine them together. These two fractions have the same denominator, so the equal parts that the whole has been split into are the same size.

Question 9.
Logic
Find a.
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 70
Answer:
a = \small \frac{7}{10}\small \frac{1}{2}
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 10 is a multiple of 2, so rewrite \small \frac{1}{2} with a denominator of 10
Rewrite \small \frac{1}{2} as \small \frac{1 \times 5}{2 \times 5} = \small \frac{5}{10}
a = \small \frac{7}{10}\small \frac{1}{2} = \small \frac{7}{10}\small \frac{5}{10}
a = \small \frac{2}{10} = \small \frac{1}{5}

Question 10.
DIG DEEPER!
Write and solve an equation to find the difference between Length A and Length B on the ruler.
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 71
Answer:
\(\frac{1}{10}\) × \(\frac{2}{2}\) = \(\frac{2}{20}\)
\(\frac{9}{10}\) × \(\frac{2}{2}\) = \(\frac{18}{20}\)
\(\frac{18}{20}\) – \(\frac{2}{20}\) = \(\frac{16}{20}\)

Question 11.
Modeling Real Life
You want to stack cups in \(\frac{1}{4}\) minute. Your first attempt takes \(\frac{1}{2}\) minute. Your second attempt takes \(\frac{3}{10}\) minute less than your first attempt. Do you meet your goal?
Answer:
\small \frac{1}{2}\small \frac{3}{10}
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 10 is a multiple of 2, so rewrite \small \frac{1}{2} with a denominator of 10
Rewrite \small \frac{1}{2} as \small \frac{1 \times 5}{2 \times 5} = \small \frac{5}{10}
\small \frac{1}{2}\small \frac{3}{10} = \small \frac{5}{10}\small \frac{3}{10}
= \small \frac{2}{10}
= \small \frac{1}{5}
So my second attempt takes \small \frac{1}{5} minute and I did not meet my goal.

Question 12.
Modeling Real Life
You and your friend each have a canvas of the same size. You divide your canvas into 5 sections and paint 3 of them. Your friend divides her canvas into 7 sections and paints 4 of them. Who paints more? How much more?
Answer:
My canvas = \small \frac{3}{5}
My friend canvas = \small \frac{4}{7}
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 7 is a multiple of 5, so rewrite both with a denominator of 7 x 5 = 35
Rewrite \small \frac{3}{5} as \small \frac{3 \times 7}{5 \times 7} = \small \frac{21}{35}
\small \frac{4}{7} as \small \frac{4 \times 5}{7 \times 5} = \small \frac{20}{35}
\small \frac{3}{5}\small \frac{4}{7} = \small \frac{21}{35}\small \frac{20}{35} = \small \frac{1}{35}
I paint \small \frac{1}{35} more canvas than my friend.

Review & Refresh

Evaluate. Check whether your answer is reasonable.

Question 13.
1.7 + 5 + 4.3 = ___
Answer: 11

Question 14.
15.24 + 6.13 – 7 = ___
Answer: 14.37

Lesson 8.6 Add Mixed Numbers

Explore and Grow

Use a model to find the sum.
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 72

Construct Arguments
How can you add mixed numbers with unlike denominators without using a model? Explain why your method makes sense.

Think and Grow: Add Mixed Numbers

Key Idea
A proper fraction is a fraction less than 1. An improper fraction is a fraction greater than 1. A mixed number represents the sum of a whole number and a proper fraction. You can use equivalent fractions to add mixed numbers.
Example
Find 1\(\frac{1}{2}\) + 2\(\frac{5}{6}\)
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 73

Show and Grow

Add.

Question 1.
2\(\frac{2}{3}\) + 2\(\frac{1}{6}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator.
2 \small \frac{2}{3}  = 2 \small \frac{4}{6}
2 \small \frac{1}{6}  = 2 \small \frac{1}{6}
2 \small \frac{4}{6}  + 2 \small \frac{1}{6} = 4 \small \frac{5}{6}

Question 2.
1\(\frac{5}{12}\) + 3\(\frac{3}{4}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator.
1 \small \frac{5}{12} = 1 \small \frac{5}{12}
3 \small \frac{3}{4} = 3 \small \frac{9}{12}
1 \small \frac{5}{12} + 3 \small \frac{9}{12} = 4 \small \frac{14}{12} = 4 \small \frac{7}{6}

Apply and Grow: Practice

Add.

Question 3.
5\(\frac{4}{9}\) + 1\(\frac{2}{3}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator.
5 \small \frac{4}{9} = 5 \small \frac{4}{9}
1 \small \frac{2}{3} = 1 \small \frac{6}{9}
5 \small \frac{4}{9} + 1 \small \frac{6}{9} = 6 \small \frac{10}{9} = \small \frac{64}{9} = 7 \small \frac{1}{9}

Question 4.
3\(\frac{1}{2}\) + \(\frac{5}{12}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator.
3 \small \frac{1}{2} = 3 \small \frac{6}{12}
3 \small \frac{1}{2} + \small \frac{5}{12} = 3 \small \frac{6}{12} + \small \frac{5}{12}
= 3 \small \frac{11}{12}

Question 5.
4\(\frac{5}{6}\) + 3\(\frac{5}{12}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator.
4 \small \frac{5}{6} = 4 \small \frac{10}{12}
3 \small \frac{5}{12} = 3 \small \frac{5}{12}
4 \small \frac{10}{12} + 3 \small \frac{5}{12} = 7 \small \frac{15}{12} = \small \frac{99}{12} = 8 \small \frac{3}{12}

Question 6.
\(\frac{4}{5}\) + 8\(\frac{7}{20}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator.
Rewrite \small \frac{4}{5} as \small \frac{16}{20}
\small \frac{4}{5} + 8 \small \frac{7}{20} = \small \frac{16}{20} + 8 \small \frac{7}{20}
= 8 \small \frac{23}{20}

Question 7.
2\(\frac{1}{3}\) + \(\frac{1}{6}\) + 3\(\frac{2}{3}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator.
2 \small \frac{1}{3} = 2 \small \frac{2}{6}
3 \small \frac{2}{3} = 3 \small \frac{4}{6}
2 \small \frac{1}{3} + \small \frac{1}{6} + 3 \small \frac{2}{3} = 2 \small \frac{2}{6} + \small \frac{1}{6} + 3 \small \frac{4}{6}
= 5 \small \frac{7}{6}

Question 8.
5\(\frac{1}{2}\) + 4\(\frac{3}{4}\) + 6\(\frac{5}{8}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator.
5 \small \frac{1}{2} = 5 \small \frac{4}{8}
4 \small \frac{3}{4} = 4 \small \frac{6}{8}
5 \small \frac{1}{2} + 4 \small \frac{3}{4}  + 6 \small \frac{5}{8} = 5 \small \frac{4}{8} + 4 \small \frac{6}{8} + 6 \small \frac{5}{8}
= 15 \small \frac{15}{8}

Question 9.
Your science class makes magic milk using 1\(\frac{1}{8}\) cups of watercolor paint and 1\(\frac{3}{4}\) cups of milk. How many cups of magic milk does your class make?
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 74
Answer:
Given data,
Watercolor paint = 1 \small \frac{1}{8} cups
Milk = 1 \small \frac{3}{4} cups
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator.
1 \small \frac{3}{4} = 1 \small \frac{6}{8}
1 \small \frac{1}{8} + 1 \small \frac{6}{8} = 2 \small \frac{7}{8} = \small \frac{23}{8}
So the class makes 2 \small \frac{7}{8} cups of magic milk

Question 10.
Structure
Find 2\(\frac{3}{10}\) + 4\(\frac{2}{5}\) two different ways.
Answer:
Method 1:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator.
4 \small \frac{2}{5} = 4 \small \frac{4}{10}
2 \small \frac{3}{10} + 4 \small \frac{2}{5} = 2 \small \frac{3}{10} + 4 \small \frac{4}{10}
= 6 \small \frac{7}{10}
Method 2:
Write the mixed numbers as improper fractions with a common denominator and then add.
2 \small \frac{3}{10} = 2 + \small \frac{3}{10} = \small \frac{20}{10} + \small \frac{3}{10} = \small \frac{23}{10}
4 \small \frac{2}{5} = 4 + \small \frac{2}{5} = \small \frac{22}{5} = \small \frac{44}{10}
2 \small \frac{3}{10} + 4 \small \frac{2}{5} = \small \frac{23}{10} + \small \frac{44}{10}
= \small \frac{67}{10}
= 6 \small \frac{7}{10}

Question 11.
DIG DEEPER!
Find the missing numbers.
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 75
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator.
Rewrite 2 \small \frac{3}{4}  as 2 \small \frac{6}{8}
we can write 4 \small \frac{3}{8} as \small \frac{35}{8} = 3 \small \frac{11}{8}
2 \small \frac{6}{8} + 1 \small \frac{5}{8} = 3 \small \frac{11}{8} = 4 \small \frac{3}{8}
So the missing numbers are 1 and 5.
2 \small \frac{6}{8} + 1 \small \frac{5}{8} = 4 \small \frac{3}{8}

Think and Grow: Modeling Real Life

Example
You kayak 1\(\frac{8}{10}\) miles and then take a break. You kayak 1\(\frac{1}{4}\) more miles. How many miles do you kayak altogether?
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 76
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 77

Answer:
Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-77

Show and Grow

Question 12.
You listen to a song that is 2\(\frac{3}{4}\) minutes long. Then you listen to a song that is 3\(\frac{1}{3}\) minutes long. How many minutes do you spend listening to the two songs altogether?
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator 4 x 3 = 12.
2 \small \frac{3}{4} = 2 \small \frac{9}{12}
3 \small \frac{1}{3} = 3 \small \frac{4}{12}
2 \small \frac{3}{4} + 3 \small \frac{1}{3} = 2 \small \frac{9}{12} + 3 \small \frac{4}{12}
= 5 \small \frac{13}{12} min
So I spend 5 \small \frac{13}{12} min listening to the two songs altogether.

Question 13.
DIG DEEPER!
A beekeeper collects 3\(\frac{3}{4}\) more pounds of honey from Hive 3 than Hive 1. Which hive produces the most honey? Explain.
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 79
Answer:
From the given information,
Honey from Hive 3 = Hive 1 honey + 3 \small \frac{3}{4}
= 23 \small \frac{5}{8} + 3 \small \frac{3}{4}
= 23 \small \frac{5}{8} + 3 \small \frac{6}{8}
= 26 \small \frac{11}{8}
Use a common denominator for all the hives
Hive 1 honey = 23 \small \frac{5}{8}
Hive 2 honey = 27 \small \frac{1}{2} = 27 \small \frac{4}{8}
Hive 3 honey = 26 \small \frac{11}{8}
Therefore, Hive 2 produces the most honey.

Add Mixed Numbers Homework & Practice 8.6

Add

Question 1.
6\(\frac{2}{5}\) + 1\(\frac{3}{10}\)
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator.
6 \small \frac{2}{5}= 6 \small \frac{4}{10}
6 \small \frac{2}{5} + 1 \small \frac{3}{10} = 6 \small \frac{4}{10} + 1 \small \frac{3}{10}
= 7 \small \frac{7}{10}

Question 2.
2\(\frac{2}{3}\) + 5\(\frac{3}{6}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator.
2 \small \frac{2}{3}= 2 \small \frac{4}{6}
2 \small \frac{2}{3} + 5 \small \frac{3}{6} = 2 \small \frac{4}{6} + 5 \small \frac{3}{6}
= 7 \small \frac{7}{6}

Question 3.
\(\frac{1}{4}\) + 3\(\frac{2}{5}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator 4 x 5 = 20
\small \frac{1}{4} = \small \frac{5}{20}
3 \small \frac{2}{5} = 3 \small \frac{8}{20}
\small \frac{1}{4} + 3 \small \frac{2}{5}  = \small \frac{5}{20} + 3 \small \frac{8}{20} = 3 \small \frac{13}{20}

Question 4.
9\(\frac{5}{7}\) + \(\frac{2}{3}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator 7 x 3 = 21
9 \small \frac{5}{7} = 9 \small \frac{15}{21}
\small \frac{2}{3} = \small \frac{14}{21}
9 \small \frac{5}{7} + \small \frac{2}{3} = 9 \small \frac{15}{21} + \small \frac{14}{21} = 9 \small \frac{29}{21}

Question 5.
2\(\frac{1}{2}\) + 1\(\frac{3}{4}\) + \(\frac{1}{2}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator
2 \small \frac{1}{2} = 2 \small \frac{2}{4}
1 \small \frac{3}{4} = 1 \small \frac{3}{4}
\small \frac{1}{2} = \small \frac{2}{4}
2 \small \frac{1}{2} + 1 \small \frac{3}{4}  + \small \frac{1}{2} = 2 \small \frac{2}{4} +1 \small \frac{3}{4} + \small \frac{2}{4} = 3 \small \frac{7}{4}

Question 6.
2\(\frac{2}{3}\) + 4\(\frac{1}{2}\) + 3\(\frac{5}{6}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator
2 \small \frac{2}{3} = 2 \small \frac{4}{6}
4 \small \frac{1}{2} = 4 \small \frac{3}{6}
2 \small \frac{2}{3} + 4 \small \frac{1}{2}  + 3 \small \frac{5}{6} = 2 \small \frac{4}{6} + 4 \small \frac{3}{6}  + 3 \small \frac{5}{6} = 9 \small \frac{12}{6}
2 \small \frac{2}{3} + 4 \small \frac{1}{2}  + 3 \small \frac{5}{6} = 11

Question 7.
A veterinarian spends 3\(\frac{3}{4}\) hours helping cats and 5\(\frac{1}{2}\) hours helping dogs. How many hours does she spend helping cats and dogs altogether?
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 80
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator
3 \small \frac{3}{4}
5 \small \frac{1}{2} = 5 \small \frac{2}{4}
3 \small \frac{3}{4} + 5 \small \frac{1}{2} = 3 \small \frac{3}{4} + 5 \small \frac{2}{4}
= 8 \small \frac{5}{4}
So veterinarian spends 8 \small \frac{5}{4} hours helping cats and dogs altogether.

Question 8.
Writing
How is adding mixed numbers with unlike denominators similar to adding fractions with unlike denominators? How is it different?
Answer:
For both adding mixed numbers and adding fractions we have to use a common denominator.
How it is different?
For adding fractions, directly add the fractions with common denominator.
But for adding mixed numbers, add the fractional parts and add the whole number parts.

Question 9.
Logic
Can you add two mixed numbers and get a sum of 2? Explain.
Answer:
Yes, the sum of two mixed numbers can be equal to 2 but only of one of the mixed numbers is negative.

Question 10.
Structure
Shade the model to represent the sum. Then write an equation to represent your model.
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 81
Answer: 4 \(\frac{1}{4}\)

Question 11.
Modeling Real Life
An emperor tamarin has a body length of 9\(\frac{5}{10}\) inches and a tail length of 14\(\frac{1}{4}\) inches. How long is the emperor tamarin?
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 82
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator 10 x 4 = 40
9 \small \frac{5}{10} = 9 \small \frac{20}{40}
14 \small \frac{1}{4} = 14 \small \frac{10}{40}
9 \small \frac{5}{10} + 14 \small \frac{1}{4} = 9 \small \frac{20}{40} + 14 \small \frac{10}{40}
= 23 \small \frac{30}{40}
So, an emperor tamarin is 23 \small \frac{3}{4} inches long.

Question 12.
DIG DEEPER!
A long jumper jumps 1\(\frac{2}{3}\) feet farther on her third attempt than her second attempt. On which attempt does she jump the farthest? Explain.
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 83
Answer:
Third attempt = 1 \small \frac{2}{3} + 13 \small \frac{3}{4}
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator 3 x 4 = 12
1 \small \frac{2}{3} = 1 \small \frac{8}{12}
13 \small \frac{3}{4} = 13 \small \frac{9}{12}
1 \small \frac{2}{3} + 13 \small \frac{3}{4} = 1 \small \frac{8}{12} + 13 \small \frac{9}{12} = 14 \small \frac{17}{12}
Therefore, she jumps the farthest on her first attempt.

Review & Refresh

Find the product. Check whether your answer is reasonable.

Question 13.
354 × 781
Answer:
The number close to 354 is 350
The number close to 781 is 800.
350 × 800 = 280000
354 × 781 = 276474
Yes, the answer is reasonable.

Question 14.
4,029 × 276
Answer:
The number close to 4029 is 4000
The number close to 276 is 300
4000 × 300 = 1200000
4029 × 276 = 1112004
Yes, the answer is reasonable.

Question 15.
950 × 326
Answer:
The number close to 950 is 1000
The number close to 326 is 300
1000 × 300 = 300000
950 × 326 = 309700
Yes, the answer is reasonable.

Lesson 8.7 Subtract Mixed Numbers

Explore and Grow

Use a model to find the difference
3\(\frac{5}{6}\) – 2\(\frac{1}{3}\)

Construct Arguments
How can you subtract mixed numbers with unlike denominators without using a model? Explain why your method makes sense.

Think and Grow: Subtract Mixed Numbers

You can use equivalent fractions to subtract mixed numbers that have fractional parts with unlike denominators.
Example
Find 3\(\frac{1}{4}\) – 1\(\frac{1}{2}\).

Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 84

Show and Grow

Subtract.

Question 1.
1\(\frac{4}{5}\) – 1\(\frac{3}{10}\)
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator.
1 \small \frac{4}{5} = 1 \small \frac{8}{10}
1 \small \frac{4}{5} – 1 \small \frac{3}{10} = 1 \small \frac{8}{10} – 1 \small \frac{3}{10} = 0 + \small \frac{5}{10}
= \small \frac{1}{2}

Question 2.
5\(\frac{7}{12}\) – 3\(\frac{5}{6}\) = ___
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator.
3 \small \frac{5}{6} = 3 \small \frac{10}{12}
5 \small \frac{7}{12} – 3 \small \frac{5}{6} = 5 \small \frac{7}{12} – 3 \small \frac{10}{12}
5 \small \frac{7}{12}  = 4 + \small \frac{12}{12} + \small \frac{7}{12} = 4 \small \frac{19}{12}
5 \small \frac{7}{12} – 3 \small \frac{10}{12} = 4 \small \frac{19}{12} – 3 \small \frac{10}{12}
= 1 \small \frac{9}{12}

Apply and Grow: Practice

Subtract.

Question 3.
8\(\frac{11}{12}\) – 5\(\frac{2}{3}\) = _____
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator.
5 \small \frac{2}{3} = 5 \small \frac{8}{12}
8 \small \frac{11}{12} – 5 \small \frac{2}{3} = 8 \small \frac{11}{12} – 5 \small \frac{8}{12}
8\(\frac{11}{12}\) – 5\(\frac{2}{3}\) = 3 \small \frac{3}{12} = 3 \small \frac{1}{4}

Question 4.
6 – 4\(\frac{3}{4}\) = ___
Answer:
6 – 4 \small \frac{3}{4} = 6 – \small \frac{19}{4} = \small \frac{5}{4}

Question 5.
21\(\frac{2}{9}\) – 10\(\frac{1}{3}\) = ___
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator.
10 \small \frac{1}{3} = 10 \small \frac{3}{9}
21 \small \frac{2}{9} = 20 + \small \frac{9}{9} + \small \frac{2}{9} = 20 \small \frac{11}{9}
21 \small \frac{2}{9} – 10 \small \frac{1}{3} = 20 \small \frac{11}{9} – 10 \small \frac{3}{9}
= 10 \small \frac{8}{9}

Question 6.
7\(\frac{1}{2}\) – \(\frac{5}{8}\) = ___
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator.
7 \small \frac{1}{2} = 7 \small \frac{4}{8} = 6 + \small \frac{8}{8} + \small \frac{4}{8} = 6 \small \frac{12}{8}
7 \small \frac{1}{2}\small \frac{5}{8} = 6 \small \frac{12}{8}\small \frac{5}{8}
= 6 \small \frac{7}{8}

Question 7.
9\(\frac{7}{20}\) – 1\(\frac{3}{5}\) = ___
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator.
1 \small \frac{3}{5} = 1 \small \frac{12}{20}
9 \small \frac{7}{20} = 8 + \small \frac{20}{20} + \small \frac{7}{20} = 8 \small \frac{27}{20}
9 \small \frac{7}{20} – 1 \small \frac{3}{5} = 8 \small \frac{27}{20} – 1 \small \frac{12}{20}
= 7 \small \frac{15}{20}
= 7 \small \frac{3}{4}

Question 8.
7\(\frac{5}{6}\) – 1\(\frac{1}{6}\) – 2\(\frac{2}{3}\) = ___
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator.
2 \small \frac{2}{3} = 2 \small \frac{4}{6}
7 \small \frac{5}{6} = 6 + \small \frac{6}{6} + \small \frac{5}{6} = 6 \small \frac{11}{6}
7 \small \frac{5}{6} – 1 \small \frac{1}{6} – 2 \small \frac{2}{3} = 6 \small \frac{11}{6} – 1 \small \frac{1}{6} – 2 \small \frac{4}{6}
= 3 \small \frac{6}{6}
= 3 + 1
7\(\frac{5}{6}\) – 1\(\frac{1}{6}\) – 2\(\frac{2}{3}\) = 4

Question 9.
A volunteer at a food bank buys 3\(\frac{3}{4}\) pounds of cheese to make sandwiches. She uses 2\(\frac{7}{8}\) pounds. How much cheese does she have left?
Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 87
Answer:
Given that,
A volunteer buys 3 \small \frac{3}{4} pounds of cheese
She uses 2 \small \frac{7}{8} pounds
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator.
3 \small \frac{3}{4} = 3 \small \frac{6}{8} = 2 + \small \frac{8}{8} + \small \frac{6}{8} = 2 \small \frac{14}{8}
Cheese left = 2 \small \frac{14}{8} – 2 \small \frac{7}{8} = 0 + \small \frac{7}{8}
So she left with \small \frac{7}{8} pounds of cheese.

Question 10.
Writing
How is adding mixed numbers the same as subtracting mixed numbers? How is it different?
Answer:
Adding and subtracting mixed numbers is same because we need to use a common denominator for both.
Adding and subtracting mixed numbers is different because
For subtracting mixed numbers, the first fraction should be greater than the second number.

Question 11.
Number Sense
Write the words as an expression. Then evaluate.
Subtract the sum of four and three-fourths and two and five-eighths from eleven and seven-eighths.
Answer:
11 \small \frac{7}{8} – (4 \small \frac{3}{4} + 2 \small \frac{5}{8})
To subtract or add the fractional parts, use a common denominator.
4 \small \frac{3}{4} = 4 \small \frac{6}{8}
4 \small \frac{3}{4} + 2 \small \frac{5}{8} = 4 \small \frac{6}{8} + 2 \small \frac{5}{8} = 6 \small \frac{11}{8}
11 \small \frac{7}{8} – (4 \small \frac{3}{4} + 2 \small \frac{5}{8}) = 11 \small \frac{7}{8} – 6 \small \frac{11}{8}
11 \small \frac{7}{8} = 10 + \small \frac{8}{8} + \small \frac{7}{8} = 10 \small \frac{15}{8}
11 \small \frac{7}{8} – (4 \small \frac{3}{4} + 2 \small \frac{5}{8}) = 10 \small \frac{15}{8} – 6 \small \frac{11}{8}
11 \small \frac{7}{8} – (4 \small \frac{3}{4} + 2 \small \frac{5}{8}) = 4 \small \frac{4}{8} = 4 \small \frac{1}{2}

Question 12.
DIG DEEPER!
Find the missing number.
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 88
Answer:
To subtract the fractional parts, use a common denominator.
3 \small \frac{1}{4} = 3 \small \frac{3}{12}

3 \small \frac{1}{4} – 1 \small \frac{1}{12} = 3 \small \frac{3}{12} – 1 \small \frac{1}{12}
= 2 \small \frac{2}{12}
3 \small \frac{1}{4} – 1 \small \frac{1}{12} = 2 \small \frac{1}{6}
So the missing number is 1.

Think and Grow: Modeling Real Life

Example
A dragonfly is 1\(\frac{1}{2}\) inches long. How much longer is the walking leaf than the dragonfly?
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 89
To find how much longer the walking leaf is than the dragonfly, subtract the length of the dragonfly from the length of the walking leaf.
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 90
The walking leaf is __ inches longer than the dragonfly.

Answer:
Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-90
The walking leaf is 1 \(\frac{1}{6}\) inches longer than the dragonfly.

Show and Grow

Question 13.
You volunteer 5\(\frac{3}{4}\) hours in 1 month. You spend 3\(\frac{1}{3}\) hours volunteering at an animal shelter. You spend the remaining hours picking up litter on the side of the road. How many hours do you spend picking up litter?
Answer:
Given that,
Volunteering hours in 1 month = 5 \small \frac{3}{4}
Time spent at an animal shelter = 3 \small \frac{1}{3}
Remaining hours in a month are for picking up litter = 5 \small \frac{3}{4} – 3 \small \frac{1}{3}
To subtract the fractional parts, use a common denominator 4 x 3 =12
5 \small \frac{3}{4} = 5 \small \frac{9}{12}
3 \small \frac{1}{3} = 3 \small \frac{4}{12}
Time spend for picking up litter = 5 \small \frac{9}{12} – 3 \small \frac{4}{12} = 2 \small \frac{5}{12}.

Question 14.
A professional basketball player is 6\(\frac{3}{4}\) feet tall. Your friend is 4\(\frac{5}{6}\) feet tall. How much taller is the basketball player than your friend?
Answer:
To find how much taller is the basketball player than the friend, subtract the height of the friend from the height of the basketball player.
Given that,
Basketball player is 6 \small \frac{3}{4} feet tall.
My friend is 4 \small \frac{5}{6} feet tall.
To subtract the fractional parts, use a common denominator 4 x 6 = 24
6 \small \frac{3}{4} = 6 \small \frac{18}{24} = 5 + \small \frac{24}{24} + \small \frac{18}{24} = 5 \small \frac{42}{24}
4 \small \frac{5}{6} = 4 \small \frac{20}{24}
6 \small \frac{3}{4} – 4 \small \frac{5}{6} = 5 \small \frac{42}{24} – 4 \small \frac{20}{24}
= 1 \small \frac{22}{24}
= 1 \small \frac{11}{12}
The basketball player is 1 \small \frac{11}{12} feet taller than my friend.

Question 15.
Your rain gauge has 2\(\frac{1}{2}\) inches of water. After a rainstorm, your rain gauge has 1\(\frac{3}{4}\) more inches of water. It is sunny for a week. Now your rain gauge has 2\(\frac{2}{3}\) inches of water. How many inches of water evaporated?
Answer:
After a rainstorm, water in the rain gauge = 2 \small \frac{1}{2} + 1 \small \frac{3}{4}
To subtract or add the fractional parts, use a common denominator.
2 \small \frac{1}{2} = 2 \small \frac{2}{4}
Water in the rain gauge = 2 \small \frac{1}{2} +1 \small \frac{3}{4} = 2 \small \frac{2}{4} + 1 \small \frac{3}{4} = 3 \small \frac{5}{4} inches
Water evaporated = 3 \small \frac{5}{4} – 2 \small \frac{2}{3}
3 \small \frac{5}{4} = 3 \small \frac{15}{12}
2 \small \frac{2}{3} = 2 \small \frac{8}{12}

3 \small \frac{5}{4} – 2 \small \frac{2}{3} = 3 \small \frac{15}{12} – 2 \small \frac{8}{12} = 1 \small \frac{7}{12}
So, 1 \small \frac{7}{12} inches of water evaporated.

Subtract Mixed Numbers Homework & Practice 8.7

Subtract

Question 1.
9\(\frac{5}{6}\) – 4\(\frac{1}{2}\) = ___
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator.
4 \small \frac{1}{2} = 4 \small \frac{3}{6}
9 \small \frac{5}{6} – 4 \small \frac{1}{2} = 9 \small \frac{5}{6} – 4 \small \frac{3}{6}
= 5 \small \frac{2}{6}
9\(\frac{5}{6}\) – 4\(\frac{1}{2}\) = 5 \small \frac{2}{6} = 5 \small \frac{1}{3}

Question 2.
3\(\frac{2}{3}\) – \(\frac{1}{9}\) = ___
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator.
3 \small \frac{2}{3} = 3 \small \frac{6}{9}
3 \small \frac{2}{3}\small \frac{1}{9} = 3 \small \frac{6}{9}\small \frac{1}{9} = 3 \small \frac{5}{9}

Question 3.
6\(\frac{1}{3}\) – 1\(\frac{11}{12}\) = ___
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator.
6 \small \frac{1}{3} = 6 \small \frac{4}{12} = 5 \small \frac{16}{12}
6 \small \frac{1}{3} – 1 \small \frac{11}{12} = 5 \small \frac{16}{12} – 1 \small \frac{11}{12}
= 4 \small \frac{5}{12}

Question 4.
12\(\frac{5}{6}\) – 7\(\frac{3}{10}\) = ___
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator 6 x 10 = 60
12 \small \frac{5}{6} = 12 \small \frac{50}{60}
7 \small \frac{3}{10} = 7 \small \frac{18}{60}
12 \small \frac{5}{6} – 7 \small \frac{3}{10} = 12 \small \frac{50}{60} – 7 \small \frac{18}{60}
= 5 \small \frac{32}{60}
12\(\frac{5}{6}\) – 7\(\frac{3}{10}\) = 5 \small \frac{32}{60} = 5 \small \frac{8}{15}

Question 5.
5 – 2\(\frac{3}{4}\) = ___
Answer:
5 – 2 \small \frac{3}{4} = 5 – \small \frac{11}{4} = \small \frac{9}{4}

Question 6.
4\(\frac{1}{5}\) – 2\(\frac{1}{4}\) = __
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator 5 x 4 = 20
4 \small \frac{1}{5} = 4 \small \frac{4}{20} = 3 \small \frac{24}{20}
2 \small \frac{1}{4} = 2 \small \frac{5}{20}

4 \small \frac{1}{5} – 2 \small \frac{1}{4} = 3 \small \frac{24}{20} – 2 \small \frac{5}{20} = 1 \small \frac{19}{20}

Subtract.

Question 7.
7\(\frac{5}{8}\) – 1\(\frac{5}{6}\) = ___
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator 8 x 6 = 48
7 \small \frac{5}{8} = 7 \small \frac{30}{48} = 6 \small \frac{78}{48}
1 \small \frac{5}{6} = 1 \small \frac{40}{48}
7 \small \frac{5}{8} – 1 \small \frac{5}{6} = 6 \small \frac{78}{48} – 1 \small \frac{40}{48} = 5 \small \frac{38}{48}
= 5 \small \frac{19}{24}

Question 8.
8\(\frac{1}{9}\) – 6\(\frac{7}{8}\) = ___
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator 8 x 9 = 72
8 \small \frac{1}{9} = 8 \small \frac{8}{72} = 7 \small \frac{80}{72}
6 \small \frac{7}{8} = 6 \small \frac{63}{72}
8 \small \frac{1}{9} – 6 \small \frac{7}{8} = 7 \small \frac{80}{72} – 6 \small \frac{63}{72}
= 1 \small \frac{17}{72}

Question 9.
1\(\frac{6}{7}\) + 5\(\frac{13}{14}\) – 2\(\frac{1}{2}\) = ___
Answer:
To subtract or add the fractional parts, use a common denominator
1 \small \frac{6}{7} = 1 \small \frac{12}{14}
2 \small \frac{1}{2} = 2 \small \frac{7}{14}

1 \small \frac{6}{7} + 5 \small \frac{13}{14} – 2 \small \frac{1}{2} = 1 \small \frac{12}{14} + 5 \small \frac{13}{14} – 2 \small \frac{7}{14}
= 4 \small \frac{18}{14}
= 4 \small \frac{9}{7}

Question 10.
Your friend says the difference of 8 and 3\(\frac{7}{10}\) is 5\(\frac{7}{10}\). Is your friend correct? Explain.
Answer:
8 – 3 \small \frac{7}{10} = 8 – \small \frac{37}{10} = \small \frac{43}{10}

Question 11.
DIG DEEPER!
Use a symbol card to complete the equation. Then find b.
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 91
Answer:
4 \small \frac{1}{4} – 1 \small \frac{17}{20} – b = 1 \small \frac{1}{2}
4 \small \frac{1}{4} = 4 \small \frac{5}{20} = 2 \small \frac{45}{20}
1 \small \frac{1}{2} = 1 \small \frac{10}{20}
b = 4 \small \frac{1}{4} – 1 \small \frac{17}{20} – 1 \small \frac{1}{2}
= 2 \small \frac{45}{20} – 1 \small \frac{17}{20} – 1 \small \frac{10}{20}
= \small \frac{18}{20}
b = \small \frac{18}{20} = \small \frac{9}{10}

Question 12.
Modeling Real Life
The world record for the heaviest train pulled with a human beard is 2\(\frac{3}{4}\) metric tons. The world record for the heaviest train pulled by human teeth is 4\(\frac{1}{5}\) metric tons. How much heavier is the train pulled by teeth than the train pulled with a beard?
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator 4 x 5 = 20
2 \small \frac{3}{4} = 2 \small \frac{15}{20}
4 \small \frac{1}{5} = 4 \small \frac{4}{20} = 3 \small \frac{24}{20}
4 \small \frac{1}{5} – 2 \small \frac{3}{4} = 3 \small \frac{24}{20} – 2 \small \frac{15}{20}
= 1 \small \frac{9}{20}
The train pulled by teeth 1 \small \frac{9}{20} metric tons heavier than the train pulled with a beard.

Question 13.
Modeling Real Life
Your friend’s hair is 50\(\frac{4}{5}\) centimeters long. Your hair is 8\(\frac{9}{10}\) centimeters long. How much longer is your friend’s hair than yours?
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 92
Answer:
My friend’s hair = 50 \small \frac{4}{5} cm
My hair = 8 \small \frac{9}{10} cm
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator
50 \small \frac{4}{5} = 50 \small \frac{8}{10} = 49 \small \frac{18}{10}
50 \small \frac{4}{5} – 8 \small \frac{9}{10} = 49 \small \frac{18}{10} – 8 \small \frac{9}{10} = 41 \small \frac{9}{10}
My friend’s hair is 41 \small \frac{9}{10} cms longer than my hair.

Review & Refresh

Question 14.
Round 6.294.
Nearest whole number:
Nearest tenth:
Nearest hundredth:
Answer:
Nearest whole number: 6
Nearest tenth: 60
Nearest hundredth: 600

Question 15.
Round 10.571.
Nearest whole number:
Nearest tenth:
Nearest hundredth:
Answer:
Nearest whole number: 11
Nearest tenth: 110
Nearest hundredth: 1100

Lesson 8.8 Problem Solving: Fractions

Explore and Grow

Make a plan to solve the problem.

At a state park, every \(\frac{1}{10}\) mile of walking trail is marked. Every \(\frac{1}{4}\) mile of a separate biking trail is marked. The table shows the number of mileage markers you and your friend pass while walking and biking on the trails. Who travels farther? How much farther?
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 93
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 94

Make Sense of Problems
You decide to walk farther and you pass 4 more mileage markers on the walking trail. Does this change your plan to solve the problem? Explain.
Answer:
At a state park, every \(\frac{1}{10}\) mile of the walking trail is marked.
8 × \(\frac{1}{10}\) = \(\frac{8}{10}\)
Every \(\frac{1}{4}\) mile of a separate biking trail is marked.
9 × \(\frac{1}{4}\) = 2 \(\frac{1}{4}\)
\(\frac{8}{10}\) + \(\frac{4}{10}\) = \(\frac{12}{10}\)
= 1 \(\frac{2}{10}\)
Your friend travels more farther.

Think and Gow: Problem Solving: Fractions

Example
To repair a skate ramp, you cut a piece of wood from a 9\(\frac{1}{2}\)-foot-long board. Then you cut the remaining piece in half. Each half is 3\(\frac{5}{12}\) feet long. How long is the first piece you cut?
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 95

Understand the Problem

What do you know?

  • The board is 9 feet long.2first piece you cut.
  • You cut a piece from the board.
  • You cut the rest into two pieces that are each 3\(\frac{5}{12}\) feet long.

What do you need tofind?

  • You need to find the length of the first piece you cut.

Make a Plan

How will you solve?
Write and solve an equation: Subtract the sum of the lengths of the last two pieces you cut from the total length of the board.

Solve
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 96
Let g represent the length of the first piece you cut.
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 97
So, the length of the first piece you cut is __ feet.

Answer:
Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-97
So, the length of the first piece you cut is 2 \(\frac{2}{3}\) feet.

Show and Grow

Question 1.
Explain how you can check your answer in the example above.
Answer:
Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-97

Apply and Grow: Practice

Understand the problem. What do you know? What do you need to find? Explain.

Question 2.
A racehorse eats 38\(\frac{1}{2}\) pounds of food each day. He eats 22\(\frac{3}{4}\) pounds of hay and 7\(\frac{1}{2}\) pounds of grains. How many pounds of his daily diet is not hay or grains?
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 98
Answer:
Given,
A racehorse eats 38\(\frac{1}{2}\) pounds of food each day.
He eats 22\(\frac{3}{4}\) pounds of hay and 7\(\frac{1}{2}\) pounds of grains.
38\(\frac{1}{2}\) – 22\(\frac{3}{4}\)
= 15 \(\frac{3}{4}\)
Thus 15 \(\frac{3}{4}\) pounds of his daily diet is not grains.

Question 3.
In 2015, American Pharoah won all of the horse races shown in the table. How many kilometers did American Pharoah run in the races altogether?
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 99

Understand the problem. Then make a plan. How will you solve? Explain.
Answer:
Add all the lengths to find how many kilometers did American Pharoah run in the races altogether.
2 + 1 \(\frac{9}{10}\) + 2 \(\frac{2}{5}\)
First add all the whole numbers.
2 + 1 + 2 = 5
Now add the fractions
\(\frac{9}{10}\) + \(\frac{4}{10}\) = 1 \(\frac{3}{10}\)
5 + 1 \(\frac{3}{10}\) = 6 \(\frac{3}{10}\)

Question 4.
You have 2\(\frac{1}{2}\) cups of blueberries. You use 1\(\frac{1}{4}\) cups for pancakes and \(\frac{1}{2}\) cup for muffins. What fraction of a cup of blueberries do you have left?
Answer:
Given,
You have 2\(\frac{1}{2}\) cups of blueberries.
You use 1\(\frac{1}{4}\) cups for pancakes and \(\frac{1}{2}\) cup for muffins.
1\(\frac{1}{4}\) + \(\frac{1}{2}\) = 1 \(\frac{3}{4}\)
2\(\frac{1}{2}\) – 1 \(\frac{3}{4}\) = \(\frac{3}{4}\)

Question 5.
A customer orders 2 pounds of cheese at a deli. The deli worker places some cheese in a bowl and weighs it. The scale shows 1\(\frac{1}{4}\) pounds. The bowl weighs \(\frac{1}{8}\) pound. What fraction of a pound of cheese does the worker need to add to the bowl?
Answer:
Given,
A customer orders 2 pounds of cheese at a deli. The deli worker places some cheese in a bowl and weighs it.
The scale shows 1\(\frac{1}{4}\) pounds. The bowl weighs \(\frac{1}{8}\) pound.
1\(\frac{1}{4}\) + \(\frac{1}{8}\) = 1 \(\frac{3}{8}\)
2 – 1 \(\frac{3}{8}\) = \(\frac{5}{8}\)

Question 6.
Reasoning
Student A is 8\(\frac{1}{2}\) inches shorter than Student B. Student B is 3\(\frac{1}{4}\) inches taller than Student C. Student C is 56\(\frac{3}{8}\) inches tall. How tall is Student A? Student B?
Answer:
Student A is 8\(\frac{1}{2}\) inches shorter than Student B.
Student B is 3\(\frac{1}{4}\) inches taller than Student C.
Student C is 56\(\frac{3}{8}\) inches tall.
Student B is 56\(\frac{3}{8}\) + 3\(\frac{1}{4}\) = 59 \(\frac{5}{8}\)
Thus the height of student B is 59 \(\frac{5}{8}\) inches.
Student A is 59 \(\frac{5}{8}\) – 8\(\frac{1}{2}\) = 51 \(\frac{1}{8}\)
Thus the height of Student A is 51 \(\frac{1}{8}\) inches.

Question 7.
DIG DEEPER!
A police dog spends \(\frac{1}{8}\) of his workday in a police car, \(\frac{3}{4}\) of his workday in public, and the rest of his workday at the police station. What fraction of the dog’s day is spent at the police station?
Answer:
Given,
A police dog spends \(\frac{1}{8}\) of his workday in a police car, \(\frac{3}{4}\) of his workday in public, and the rest of his workday at the police station.
\(\frac{1}{8}\) + \(\frac{3}{4}\) = \(\frac{7}{8}\)
1 – \(\frac{7}{8}\) = \(\frac{1}{8}\)
Thus \(\frac{1}{8}\) fraction of the dog’s day is spent at the police station

Think and Grow: Modeling Real Life

Example
The Magellan spacecraft, launched by the United States, spent 5\(\frac{5}{12}\) years in space before it burned in Venus’s atmosphere. Its first 4 cycles around Venus each lasted \(\frac{2}{3}\) year. The remaining cycles around Venus lasted a total of 1\(\frac{1}{2}\) years. How long did it take to travel from Earth to Venus?
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 100
Think: What do you know? What do you need to find? How will you solve?
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 101

Answer:
Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-101

Show and Grow

Question 8.
You have one of each euro coin shown. Your friend has four euro coins that have a total weight of 21\(\frac{3}{10}\) grams. Whose coins weigh more? How much more?
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 102
Answer:
2 \(\frac{3}{10}\) + 5 \(\frac{3}{4}\) + 7 \(\frac{4}{5}\) + 7 \(\frac{1}{2}\)
= 23 \(\frac{7}{20}\)
23 \(\frac{7}{20}\) – 21\(\frac{3}{10}\)
= 2 \(\frac{1}{20}\)

Problem Solving: Fractions Homework & Practice 8.8

Understand the problem. What do you know? What do you need to find? Explain.

Question 1.
Your goal is to exercise for 15 hours this month. You exercise for 3\(\frac{1}{2}\) hours the first week and 3\(\frac{3}{4}\) hours the next week. How many more hours do you need to exercise to reach your goal?
Answer:
Given,
Your goal is to exercise for 15 hours this month.
You exercise for 3\(\frac{1}{2}\) hours the first week and 3\(\frac{3}{4}\) hours the next week.
3\(\frac{1}{2}\) + 3\(\frac{3}{4}\) = 7 \(\frac{1}{4}\)
15 – 7 \(\frac{1}{4}\) = 7 \(\frac{3}{4}\) hours

Question 2.
A taxi driver travels 4\(\frac{5}{8}\) miles to his first stop. He travels 1\(\frac{3}{4}\) miles less to his second stop. How many miles does the taxi driver travel for the two stops?
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 103

Understand the problem. Then make a plan. How will you solve? Explain.
Answer:
Given,
A taxi driver travels 4\(\frac{5}{8}\) miles to his first stop. He travels 1\(\frac{3}{4}\) miles less to his second stop.
4\(\frac{5}{8}\) + 1\(\frac{3}{4}\) = 7 \(\frac{1}{4}\)

Question 3.
During the U.S. Civil War, \(\frac{5}{9}\) of the states fought for the Union, and \(\frac{11}{36}\) of the states fought for the Confederacy. The rest of the states were border states. What fraction of the states were border states?
Answer:
Given,
During the U.S. Civil War, \(\frac{5}{9}\) of the states fought for the Union, and \(\frac{11}{36}\) of the states fought for the Confederacy. The rest of the states were border states.
\(\frac{5}{9}\) + \(\frac{11}{36}\) = \(\frac{31}{36}\)

Question 4.
You have 6\(\frac{3}{4}\) pounds of clay. You use 4\(\frac{1}{6}\) pounds to make a medium-sized bowl and 1\(\frac{1}{2}\) pounds to make a small bowl. How many pounds of clay do you have left?
Answer:
Given,
You have 6\(\frac{3}{4}\) pounds of clay.
You use 4\(\frac{1}{6}\) pounds to make a medium-sized bowl and 1\(\frac{1}{2}\) pounds to make a small bowl.
4\(\frac{1}{6}\) + 1\(\frac{1}{2}\) = 5 \(\frac{2}{3}\)
6\(\frac{3}{4}\) – 5 \(\frac{2}{3}\) = 1 \(\frac{1}{12}\)

Question 5.
DIG DEEPER!
Newton and Descartes have a 70-day summer vacation. They go to camp for \(\frac{23}{70}\) of their vacation, and they travel for \(\frac{6}{35}\) of their vacation. They stay home the rest of their vacation. How many weeks do Newton and Descartes spend at home?
Answer:
Given,
Newton and Descartes have a 70-day summer vacation. They go to camp for \(\frac{23}{70}\) of their vacation, and they travel for \(\frac{6}{35}\) of their vacation.
\(\frac{23}{70}\) + \(\frac{6}{35}\) = \(\frac{1}{2}\)
That means Newton and Descartes spend 5 weeks at home.

Question 6.
Modeling Real Life
A farmer plants beets in a square garden with side lengths of 12\(\frac{2}{3}\) feet. He plants squash in a garden with a perimeter of 50\(\frac{1}{2}\) feet. Which garden has a greater perimeter? How much greater is it?
Answer:
Given,
A farmer plants beets in a square garden with side lengths of 12\(\frac{2}{3}\) feet.
The perimeter of the square = 4s
P = 4 × 12\(\frac{2}{3}\)
P = 50 \(\frac{2}{3}\)
50 \(\frac{2}{3}\) is greater than 50\(\frac{1}{2}\)

Question 7.
DIG DEEPER!
Which grade uses more leafy greens daily for its classroom rabbits? How much more does it use?
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 104
Answer: 4th Grade uses more leafy greens.

Review & Refresh

Find the product.

Question 1.
0.43 × 1,000 = 430
Answer:
43 x 10-2 x 103 = 43 x 101
= 430

Question 2.
25.8 × 0.1 = 2.58
Answer:
258 x 10-1​​​​​​​ x 10-1= 2.58

Add and Subtract Fractions Performance Task 8

Many historic landmarks are located in Washington, D.C.

Question 1.
Initial construction of the Washington Monument began in 1848. When the height of the monument reached 152 feet, construction halted due to lack of funds. How many feet were added to the height of the monument when construction resumed 23 years later?
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 105
Answer:
The initial construction of the Washington Monument began in 1848. When the height of the monument reached 152 feet, construction halted due to lack of funds.
554 \(\frac{3}{4}\) – 152 = 402 \(\frac{3}{4}\)

Question 2.
You visit several historic landmarks. You start at the Capitol Building and walk to the Washington Monument, then the Lincoln Memorial, then the White House, and then back to the Capitol Building.
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 106
a. You walk 3 miles each hour. It takes you \(\frac{1}{2}\) hour to walk from the Lincoln Memorial to the White House. What is the distance from the Lincoln Memorial to the White House? Label the map.

Answer:
Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-106
b. What is the total distance you walk visiting the landmarks?
Answer: 1 \(\frac{1}{5}\) + \(\frac{4}{5}\) + 1 \(\frac{4}{5}\) + 1 \(\frac{3}{5}\)
= 5 \(\frac{2}{5}\)

Question 3.
A law in Washington, D.C., restricts a new building’s height to no more than 20 feet taller than the width of the street it faces. You design a building with stories that are each 15 feet tall for a street that is 88\(\frac{2}{3}\) feet wide. What is the greatest number of stories your building can have? How much shorter is your building than the height restriction?
Answer:
Given,
A law in Washington, D.C., restricts a new building’s height to no more than 20 feet taller than the width of the street it faces.
20 × 88\(\frac{2}{3}\) = 1773 \(\frac{1}{3}\)
You design a building with stories that are each 15 feet tall for a street that is 88\(\frac{2}{3}\) feet wide.
15 × 88\(\frac{2}{3}\) = 1330
1773 \(\frac{1}{3}\) – 1330 = 443 \(\frac{1}{3}[/latex

Add and Subtract Fractions Activity

Mixed Number Number
Subtract and Add
Directions:

  1. Each player flips four Mixed Number Cards.
  2. Each player arranges the cards to create two differences that will have the greatest possible sum.
  3. Each player records the two differences, and then adds the differences.
  4. Players repeat Steps 1–3.
  5. Each player adds Sum A and Sum B to find the total. The player with the greatest total wins!

Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 107

Answer:
Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-107

Add and Subtract Fractions Performance Chapter Practice

8.1 Simplest Form

Write the fraction in simplest form.

Question 1.
[latex]\frac{2}{12}\)
Answer:
Step 1: Find the common factors of 2 and 12.
Factors of 2:    1, 2
Factors of 12:  1, 2, 3, 4, 6, 12
The common factors of 2 and 12 are 1 and 2.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{2}{12} = \frac{2 \div 2}{12 \div 2} = \frac{1}{6}
Because 1 and 6 have no common factors other than 1, \(\frac{2}{12}\) is in simplest form.

Question 2.
\(\frac{15}{30}\)
Answer:
Step 1: Find the common factors of 15 and 30.
Factors of 15:    1, 3, 5, 15
Factors of 30:  1, 2, 3, 5, 6, 10, 15, 30
The common factors of 15 and 30 are 1, 3, 5 and 15.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.

\small \frac{15}{30} = \frac{15 \div 15}{30 \div 15} = \frac{1}{2}
Because 1 and 2 have no common factors other than 1, \(\frac{15}{30}\) is in simplest form.

Question 3.
\(\frac{16}{24}\)
Answer:
Step 1: Find the common factors of 16 and 24.
Factors of 16:    1, 2, 4, 8, 16
Factors of 24:  1, 2, 3, 4, 6, 8, 12, 24
The common factors of 16 and 24 are 1, 2, 4 and 8.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{16}{24} = \frac{16 \div 8}{24 \div 8} = \frac{2}{3}
Because 2 and 3 have no common factors other than 1, \(\frac{16}{24}\) is in simplest form.

Question 4.
\(\frac{18}{36}\)
Answer:
Step 1: Find the common factors of 18 and 36.
Factors of 18:  1, 2, 3, 6, 9, 18
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The common factors of 18 and 36 are 1, 2, 3, 6, 9 and 18.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.

\small \frac{18}{36} = \frac{18 \div 18}{36 \div 18} = \frac{1}{2}
Because 1 and 2 have no common factors other than 1, \(\frac{18}{36}\) is in simplest form.

Question 5.
\(\frac{8}{32}\)
Answer:
Step 1: Find the common factors of 8 and 32.
Factors of 8:  1, 2, 4, 8
Factors of 32: 1, 2, 4, 8, 16, 32
The common factors of 8 and 32 are 1, 2, 4 and 8.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{8}{32} = \frac{8 \div 8}{32 \div 8} = \frac{1}{4}
Because 1 and 4 have no common factors other than 1, \(\frac{8}{32}\) is in simplest form.

Question 6.
\(\frac{25}{10}\)
Answer:
Step 1: Find the common factors of 25 and 10.
Factors of 25:  1, 5, 25
Factors of 10: 1, 2, 5, 10
The common factors of 25 and 10 are 1 and 5.
Step 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.
\small \frac{25}{10} = \frac{25 \div 5}{10 \div 5} = \frac{5}{2}
Because 5 and 2 have no common factors other than 1, \(\frac{25}{10}\) is in simplest form.

8.2 Estimate Sums and Differences of Fractions

Estimate the sum or difference.

Question 7.
\(\frac{7}{8}\) – \(\frac{1}{5}\)
Answer:
Step 1: Use mental math to estimate each fraction.
\small \frac{7}{8} is about
Think: The numerator is about the same as the denominator.
\small \frac{1}{5} is about
Think: The numerator is near to zero.
Step 2: Estimate the difference.
An estimate of \small \frac{7}{8}\small \frac{1}{5}  is 1 – 0 = 1.

Question 8.
\(\frac{5}{6}\) + \(\frac{9}{10}\)
Answer:
Step 1: Estimate each fraction.
\small \frac{5}{6} is between \small \frac{1}{2} and 1, but is closer to 1.
\small \frac{9}{10} is between \small \frac{1}{2} and 1, but is closer to 1.
Step 2: Estimate the sum.
An estimate of \(\frac{5}{6}\) + \(\frac{9}{10}\) = 1 + 1 = 2.

Question 9.
\(\frac{11}{12}\) – \(\frac{89}{100}\)
Answer:
Step 1: Use mental math to estimate each fraction.
\small \frac{11}{12} is about
Think : The numerator is about the same as the denominator.
\small \frac{89}{100} is about
Think : The numerator is closer to denominator.
Step 2: Estimate the difference.
An estimate of \small \frac{11}{12}\small \frac{89}{100}  is 1 – 1 = 0.

Question 10.
Precision
Your friend says \(\frac{7}{8}\) – \(\frac{5}{12}\) is about 0. Find a closer estimate. Explain why your estimate is closer.
Answer:
\(\frac{7}{8}\) – \(\frac{5}{12}\) = \(\frac{11}{24}\)
\(\frac{11}{24}\) = 0.45
The number 0.45 is close to 0.

8.3 Find Common Denominators

Use a common denominator to write an equivalent fraction for each fraction.

Question 11.
\(\frac{1}{4}\) and \(\frac{1}{2}\)
Answer:
Use the product of the denominators: 4 \small \times 2 = 8
Write equivalent fractions with denominators of 8
\small \frac{1}{4} = \frac{1\times 2}{4\times 2} = \frac{2}{8}
\small \frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}
Therefore, equivalent fractions are \small \frac{2}{8}  and \small \frac{4}{8}.

Question 12.
\(\frac{2}{3}\) and \(\frac{2}{9}\)
Answer:
Use the product of the denominators : 3 \small \times 9 = 27
Write equivalent fractions with denominators of 27
\small \frac{2}{3} = \frac{2 \times 9}{3 \times 9} = \frac{18}{27}
\small \frac{2}{9} = \frac{2 \times 3}{9 \times 3} = \frac{6}{27}
Therefore, equivalent fractions are \small \frac{18}{27}  and \small \frac{6}{27}.

Question 13.
\(\frac{2}{3}\) and \(\frac{5}{6}\)
Answer:
Use the product of the denominators : 3 \small \times 6 = 18
Write equivalent fractions with denominators of 18
\small \frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18}
\small \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}
Therefore, equivalent fractions are \small \frac{12}{18}  and \small \frac{15}{18}.

Question 14.
\(\frac{4}{5}\) and \(\frac{1}{3}\)
Answer:
Use the product of the denominators : 5 \small \times 3 = 15
Write equivalent fractions with denominators of 15
\small \frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}
\small \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
Therefore, equivalent fractions are \small \frac{12}{15}  and \small \frac{5}{15}.

Question 15.
\(\frac{5}{6}\) and \(\frac{8}{9}\)
Answer:
Use the product of the denominators : 6 \small \times 9 = 54
Write equivalent fractions with denominators of 54
\small \frac{5}{6} = \frac{5 \times 9}{6 \times 9} = \frac{45}{54}
\small \frac{8}{9} = \frac{8 \times 6}{9 \times 6} = \frac{48}{54}
Therefore, equivalent fractions are \small \frac{45}{54}  and \small \frac{48}{54}.

Question 16.
\(\frac{4}{5}\) and \(\frac{3}{4}\)
Answer:
Use the product of the denominators : 5 \small \times 4 = 20
Write equivalent fractions with denominators of 20
\small \frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20}
\small \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}
Therefore, equivalent fractions are \small \frac{16}{20}  and \small \frac{15}{20}.

8.4 Add Fractions with Unlike Denominators

Add

Question 17.
\(\frac{2}{15}\) + \(\frac{2}{3}\) = __
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 15 is a multiple of 3, so rewrite \(\frac{2}{3}\) with a denominator of 15.
Rewrite \small \frac{2}{3}  as \small \frac{2 \times 5}{3 \times 5} = \small \frac{10}{15}
\small \frac{2}{15} + \small \frac{2}{3} = \small \frac{2}{15} + \small \frac{10}{15}
= \small \frac{12}{15}

Question 18.
\(\frac{3}{4}\) + \(\frac{1}{8}\) = __
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 8 is a multiple of 4, so rewrite \(\frac{3}{4}\) with a denominator of 8.
Rewrite \small \frac{3}{4}  as \small \frac{3 \times 2}{4 \times 2} = \small \frac{6}{8}
\small \frac{3}{4} + \small \frac{1}{8} = \small \frac{6}{8} + \small \frac{1}{8}
= \small \frac{7}{8}

Question 19.
\(\frac{7}{2}\) + \(\frac{1}{6}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 6 is a multiple of 2, so rewrite \(\frac{7}{2}\) with a denominator of 6.
Rewrite \small \frac{7}{2}  as \small \frac{7 \times 3}{2 \times 3} = \small \frac{21}{6}

\small \frac{7}{2} + \small \frac{1}{6} = \small \frac{21}{6} + \small \frac{1}{6}
= \small \frac{22}{6}
= \small \frac{11}{3}

Question 20.
\(\frac{5}{9}\) + \(\frac{1}{2}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 9 is not a multiple of 2, so rewrite each fraction with a denominator of 9 x 2 = 18.
Rewrite \small \frac{5}{9}  as \small \frac{5 \times 2}{9 \times 2} = \small \frac{10}{18}
\small \frac{1}{2} as \small \frac{1 \times 9}{2 \times 9} = \small \frac{9}{18}
\small \frac{5}{9} + \small \frac{1}{2} = \small \frac{10}{18} + \small \frac{9}{18}
= \small \frac{19}{18}

Question 21.
\(\frac{7}{10}\) + \(\frac{5}{6}\) = ___
Answer:

Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 10 is not a multiple of 6, so rewrite each fraction with a denominator of 10 x 6 = 60.

Rewrite \small \frac{7}{10}  as \small \frac{7 \times 6}{10 \times 6} = \small \frac{42}{60}

\small \frac{5}{6} as \small \frac{5 \times 10}{6 \times 10} = \small \frac{50}{60}

\small \frac{7}{10} + \small \frac{5}{6} = \small \frac{42}{60} + \small \frac{50}{60}

= \small \frac{92}{60}

Question 22.
\(\frac{1}{6}\) + \(\frac{11}{12}\) + \(\frac{4}{6}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the sum.
Think: 12 is a multiple of 6, so rewrite each fraction with a denominator of 12.

Rewrite \small \frac{1}{6}  as \small \frac{1 \times 2}{6 \times 2} = \small \frac{2}{12}

\small \frac{4}{6} as \small \frac{4 \times 2}{6 \times 2} = \small \frac{8}{12}

\small \frac{1}{6} + \small \frac{11}{12} + \small \frac{4}{6} = \small \frac{2}{12} + \small \frac{11}{12} + \small \frac{8}{12}

= \small \frac{21}{12}

= \small \frac{7}{4}

8.5 Subtract Fractions with Unlike Denominators

Subtract

Question 23.
\(\frac{1}{4}\) – \(\frac{1}{8}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 8 is a multiple of 4, so rewrite \(\frac{1}{4}\) with a denominator of 8.
Rewrite \small \frac{1}{4}  as \small \frac{1 \times 2}{4 \times 2} = \small \frac{2}{8}
\small \frac{1}{4}\small \frac{1}{8} = \small \frac{2}{8}\small \frac{1}{8}
= \small \frac{1}{8}

Question 24.
\(\frac{3}{2}\) – \(\frac{7}{10}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 10 is a multiple of 2, so rewrite \(\frac{3}{2}\) with a denominator of 10.
Rewrite \small \frac{3}{2}  as \small \frac{3 \times 5}{2 \times 5} = \small \frac{15}{10}
\small \frac{3}{2}\small \frac{7}{10} = \small \frac{15}{10}\small \frac{7}{10}
= \small \frac{8}{10}
= \small \frac{4}{5}

Question 25.
\(\frac{15}{16}\) – \(\frac{7}{8}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 16 is a multiple of 8, so rewrite \(\frac{7}{8}\) with a denominator of 16.
Rewrite \small \frac{7}{8}  as \small \frac{7 \times 2}{8 \times 2} = \small \frac{14}{16}
\small \frac{15}{16}\small \frac{7}{8} = \small \frac{15}{16}\small \frac{14}{16}
= \small \frac{1}{16}

Question 26.
\(\frac{4}{3}\) – \(\frac{2}{5}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 5 is not a multiple of 3, so rewrite each fraction with a denominator of 5 x 3 = 15.
Rewrite \small \frac{4}{3}  as \small \frac{4 \times 5}{3 \times 5} = \small \frac{20}{15}
\small \frac{2}{5} as \small \frac{2 \times 3}{5 \times 3} = \small \frac{6}{15}
\small \frac{4}{3}\small \frac{2}{5} = \small \frac{20}{15}\small \frac{6}{15}
= \small \frac{14}{15}

Question 27.
\(\frac{5}{6}\) – \(\frac{3}{4}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 6 is not a multiple of 4, so rewrite each fraction with a denominator of 6 x 4 = 24.
Rewrite \small \frac{5}{6}  as \small \frac{5 \times 4}{6 \times 4} = \small \frac{20}{24}
\small \frac{3}{4} as \small \frac{3 \times 6}{4 \times 6} = \small \frac{18}{24}
\small \frac{5}{6}\small \frac{3}{4} = \small \frac{20}{24}\small \frac{18}{24}
= \small \frac{2}{24}
= \small \frac{1}{12}

Question 28.
\(\frac{7}{10}\) – \(\frac{2}{5}\) + \(\frac{11}{20}\) = ___
Answer:
Use equivalent fractions to write the fractions with a common denominator. Then find the difference.
Think: 20 is a multiple of 10 and 5, so rewrite each fraction with a denominator of 20.
Rewrite \small \frac{7}{10}  as \small \frac{7 \times 2}{10 \times 2} = \small \frac{14}{20}
\small \frac{2}{5} as \small \frac{2 \times 4}{5 \times 4} = \small \frac{8}{20}

\small \frac{7}{10}\small \frac{2}{5} + \small \frac{11}{20} = \small \frac{14}{20}\small \frac{8}{20} + \small \frac{11}{20}

8.6 Add Mixed Numbers

Add

Question 29.
1\(\frac{3}{4}\) + 7\(\frac{5}{8}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator
1 \small \frac{3}{4} = 1 \small \frac{6}{8}
1 \small \frac{3}{4} + 7 \small \frac{5}{8} = 1 \small \frac{6}{8} + 7 \small \frac{5}{8}
= 8 \small \frac{11}{8}

Question 30.
3\(\frac{3}{10}\) + 2\(\frac{7}{20}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator
3 \small \frac{3}{10} = 3 \small \frac{6}{20}
3 \small \frac{3}{10} + 2 \small \frac{7}{20} = 3 \small \frac{6}{20} + 2 \small \frac{7}{20}
= 5 \small \frac{13}{20}

Question 31.
\(\frac{1}{3}\) + 6\(\frac{4}{5}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator 3 x 5 = 15
\small \frac{1}{3} = \small \frac{5}{15}
6 \small \frac{4}{5} = 6 \small \frac{12}{15}
\small \frac{1}{3} + 6 \small \frac{4}{5}  = \small \frac{5}{15} + 6 \small \frac{12}{15}
= 6 \small \frac{17}{15}

Question 32.
5\(\frac{8}{9}\) + \(\frac{5}{6}\) = _____
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator 9 x 6 = 54
5 \small \frac{8}{9} = 5 \small \frac{48}{54}
\small \frac{5}{6} = \small \frac{45}{54}
5 \small \frac{8}{9} + \small \frac{5}{6}  = 5 \small \frac{48}{54} + \small \frac{45}{54}
= 5 \small \frac{93}{54}

Question 33.
2\(\frac{2}{3}\) + \(\frac{4}{9}\) + 4\(\frac{1}{3}\) = ___
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator
2 \small \frac{2}{3} = 2 \small \frac{6}{9}
4 \small \frac{1}{3} = 4 \small \frac{3}{9}
2 \small \frac{2}{3} + \small \frac{4}{9} + 4 \small \frac{1}{3}   = 2 \small \frac{6}{9} + \small \frac{4}{9} + 4 \small \frac{3}{9}
= 6 \small \frac{13}{9}

Question 34.
5\(\frac{1}{2}\) + 2\(\frac{5}{8}\) + 3\(\frac{3}{4}\) = _____
Answer:
Add the fractional parts and add the whole number parts.
To add the fractional parts, use a common denominator
5 \small \frac{1}{2} = 5 \small \frac{4}{8}
3 \small \frac{3}{4} = 3 \small \frac{6}{8}
5 \small \frac{1}{2} + 2 \small \frac{5}{8} + 3 \small \frac{3}{4}   =5 \small \frac{4}{8} + 2 \small \frac{5}{8} + 3 \small \frac{6}{8}
= 10 \small \frac{15}{8}

8.7 Subtract Mixed Numbers

Subtract

Question 35.
8\(\frac{7}{10}\) – 1\(\frac{2}{5}\) = ___
Answer:

Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator.
1 \small \frac{2}{5} = 1 \small \frac{4}{10}
8 \small \frac{7}{10} – 1 \small \frac{2}{5}  = 8 \small \frac{7}{10} – 1 \small \frac{4}{10} = 7 \small \frac{3}{10}

Question 36.
15\(\frac{97}{100}\) – 10\(\frac{7}{20}\) = ___
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator.
10 \small \frac{7}{20} = 10 \small \frac{35}{100}
15 \small \frac{97}{100} – 10 \small \frac{7}{20}  = 15 \small \frac{97}{100} – 10 \small \frac{35}{100} = 5 \small \frac{62}{100}

Question 37.
4 – 3\(\frac{5}{6}\) = ___
Answer:
4 – 3 \small \frac{5}{6} = 4 – \small \frac{23}{6} = \small \frac{1}{6}

Question 38.
5\(\frac{1}{3}\) – 2\(\frac{1}{2}\) = _____
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator 3 x 2 = 6.
5 \small \frac{1}{3} = 5 \small \frac{2}{6} = 4 \small \frac{8}{6}
2 \small \frac{1}{2} = 2 \small \frac{3}{6}
5 \small \frac{1}{3} – 2 \small \frac{1}{2} = 4 \small \frac{8}{6} – 2 \small \frac{3}{6}
= 2 \small \frac{5}{6}

Question 39.
9\(\frac{2}{5}\) – 6\(\frac{3}{4}\) = ___
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator 5 x 4 = 20.
9 \small \frac{2}{5} = 9 \small \frac{8}{20} = 8 \small \frac{28}{20}
6 \small \frac{3}{4} = 6 \small \frac{15}{20}
9 \small \frac{2}{5} – 6 \small \frac{3}{4} = 8 \small \frac{28}{20} – 6 \small \frac{15}{20}
= 2 \small \frac{13}{20}

Question 40.
2\(\frac{3}{8}\) + 7\(\frac{1}{2}\) – 1\(\frac{11}{16}\) = ____
Answer:
To add or subtract the fractional parts, use a common denominator.
2 \small \frac{3}{8} = 2 \small \frac{6}{16}
7 \small \frac{1}{2} = 7 \small \frac{8}{16}
2 \small \frac{3}{8} + 7 \small \frac{1}{2}  – 1 \small \frac{11}{16} = 2 \small \frac{6}{16} + 7 \small \frac{8}{16} – 1 \small \frac{11}{16}
= 8 \small \frac{3}{16}

Question 41.
Modeling Real Life
A family adopts a puppy that weighs 7\(\frac{7}{8}\) pounds. They take him to the vet 2 weeks later, and he weighs 12\(\frac{3}{16}\) pounds. How much weight did the puppy gain?
Answer:
Subtract the fractional parts and subtract the whole number parts.
To subtract the fractional parts, use a common denominator.
7 \small \frac{7}{8} = 7 \small \frac{14}{16}
12 \small \frac{3}{16} – 7 \small \frac{7}{8} = 12 \small \frac{3}{16}  – 7 \small \frac{14}{16}
= 11 \small \frac{19}{16} – 7 \small \frac{14}{16}
= 4 \small \frac{5}{16}
So the puppy gains 4 \small \frac{5}{16} pounds weight.

8.8 Problem Solving: Fractions

Question 42.
A radio station plays three commercials between two songs. The commercials play for 2 minutes altogether. The first commercial is \(\frac{1}{2}\) minute, and the second commercial is 1\(\frac{1}{4}\) minutes. How long is the third commercial?
Answer:
Given,
A radio station plays three commercials between two songs.
The commercials play for 2 minutes altogether. The first commercial is \(\frac{1}{2}\) minute, and the second commercial is 1\(\frac{1}{4}\) minutes.
\(\frac{1}{2}\) + 1\(\frac{1}{4}\) = 1 \(\frac{3}{4}\)
2 – 1 \(\frac{3}{4}\) = \(\frac{1}{4}\)

Question 43.
Your friend plants a tree seedling on Earth Day that is 1\(\frac{1}{3}\) feet tall. In 1 year, the tree grows 1\(\frac{5}{6}\) feet. After 2 years, the tree is 4\(\frac{11}{12}\) feet tall. How much did the tree grow in the second year?
Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 109
Answer:
Given,
Your friend plants a tree seedling on Earth Day that is 1\(\frac{1}{3}\) feet tall.
In 1 year, the tree grows 1\(\frac{5}{6}\) feet. After 2 years, the tree is 4\(\frac{11}{12}\) feet tall.
4\(\frac{11}{12}\) – 1\(\frac{5}{6}\)  = 3 \(\frac{1}{12}\)
3 \(\frac{1}{12}\) – 1\(\frac{1}{3}\) = 1 \(\frac{3}{4}\)
Thus the growth of the tree in the second year is 1 \(\frac{3}{4}\) feet.

Conclusion:

Enhance your math skills and performance skills by referring to our Big Ideas Math Grade 5 Answer Key for Chapter 8 Add and Subtract Fractions. Make use of the links to complete your homework and assignments. Practice the given questions number of times to score the highest marks in the exams. Also, keep in touch with our site to get the Solution Key for all Big Ideas Math Grade 5 Chapters from 1 to 14.

Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays

Big Ideas Math Answers Grade 2 Chapter 1

Big Ideas Math Answers 2nd Grade 1st Chapter Numbers and Arrays PDF is provided here. We have given the solutions to all the questions in Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays in pdf format. BIM Grade 2 Textbook Chapter 1 Numbers and Arrays Answer Key helps the students to complete their homework in time and also to enhance their knowledge. It will also useful to learn the concepts in depth.

Download Big Ideas Math Book 2nd Grade Answer Key Chapter 1 Numbers and Arrays PDF

Apply the real-time math examples by learning the tricks using BIM Grade 2 Chapter 1 Numbers and Arrays. Have a look at the topics before you start the preparation. The quick method of solving math questions si helpful to the students to save their time. We have provided the answers for each and every section of chapter 1 numbers and arrays in the following sections.

The topics covered in Bid Ideas Math Book Grade 2 Answer Key Chapter 1 Numbers and Arrays are Even and Odd Numbers, Model Even and Odd Numbers, Equal Groups, Use Arrays, and Make Arrays. The performance task given at the end helps you to test your skills. Make use of the below links and learn the basic topics covered here.

Vocabulary

Lesson 1: Even and Odd Numbers

Lesson 2: Model Even and Odd Numbers

Lesson 3: Equal Groups

Lesson 4: Use Arrays

Lesson 5: Make Arrays

Performance Task

Numbers and Arrays Vocabulary

Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 1

Organize It

Use the review words to complete the graphic organizer.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 2
Answer: Plus sign
‘+’ is the mathematical symbol used to represent the notion of positive as well as the operation of addition.

Define It

Use your vocabulary cards to identify the word.

Question 1.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 3
Answer: Even

Question 2.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 4
Answer: Even

Question 3.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 5
Answer: Odd

Chapter 1 Vocabulary Cards

Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 6
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 7
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 8

Lesson 1.1 Even and Odd Numbers

Explore and Grow

Use linking cubes to model each story.
There are 6 students in the gym. Does each student have a partner?
There are 5 students in the library. Does each student have a partner?

Think and Grow

Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 9

Show and Grow

Question 1.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 10

Answer: Even

Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-10-1-Answer

Explanation: There are 6 parts, An even number can be shown as 2 equal parts.

Question 2.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 11

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-11-Answer
Explanation: There are 9 parts, An odd number cannot be shown as 2 equal parts.

Color cubes to show the number. Circle even or odd.

Question 3.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 12

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-12-Answer
Explanation: 11 is odd number and cannot be shown as 2 equal parts.

Question 4.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 13

Answer: Even
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-13-Answer
Explanation: 16 is even number and can be shown as 2 equal parts.

Apply and Grow: Practice

Color cubes to show the number. Circle even or odd.

Question 5.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 14

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-14-Answer
Explanation: 13 is odd number and cannot be shown as 2 equal parts.

Question 6.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 15

Answer: Even
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-15-Answer
Explanation: 10 is even number and can be shown as 2 equal parts.

Is the number even or odd?

Question 7.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 16

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-16-Answer
Explanation: 1 is odd number and cannot be shown as 2 equal parts.

Question 8.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 17

Answer: Even
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-17-Answer
Explanation: 4 is even number and can be shown as 2 equal parts.

Question 9.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 18

Answer: Even
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-18-Answer
Explanation: 18 is even number and can be shown as 2 equal parts.

Question 10.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 19

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-19-Answer
Explanation: 17 is odd number and cannot be shown as 2 equal parts.

Question 11.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 20

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-20-Answer
Explanation: 19 is odd number and cannot be shown as 2 equal parts.

Question 12.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 21

Answer: Even
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-21-Answer
Explanation: 20 is even number and can be shown as 2 equal parts.

Question 13.
Number Sense
Circle even or odd to describe each group. Then write each number in the correct group.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 22

Answer: Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-22-Answer

Think and Grow: Modeling Real Life

There is an even number of students in your class. There are more than 16 but fewer than 20 students. How many students are in your class?
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 23

Answer: 18 Students
Explanation: Between 16 and 20, Even number is 18.

Show how you know:

Show and Grow

Question 14.
There is an odd number of cows in a field. There are more than 13 but fewer than 17 cows. How many cows are in the field?
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 24

Answer: 15 cows
Explanation: Between 13 and 17, Odd number is 15.

Question 15.
There are 14 geese on a farm. There are 2 more chickens than geese. Is there an even or odd number of chickens?
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 25

Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 26

Answer: Even
Explanation: There are total 16 Chickens on a farm, which is Even number.

Even and Odd Numbers Home & Practice 1.1

Question 1.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 27

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-27-Answer
Explanation: Total 11 parts, which cannot be shown as 2 equal parts.

Question 2.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 28

Answer: Even
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-28-Answer
Explanation: Total 10 parts, which can be shown as 2 equal parts.

Color cubes to show the number. Circle even or Odd

Question 3.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 29

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-29-Answer
Explanation: 9 is Odd number which cannot be shown in 2 equal parts.

Question 4.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 30

Answer: Even
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-30-Answer
Explanation: 14 is Even number which can be shown in 2 equal parts.

Question 5.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 31

Answer: Even
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-31-Answer
Explanation: 18 is Even number which can be shown in 2 equal parts.

Question 6.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 32

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-32-Answer
Explanation: 15 is Odd number which cannot be shown in 2 equal parts.

Is the number even or odd?

Question 7.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 33

Answer: Even
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-33-Answer
Explanation: 2 is Even number which can be shown in 2 equal parts.

Question 8.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 34

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-34-Answer
Explanation: 5 is Odd number which cannot be shown in 2 equal parts.

Review & Refresh

Question 9.
DIG DEEPER!
You break apart a linking cube train to make two equal parts. There is 1 cube left over. Is the number of cubes even or odd? Explain.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 35

Answer: Odd
Explanation: There are 5 parts in cube train, when it is broken in 2 equal parts then there is 1 cube left (2+2+1) which is Odd number.

Question 10.
Modeling Real Life
There is an even number of eggs in a nest. There are more than 10 but fewer than 14 eggs. How many eggs are in the nest?
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 36

Answer: 12 eggs
Explanation: 12 is even number and also between 10 and 14, 12 is the only even number.

Question 11.
Modeling Real Life
You have 6 green crayons. You have 1 more blue crayon than green crayons. Do you have an even or an odd number of blue crayons?
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 37
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 38

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-37-Answer
Explanation:  Total 7 blue crayon which is Odd number so it cannot be shown in 2 equal parts.

Review & Refresh

Question 12.
6 + 6 = ___
Answer: 12
Explanation: 12 is Even number which can be shown in 2 equal parts.

Question 13.
9 + 9 = ___
Answer: 18
Explanation: 18 is Even number which can be shown in 2 equal parts.

Question 14.
7 + 7 = ___
Answer: 14
Explanation: 14 is Even number which can be shown in 2 equal parts.

Question 15.
8 + 8 = ___
Answer: 16
Explanation: 16 is Even number which can be shown in 2 equal parts.

Lesson 1.2 Model Even and Odd Numbers

Explore and Grow

Use linking cubes to model each sum. Is the sum even or odd?

Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 19.1

Answer: Even
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-20.1-Answer
Explanation: 4+4=8, 8 is Even number which can be shown in 2 equal parts.

Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 20.1

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-20.1--Answer
Explanation: 5+4=9, 9 is Odd number which cannot be shown in 2 equal parts.

Show and Grow

Question 1.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 22.1

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-22.1-Answer
Explanation: 7=4+3, Odd number

Question 2.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 23.1

Answer: Even
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-23.1-Answer
Explanation: 10=5+5, Even number

Question 3.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 24.1
Answer: Even

Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-24.1-Answer
Explanation: 14=7+7, Even number

Question 4.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 25.1
Answer: Odd

Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-25.1-Answer

Explanation: 17=9+8, Odd number

Question 5.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 26.1

Answer: Even
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-26.1-Answer
Explanation: 18=9+9, Even number

Question 6.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 27.1

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-27.1-Answer
Explanation: 13=7+6, Odd number

Question 7.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 28.1

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-28.1-Answer
Explanation: 15=8+7, Odd number

Question 8.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 29.1

Answer: Even
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-29.1-Answer

Explanation: 20=10+10, Even number

Question 9.
YOU BE THE TEACHER
Descartes uses doubles plus 1 to model an odd number. Is he correct? Explain.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 30.1

Answer: Yes
Explanation: 3+4=7, Odd number which cannot be shown as 2 equal parts.

Question 10.
You do 6 sit-ups on Saturday and 7 on Sunday. Do you do an even or odd number of sit-ups in all?
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 31.1

Answer: Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-31.1-Answer
Explanation: 6+7=13, It is an Odd number

Think and Grow: Modeling Real Life

There is an even number of marbles in one bag and an odd number of marbles in another bag. Is there an even or an odd number of marbles in all?
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 32.1

Which equation could match the story?
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 33.1
There is an ___ number of marbles in all.
Answer: Odd
Explanation: 8+7=15, 8 is even and 7 is odd number, in total 15 is Odd number of marbles.

Show and Grow

Question 11.
Two buckets each have an odd number of seashells. Is there an even or an odd number of seashells in all?
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 34.1
Which equation could match the story?
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 35.1
There is an __ number of seashells in all.
Answer: Odd
Explanation: 9+5=14, 9 and 5 are odd numbers which in total 14 is Even number.

Question 12.
DIG DEEPER!
You have an odd number of flowers. You and your friend have an even number of flowers in all. Does your friend have an even or an odd number of flowers?
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 36.1
Your friend has an ___ number of flowers.
Answer: Even
Explanation: Friend has only even number of flowers.

Model Even and Odd Numbers Homework & Practice 1.2

Question 1.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 37.1
Answer: Even
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-37.1-Answer
Explanation: 8=4+4, Even number

Question 2.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 38.1

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-38.1-Answer
Explanation: 17=9+8, Odd number

Question 3.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 39

Answer: Odd
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-39-Answer
Explanation: 9=5+4, Odd number

Question 4.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 40

Answer: Even
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-40-Answer
Explanation: 16=8+8, Even number

Question 5.
Reasoning
Fill in the blanks using even or odd.
The sum of two even numbers is ___.
Answer: Even
The sum of two odd numbers is ___.
Answer: Even
The sum of an even number and an odd number is __.
Answer: Odd

Question 6.
You do 10 jumping jacks on Saturday and 10 on Sunday. Do you do an even or odd number of jumping jacks in all?
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 41

Answer: Even
Explanation: 10+10=20, which is Even number.

Question 7.
Modeling Real Life
You and your friend each have an even number of googly eyes. Do you and your friend have an even or an odd number of googly eyes in all?
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 42

Which equation could match the story?
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 43
You have an __ number of googly eyes in all.
Answer: 4+6=10
Explanation: 4 and 6 are Even numbers. So totally 10 googly eyes which is even number.

Question 8.
DIG DEEPER!
You hop an even number of times. You and your friend hop an odd number of times in all. Does your friend hop an even or an odd number of times?
Your friend hops an ___ number of times.
Answer: Your Friend hops an Odd number of times.
Explanation: you hop an even and overall odd number, so your friend has odd number of times.

Review & Refresh

Circle the shape that shows equal shares.

Question 9.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 44
Answer: Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-44-Answer

Question 10.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 45

Answer: Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-45-Answer

Lesson 1.3 Equal Groups

Explore and Grow

Circle groups of two oranges. Complete the sentence.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 46
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 47

Answer: 4 groups of 2 is 8.

Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-46-Answer

Show and Grow

Question 1.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 49

Answer: 5 groups of 2
5+5=10

Question 2.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 50

Answer: 2 groups of 3
2+2+2=6

Question 3.
Circle groups of 3. Write a repeated addition equation.
Big Ideas Math Solutions Grade 2 Chapter 1 Numbers and Arrays 51

Answer: 5 groups of 3
5+5+5+5+5=25
Big-Ideas-Math-Solutions-Grade-2-Chapter-1-Numbers-and-Arrays-51-Answer

Apply and Grow: Practice

Question 4.
Circle groups of 5. Write a repeated addition equation.
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 52

Answer: 3 groups of 5
5+5=15
Big-Ideas-Math-Answers-Grade-2-Chapter-1-Numbers-and-Arrays-52-Answer

Question 5.
Circle groups of 4. Write a repeated addition equation.
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 53

Answer: 4 groups of 4
Answer: 4+4+4+4=16
Big-Ideas-Math-Answers-Grade-2-Chapter-1-Numbers-and-Arrays-53-Answer

Question 6.
YOU BE THE TEACHER
Newton says he can circle 5 equal groups. Is he correct? Explain.
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 54

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-1-Numbers-and-Arrays-54-Answer
Yes he is correct. Newton can circle 3 groups of 5 parts. So, 3+3+3+3+3=15

Think and Grow: Modeling Real Life

You have 3 boxes. There are 5 pencils in each box. How many pencils are there in all?
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 55
Model:
Repeated addition equation:
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 56

Answer: 15 pencils in total. 5+5+5=15.

Show and Grow

Question 7.
You have 5 bags. There are 4 notebooks in each bag. How many notebooks are there in all?
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 57
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 58

Answer: 20 notebooks in total. 5+5+5+5=20.

Question 8.
DIG DEEPER!
There are 4 boxes. Each box has the same number of glue sticks. There are 16 in all. How many glue sticks are in each box?
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 59

Answer: There are 4 glue sticks in each box.

Question 9.
Explain how you solved Exercises 7 and 8. What did you do differently?
_______________________________________
_______________________________________

Answer: Adding the number with the given number of times.

Equal Groups Homework & Practice 1.3

Question 1.
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 60

Answer: 3 groups of 2
3+3=6

Question 2.
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 61

Answer: 4 groups of 3
4+4+4=12

Question 3.
Circle groups of 2. Write a repeated addition equation.
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 62

Answer: 4 groups of 2
Big-Ideas-Math-Answers-Grade-2-Chapter-1-Numbers-and-Arrays-62-Answer
Answer: 2+2+2+2=8

Question 4.
Structure
Show two different ways to put the buttons in equal groups.
One Way:
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 63
Another Way:
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 64

Answer: Big-Ideas-Math-Answers-Grade-2-Chapter-1-Numbers-and-Arrays-63-Answer

Question 5.
Modeling Real Life
You have 3 jars of paint brushes.There are 6 paint brushes in each jar. How many paint brushes are there in all?
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 65

Answer: 18 paintbrushes
Explanation: 6+6+6=18
Review & Refresh

Question 6.
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 66
How many students chose baseball? ___

Answer: 5 students chose baseball
Which sport is the most favorite? Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 67

Answer: Favorite sport is Soccer

Lesson 1.4 Use Arrays

Explore and Grow

How many equal groups are there? Write an addition equation to tell how many cars there are in all.
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 67.1
Number of equal groups: ___
Answer: 2
Addition equation:
3+3=6

Show and Grow

Question 1.
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 68

Answer: 2 rows of 4
4+4=8

Question 2.
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 69

Answer: 3 rows of 4
4+4+4=12

Question 3.
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 70

Answer: 4 rows of 4
4+4+4+4=16

Apply and Grow: Practice

Question 4.
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 71

Answer: 2 rows of 5
5+5=10

Question 5.
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 72

Answer: 3 rows of 3
3+3+3=9

Question 6.
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 73

Answer: 3 rows of 5
5+5+5=15

Question 7.
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 74

Answer: 5 rows of 4
5+5+5+5=20

Question 8.
Logic
Which arrays show the same number of circles?
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 75

Answer: Red and Blue circles show the same number.

Think and Grow: Modeling Real Life

The arrays show the desks in two classrooms. Which classroom has more desks?
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 76
Repeated addition equations:
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 77

Classroom A: 5+5+5+5+5=25
Classroom B: 7+7+7+7=28
Answer: Classroom B has more number of desks.

Show and Grow

Question 9.
The arrays show gardens of green and yellow pepper plants. Are there more green pepper plants or yellow pepper plants?
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 78

Answer: Green pepper plants
Explanation: There are 15 Green pepper plants and 12 Yellow pepper plants.

Use Arrays Homework & Practice 1.4

Question 1.
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 79

Answer: 3 rows of 2
2+2+2=6

Question 2.
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 80

Answer: 2 rows of 2
2+2=4

Question 3.
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 81

Answer: 1 rows of 1
1+1+1+1=4

Question 4.
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 82

Answer: 3 rows of 6
6+6+6= 18

Question 5.
Number Sense
Use the array to complete the equation.
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 83

Answer: 6+6=12

Question 6.
Modeling Real Life
The arrays show toy cars. Are there more orange cars or blue cars?
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 84

Answer: Orange cars
Explanation: There are 16 orange cars and 15 blue cars.

Question 7.
DIG DEEPER!
The arrays show a sheet of stickers separated into two pieces. How many rows and columns of stickers did the sheet have before it was separated?
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 85

Answer: 5 rows and 5 columns

Review & Refresh

Question 8.
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 86

Answer: 6 flat surfaces
8 vertices
12 edges

Question 9.
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 87

Answer: 0 flat surfaces
0  vertices
0 edges

Lesson 1.5 Make Arrays

Explore and Grow

Use counters to model the story. Write an addition equation to match.

There are 4 rows of students. There are 3 students in each row. How many students are there in all?

Addition equation:

Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 87.1

Answer: 12 students
Explanation: 3+3+3+3=12 students.

Show and Grow

Question 1.
A photo album has 3 rows of photos. There are 2 photos in each row. How many photos are there in all?
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 88
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 89

Answer: 6 photos
Explanation: 2+2+2=6

Question 2.
You have 4 rows of stickers. There are 5 stickers in each row. How many stickers do you have in all?
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 90

Answer: 20 stickers
Explanation: 5+5+5+5=20

Apply and Grow: Practice

Question 3.
An ice cube tray has 5 rows. There are 2 ice cubes in each row. How many ice cubes are there in all?
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 91
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 92

Answer: 10 ice cubes
Explanation: 2+2+2+2+2=10

Question 4.
A bookcase has 3 shelves. There are 5 stuffed animals on each shelf. How many stuffed animals are there in all?
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 93

Answer: 15 stuffed animals
Explanation: 5+5+5=15 stuffed animals

Question 5.
A closet has 4 shelves. There are 2 games on each shelf. How many games are there in all?
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 94

Answer: 8 games
Explanation: 2+2+2+2=8

Question 6.
Structure
Make an array to match the equation.
5 + 5 + 5 + 5 = 20

Answer: Big-Ideas-Math-Answer-Key-Grade-2-Chapter-1-Numbers-and-Arrays-Lesson 1.5 (6)-Answer

Think and Grow: Modeling Real Life

A marching band has 3 equal rows of drummers. There are 15 drummers in all. How many drummers are in each row?
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 95
Model:
Repeated addition equation:
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 96

Answer: 5 Drummers
Explanation: 5+5+5=15

Show and Grow

Question 7.
A quilt has 4 equal rows of patches. There are 24 patches in all. How many patches are in each row?
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 97

Answer: 6 patches
Explanation: 6+6+6+6=24

Question 8.
A building has 3 equal rows of windows. There are 18 windows in all. How many columns are there?
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 98

Answer: 6 columns
Explanation: 3+3+3+3+3+3=18

Make Arrays Homework & Practice 1.5

Question 1.
A parking lot has 3 rows. There are 5 parking spots in each row. How many parking spots are there in all?
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 99

Answer: 15 parking spots
Explanation: 5+5+5=15

Question 2.
A bookcase has 4 shelves. There are 3 books on each shelf. How many books are there in all?
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 100

Answer: 12 books
Explanation: 3+3+3+3=12

Question 3.
Reasoning
Newton has 10 tokens. Which equations can Newton use to make an array with his tokens?
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 101

Answer: 2+2+2+2+2=10  and 5+5=10

Question 4.
Modeling Real Life
A theater has 4 equal rows of seats. There are 16 seats in all. How many seats are in each row?
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 102

Answer: 4 seats
Explanation: 4+4+4+4=16

Question 5.
Modeling Real Life
A chorus has 5 equal rows of singers. There are 30 singers in all. How many singers are in each row?
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 103

Answer: 6 singers
Explanation: 6+6+6+6+6=30

Review & Refresh

Question 6.
There are 9 lions in all. How many lions are in the den?
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 104

Answer: 0 lions are in den.
Explanation: All 9 lions are outside the den. Therefore, 0 lions are in the den.

Numbers and Arrays Performance Task

Question 1.
Your art supplies are packaged in boxes as described below.
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 105
a. What do you have the most of ?
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 106

Answer: 16 Crayons
Explanation: Colored Pencils= 5+5+5=15
Markers= 7+7=14
Crayons= 4+4+4+4=16
Crayons are more than Colored Pencils and Markers.
b. Do you have an even or an odd number of markers?
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 107

Answer: Even number of markers

Question 2.
a. You have 5 equal rows of paint bottles. You have 20 paint bottles in all. How many paint bottles are in each row?
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 108

Answer: 4 paint bottles are in each row.
b. You add another row of paint bottles. How many paint bottles do you have now?
Answer: 24 paint bottles
c. Describe another way to arrange the paint bottles you have now.
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 109

Answer: 6+6+6+6=24 paint bottles

Numbers and Arrays Activity

Array Flip and Find

To Play: Place the Array Flip and Find Cards face down in the boxes. Take turns flipping two cards. If your cards show the same total, keep the cards. If your cards show different totals, flip the cards back over. Play until all matches are made.
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 110

Numbers and Arrays Chapter Practice

1.1 Even and Odd Numbers

Question 1.
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 111

Answer:  Odd number
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-1-Numbers-and-Arrays-111-Answer
Explanation: 5 cube part

Question 2.
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 112

Answer: Even number
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-1-Numbers-and-Arrays-112-Answer
Explanation: 14 cube part

Color cubes to show the number. Circle even or odd.

Question 3.
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 113
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-1-Numbers-and-Arrays-113-Answer

Question 4.
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 114
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-1-Numbers-and-Arrays-114-Answer

Question 5.
Modeling Real Life
You see an odd number of boats. There are more than 15 but fewer than 19 boats. How many boats do you see?
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 115

Show how you know:

Answer: 17 boats
Explanation: Between 15 and 19 there is Odd number 17.

1.2 Model Even and Odd Numbers

Question 6.
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 116

Answer: 9=5+4
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-1-Numbers-and-Arrays-116-Answer

Question 7.
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 117

Answer: 18=9+9
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-1-Numbers-and-Arrays-117-Answer

Question 8.
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 118

Answer: 10=5+5
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-1-Numbers-and-Arrays-118-Answer

Question 9.
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 119

Answer: 7+6=13
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-1-Numbers-and-Arrays-119-Answer

1.3 Equal Groups

Question 10.
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 120

Answer: 4 groups of 2
Answer: 4+4=8

Question 11.
Circle groups of 3. Write a repeated addition equation.
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 121

Answer: 4 groups of 3
Answer: 3+3+3+3=12
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-1-Numbers-and-Arrays-121-Answer

Question 12.
Structure
Show two different ways to put the balls in equal groups.
One Way:
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 122
Another Way:
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 123
Answer: Big-Ideas-Math-Answer-Key-Grade-2-Chapter-1-Numbers-and-Arrays-122-Answer

1.4 Use Arrays

Question 13.
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 124

Answer: 3 rows of 2
Answer: 2+2+2=6

Question 14.
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 125

Answer: 2 rows of 4
Answer: 4+4=8

Question 15.
Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays 126

Answer: 5 rows of 3
Answer: 3+3+3+3+3=15

Question 16.
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 127

Answer: 4 rows of 5
Answer: 5+5+5+5=20

1.5 Make Arrays

Question 17.
A cupboard has 4 shelves. There are 3 glasses on each shelf. How many glasses are there in all?
Big Ideas Math Answers 2nd Grade Chapter 1 Numbers and Arrays 128

Answer: 12 glasses
Answer: 3+3+3+3=12

Question 18.
A bingo card has 5 rows. There are 5 squares in each row. How many squares are there in all?
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 129

Answer: 25 squares
Answer: 5+5+5+5+5=25

Question 19.
Modeling Real Life
A pet store has 5 equal rows of fish tanks. There are 20 fish tanks in all. How many fish tanks are in each row?
Big Ideas Math Answer Key Grade 2 Chapter 1 Numbers and Arrays 130

Answer: 4 fish tanks
Explanation: 4+4+4+4+4=20

Conclusion:

We wish that the data provided in Big Ideas Math Book Grade 2 Chapter 1 Numbers and Arrays Answer Key is satisfactory for all students. This Big Ideas Math Answers Grade 2 Chapter 1 Numbers and Arrays is not only useful for the students but also for the parents. To clear your doubts, please write a comment in the below comment section. Stay tuned to our site bigideasmathanswers.com to get the answer key of other grades and grade 2 chapters.

Big Ideas Math Answers Grade 2 Chapter 7 Understand Place Value to 1,000

Big Ideas Math Answers Grade 2 Chapter 7

Big Ideas Math Grade 2 Chapter 7 Understand Place Value to 1,000 Answer Key is provided in a comprehensive manner for better understanding. Students must solve as many questions as possible in BIM 2nd Grade Chapter 7 Understand Place Value to 1,000 Book and cross-check method and solutions here. If you wanted to become a pro in the place value concept, then refer to Big Ideas Math Answers Grade 2 Chapter 7 Understand Place Value to 1,000.

Big Ideas Math Book 2nd Grade Answer Key Chapter 7 Understand Place Value to 1,000

The list of concepts covered in Big Ideas Math Book 2nd Grade 7th Chapter Understand Place Value to 1,000 is given in the below section. It is one of the important concepts that must be learned at the elementary. So, no student is supposed to skip this chapter. Download BIM Grade 2 Chapter 7 Understand Place Value to 1,000 PDF for free of cost and start preparation.

Parents and teachers can have a look at this free Big Ideas Math 2nd Grade Chapter 7 Understand Place Value to 1,000 Answers for a better understanding. After solving the questions available here, you will be able to solve any kind of question framed on the concept and clear your tests with a good score. If you have a doubt just tap on the respective link you wanted to prepare and learn the fundamental topics included within it easily.

Vocabulary

Lesson: 1 Hundreds

Lesson: 2 Model Numbers to 1,000

Lesson: 3 Understand Place Value

Lesson: 4 Write Three-Digit Numbers

Lesson: 5 Represent Numbers in Different Ways

Understand Place Value to 1,000

Understand Place Value to 1,000 Vocabulary

Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 v 1

Organize It
Use the review words to complete the graphic organizer.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 v 2

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-7-Understand-Place-Value-to-1000-v-2

Explanation:
Tens Place: The first digit on the right of the decimal point means tenths.
Ones Place The ones place is just to the left of the decimal point.

Define It
Use your vocabulary cards to identify the word.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 v 3

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-7-Understand-Place-Value-to-1000-v-3

Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 v 4
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 v 5

Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 v 6
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 v 7

Lesson 7.1 Hundreds

Explore and Grow
How many unit cubes and rods are in a flat?
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.1 1
Answer: 100 cubes and 10 rods
Explanation
Given that, For counting cubes, should count all the rows and columns. By counting all the boxes there are
10 rows and 10 columns= 100 cubes To find out the rods count only the columns, by counting columns there are 10 rods.
Show and Grow
Write how many tens. Circle groups of 10 tens. Write how many hundreds. Then write the number.
Question 1.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.1 2
______ tens
______ hundred
______
Answer: 20 tens & 2 hundred (200)
Explanation
Given that 20 tens are there by circling 10 tens
For counting tens, count columns and for counting hundreds count all the boxes.
Question 2.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.1 3
______ tens
______ hundred
______
Answer: 40 tens & 4 hundred (400)
Explanation
Given that 40 tens are there by circling 10 tens
For counting tens, count columns and for counting hundreds count all the boxes.

Apply and Grow: Practice

Write how many tens. Circle groups of 10 tens. Write how many hundreds. Then write the number.
Question 3.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.1 4
______ tens
______ hundred
______
Answer: 30 tens &  3 hundreds (300)
Explanation
Given that 30 tens are there by circling 10 tens
for counting tens, count columns and for counting hundreds count all the boxes.

Question 4.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.1 5
______ tens
______ hundred
______
Answer: 60 tens & 6 hundreds
Explanation
Given that 60 tens are there by circling 10 tens.
for counting tens, count columns and for counting hundreds count all the boxes.

Question 5.
DIG DEEPER!
How many hundreds are in 700? How many tens?
_____ hundreds
______ tens
Answer: 7 hundreds are in 700 and 70 tens are in 700.
Explanation
there are 7 hundreds in 700 and 70 tens in 700. 10 tens gives  1 hundreds totally there are 70 tens is 700.

Question 6.
You have 80 bags of crayons. There are 10 crayons in each bag. How many crayons do you have in all?
_____ crayons
Answer: 800 crayons
Explanation
Given that, There are 80 bags of crayons each bags contains 10 crayons.10 x 80=800 ( 10 crayons in each bags x 80 totally bags = 800 )
Thus, There are 800 crayons do we have in all.

Think and Grow: Modeling Real Life

A store sells oranges in bags of 10. The store sells 500 oranges. How many bags do they sell?
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.1 6
Make a quick sketch:
_____ bags
Answer: 50 bags
Explanation
Given that, The store sells 500 oranges each bags contains 10 oranges.10 X 50 = 500  (10 oranges in each bags x 50 bags = 500 oranges)
Thus, The store sell the 50 bags of oranges.

Question 7.
A store sells bottles of glitter glue in boxes of 10. The store sells 600 bottles. How many boxes do they sell?
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.1 7
_____ boxes
Answer:  60 boxes
Explanation
Given that, The store sells 600 bottles of glitter glue each boxes contains 10 glitter glue bottles.
10 X 60 = 600  (10 bottle of glitter glue in each boxes x 60 boxes = 600 bottles of glitter glue)
Thus, The store sell the 60 boxes of glitter glue.

Question 8.
DIG DEEPER!
You have 10 packages of invitations. Each package has 10 invitations. You need 300 invitations. How many more packages do you need?
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.1 8
_____ more packages
Answer: 30 packages
Explanation
Given that, There are 10 packages of invitations each packages has 10 invitations you needed 300 invitations
10 x 30 = 300 (10 invitations of  packages x 30 packages = 300 invitations)
Thus, 30 packages of invitations are needed.

Hundreds Homework & Practice 7.1

Write how many tens. Circle groups of 10 tens. Write how many hundreds. Then write the number.
Question 1.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.1 9
_____ tens
______ hundreds
______
Answer: 50 tens & 5 hundreds.
Explanation
Given that 50 tens are there by circling 10 tens
For counting tens, count columns and for counting hundreds count all the boxes.

Question 2.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.1 10
_____ tens
______ hundreds
______
Answer: 80 tens & 8 hundreds
Explanation
Given that 80 tens are there by circling 10 tens
For counting tens, count columns and for counting hundreds count all the boxes.

Question 3.
Which One Doesn’t Belong?
Which does not belong with the other three?
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.1 11
Answer: 70

Question 4.
Modeling Real Life
A class has 30 boxes of pencils. Each box has 10 pencils. The class needs 600 pencils. How many more boxes does the class need?
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.1 12
______ boxes
Answer: 30 boxes
Explanation
Given that, the class has 30 boxes of pencils each boxes contains 10 pencils. The class needs 600 pencils.
10 x 60 (30 +30)=600 (10 Pencils in each boxes X 60 boxes (30 boxes which you have + 30 boxes of pencils you need)= 600 pencils)
Thus, the class needs another 30 boxes.

Question 5.
Modeling Real Life
You have 10 packages of cards. Each package has 10 cards. You need 200 cards. How many more packages do you need?
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.1 13
______ more packages
Answer: 10 package
Explanation
Given that, 10 packages of cards each packages contains 10 cards, you need 200 cards
10 x 20= 200 (10 cards in each packages X 20 packages of cards (10 packages which you have+10 packages you needed) =200 cards)
Thus, you need another 10 packages of cards.

Review & Refresh

Question 6.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.1 14
Answer: 99

Question 7.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.1 15
Answer: 75

Lesson 7.2 Model Numbers to 1,000

Explore and Grow

Model the number. Make a quick sketch to match.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 7.2 1
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-7-Understand-Place-Value-to-1000-7.2-2

Show and Grow

Question 1.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 7.2 2
______ hundreds, _______ tens, and ______ ones is ______.
Answer: 7 hundreds, 4 tens and 5 ones is 745
Explanation
There are 7 unit of cubes each unit of cubes contains 10 tens which gives 700(10 tens in one unit of cubes x 70 tens in the whole unit of cubes = 700)
and there are 4 rod each contains 10 cubes that gives 4 tens is 40 and plus the ones 5 is 745.

Apply and Grow: Practice

Question 2.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 7.2 3
______ hundreds, _______ tens, and ______ ones is ______.
Answer: 4 hundreds, 6 tens and 3 ones is 463.
Explanation
There are 4 unit of cubes each unit of cubes contains 10 tens which gives 400(10 tens in one unit of cubes x 40 tens in the whole unit of cubes = 400)
and there are 6 rod each contains 10 cubes that gives 6 tens is 60 and plus the ones 3 is 463.

Question 3.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 7.2 4
______ hundreds, _______ tens, and ______ ones is ______.
Answer: 6 hundreds, 0 tens and 9 ones is 609.
Explanation
There are 6 unit of cubes each unit of cubes contains 10 tens which gives 600(10 tens in one unit of cubes x 70 tens in the whole unit of cubes = 700)
The place value of 0 (0 x 10 tens = 0) and plus the ones 9 is 609.

Question 4.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 7.2 5
______ hundreds, _______ tens, and ______ ones is ______.
Answer: 3 hundreds, 4 tens and 6 ones is 346.
Explanation
There are 3 unit of cubes each unit of cubes contains 10 tens which gives 300(10 tens in one unit of cubes x 30 tens in the whole unit of cubes = 300)
and there are 4 rod each contains 10 cubes that gives 4 tens is 40 and plus the ones 6 is 346.

Question 5.
DIG DEEPER!
What number is Newton thinking about?
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 7.2 6
Answer:58

Think and Grow: Modeling Real Life

You buy the markers shown. How many markers do you buy?
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 7.2 7
Write the missing numbers:
_______ hundreds, _______ tens, and ______ ones
_______ markers
Answer: 3 hundreds, 2 tens and 4 ones is 324 markers.
Explanation
The above images shows that 3 packs of 100 markers(100+100+100=300) 2 packs of 10 markers(10+10=20) with additional of 4 markers, that gives
(300+20+4=324)Totally 324 markers you buy.

Show and Grow

Question 6.
You buy the balloons shown. How many balloons do you buy?
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 7.2 8
______ balloons
Answer:  570 balloons
Explanation
The above images shows that 5 packs of 100 balloons(100+100+100+100+100= 500) 7 packs of 10 balloons(10+10+10+10+10+10+10=70),
that gives ( 500+70=570)Totally 570 balloons you buy.

Model Numbers to 1,000 Homework & Practice 7.2

Question 1.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 7.2 9
______ hundreds, _______ tens, and ______ ones is ______.
Answer: 4 hundreds,7 tens 2 ones is 472
Explanation
There are 4 unit of cubes each unit of cubes contains 10 tens which gives 400(10 tens x 40 tens of whole cubes =400)
There are 7 rod gives you a 7 tens is 70 and plus 2 ones is 472.

Question 2.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 7.2 10
______ hundreds, _______ tens, and ______ ones is ______.
Answer: 7 hundreds 4 tens 0 ones is 740.
Explanation
There are 7 unit of cubes each unit of cubes contains 10 tens which gives 700(10 tens in one unit of cubes x 70 tens in the whole unit of cubes = 700)
and there are 4 rod each contains 10 cubes that gives 4 tens is 40 and plus the ones place above picture there were no ones 0 is 740

Question 3.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 7.2 11
______ hundreds, _______ tens, and ______ ones is ______.
Answer: 2 hundreds 8 tens and 6 ones is 286.
Explanation
There are 2 unit of cubes each unit of cubes contains 10 tens which gives you 200 (10 tens in one unit of cubes x 20 tens in the whole unit of cubes = 200) and there are 8 rod each contains 10 cubes that gives 8 tens is 80 and plus the ones 6 is 286.

Question 4.
YOU BE THE TEACHER
Your friend writes 8 hundreds and 3 ones as 83. Is your friend correct? Explain.
_________________________
_________________________
Answer:  No, 8 is tens and 3 is ones as 83.
Explanation
The first digit is the tens place it tells you that there are 8 tens in the number 83. The next digit is the ones place which is 3.
Therefore there are 8 sets of 10 tens and plus 3 ones in the number 83.

Question 5.
Modeling Real Life
You buy the stickers shown. How many stickers do you buy?
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 7.2 12
______ stickers
Answer: 620 stickers
Explanation
Given that, There are 6 packs of stickers each contains 100 stickers that is (100+100+100+100+100+100=600
and 2 packs of stickers each contains 10 stickers that is (10+10= 20) Therefore 600 +20= 620
Thus, 620 sticker you buy.

Review & Refresh

Question 6.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 7.2 13
Answer: 82

Question 7.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 7.2 14
Answer: 83

Question 8.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 7.2 15
Answer: 71

Lesson 7.3 Understand Place Value

Explore and Grow

Make quick sketches to model each number.
Big Ideas Math Answers Grade 2 Chapter 7 Understand Place Value to 1,000 7.3 1
What do you notice about the numbers?
_________________________
_________________________
Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-7-Understand-Place-Value-to-1000-7.3-1

Show and Grow

Circle the value of the underlined digit.
Question 1.
483
300
30
3
Answer: 3
Explanation
Given that there are 3 digit number which is 483. A number can have many digits and each
digit has a special place and value. the 8 is in ones place and its place value is 8.

Question 2.
791
9 hundreds
9 tens
9 ones
Answer: 9 tens
Explanation
Given that there are 3 digit number which is 791. A number can have many digits and each
digit has a special place and value. the second digit at tens place. The 9 is in tens place value is 90.
Question 3.
612
6
60
600
Answer: 600
Explanation
Given that there are 3 digit number which is 612. A number can have many digits and each
digit has a special place and value. the first digit at hundreds place. The 6 is in hundreds place value is 600.

Question 4.
578
7 hundreds
7 tens
7 ones
Answer: 7 tens
Explanation
Given that there are 3 digit number which is 578. A number can have many digits and each
digit has a special place and value. the second digit at tens place. The 7 is in tens place value is 70.

Apply and Grow: Practice

Circle the value of the underlined digit.
Question 5.
354
300
30
3
Answer: 300
Explanation
Given that there are 3 digit number which is 354. A number can have many digits and each
digit has a special place and value. the first digit at hundreds place. The 3 is in hundreds place value is 300.

Question 6.
726
2 hundreds
2 tens
2 ones
Answer: 2 tens
Explanation
Given that there are 3 digit number which is 726. A number can have many digits and each
digit has a special place and value. the second digit at tens place. The 2 is in tens place value is 20.

Question 7.
594
4
40
400
Answer: 4
Explanation
Given that there are 3 digit number which is 594. A number can have many digits and each
digit has a special place and value. the 4 is in ones place and its place value is 4.

Question 8.
475
5 hundreds
50
5 ones
Answer: 5 ones
Explanation
Given that there are 3 digit number which is 475. A number can have many digits and each
digit has a special place and value. the 5 is in ones place and its place value is 5.

Circle the values of the underlined digit.
Question 9.
639
3 tens
300
30
Answer: 3 tens
Explanation
Given that there are 3 digit number which is 639. A number can have many digits and each
digit has a special place and value. the second digit at tens place. The 3 is in tens place value is 30.

Question 10.
872
8 hundreds
80
800
Answer: 8 hundreds
Explanation
Given that there are 3 digit number which is 872. A number can have many digits and each
digit has a special place and value. the first digit at hundreds place. The 8 is in hundreds place value is 800.

Question 11.
Number Sense
Write the number that has the following values.
The tens digit has a value of 40.
The ones digit has a value of 2.
The hundreds digit has a value of 600. ______
Answer: 642
Explanation
The combination of hundreds, tens, ones of 600, 40, 2 respectively.

Think and Grow: Modeling Real Life

How many points is one ball worth in each bucket?
Big Ideas Math Answers Grade 2 Chapter 7 Understand Place Value to 1,000 7.3 2
Write the score:
______ hundreds, ______ tens, and _______ ones
Blue bucket: ______ points
Yellow bucket: _____ point
Red bucket: ______ points
Answer: Blue bucket 3 points,yellow bucket 4 points and red bucket 5 points

Show and Grow

Question 12.
How many points is one ring worth on each peg?
Big Ideas Math Answers Grade 2 Chapter 7 Understand Place Value to 1,000 7.3 3
Green peg: ______ points
Blue peg: _______ point
Purple peg: ______ points
Answer:
Green peg: 1 points
Blue peg: 3 point
Purple peg: 2 points

Understand Place Value Homework & Practice 7.3

Circle the value of the underlined digit.
Question 1.
523
500
50
5
Answer: 500
Explanation
Given that there are 3 digit number which is 523. A number can have many digits and each
digit has a special place and value. the first digit at hundreds place. The 5 is in hundreds place value is 500.

Question 2.
738
8 hundreds
8 ones
8 tens
Answer: 8 ones
Explanation
Given that there are 3 digit number which is 738. A number can have many digits and each
digit has a special place and value. the 8 is in ones place and its place value is 8.

Question 3.
364
60
6 ones
6 hundreds
Answer: 60
Explanation
Given that there are 3 digit number which is 364. A number can have many digits and each
digit has a special place and value. the second digit at tens place. The 6 is in tens place value is 60.

Circle the values of the underlined digit.
Question 4.
434
4
4 ones
4 hundreds
Answer: 4 ones
Explanation
Given that there are 3 digit number which is 434. A number can have many digits and each
digit has a special place and value. the 4 is in ones place and its place value is 4.

Question 5.
920
2
2 tens
20
Answer: 2 tens
Explanation
Given that there are 3 digit number which is 920. A number can have many digits and each
digit has a special place and value. the second digit at tens place. The 2 is in tens place value is 20.

Question 6.
DIG DEEPER!
Write the number that matches the clues.
The value of the hundreds digit is 800.
The value of the tens digit is 10 less than 70.
The value of the ones digit is an even number greater than 7.
_________
Answer:
i. 8
80
8

Question 7.
Structure
Write each number in the correct circle.
Big Ideas Math Answers Grade 2 Chapter 7 Understand Place Value to 1,000 7.3 4
Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-7-Understand-Place-Value-to-1000-7.3-4

Question 8.
Modeling Real Life
How many points is one ball worth in each hoop?
Big Ideas Math Answers Grade 2 Chapter 7 Understand Place Value to 1,000 7.3 5
Blue hoop: ______ points
Orange hoop: _______ points
Red hoop: _______ point
Answer:
Blue hoop: 4 points
Orange hoop: 2 points
Red hoop: 5 points

Review & Refresh

Question 9.
Big Ideas Math Answers Grade 2 Chapter 7 Understand Place Value to 1,000 7.3 6
Answer: 19

Question 10.
Big Ideas Math Answers Grade 2 Chapter 7 Understand Place Value to 1,000 7.3 7
Answer: 42

Question 11.
Big Ideas Math Answers Grade 2 Chapter 7 Understand Place Value to 1,000 7.3 8
Answer: 38

Lesson 7.4 Write Three-Digit Numbers

Explore and Grow

Identify the value of the base ten blocks.
Big Ideas Math Solutions Grade 2 Chapter 7 Understand Place Value to 1,000 7.4 1
What is the total value of the base ten blocks? ________

How can you write the value of the base ten blocks as an equation?
Big Ideas Math Solutions Grade 2 Chapter 7 Understand Place Value to 1,000 7.4 2
Answer:
Standard Form is 246
Expanded Form is 200 + 40 + 6 = 246
Word Form is Two Hundred and Forty Six

Show and Grow

Write the number in standard form, expanded form, and word form.
Question 1.
Big Ideas Math Solutions Grade 2 Chapter 7 Understand Place Value to 1,000 7.4 3
Answer: Standard form 528,
Expanded form 500+20+8,
Word form Five Hundred Twenty Eight.

Question 2.
Big Ideas Math Solutions Grade 2 Chapter 7 Understand Place Value to 1,000 7.4 4
Answer: Standard form 709,
Expanded form 700+9,
Word form Seven Hundred Nine.

Apply and Grow: Practice 

Write the number in expanded form and word form.
Question 3.
837
_____ + _____ + _____
______________
Answer: 800+30+7 and Eight hundred thirty seven
Explanation
In expanded form, write the number by showing the value of each digit (800+30+7)
In Word form write the number by using words but no numbers (Eight hundred thirty seven)
Question 4.
954
_____ + _____ + ______
_____________
Answer:900+50+4 and Nine hundred fifty four
Explanation
In expanded form, write the number by showing the value of each digit (900+50+4)
In Word form write the number by using words but no numbers ( Nine hundred fifty four)
Write the number in standard form and word form.
Question 5.
500 + 60
______
__________
Answer: 560 and Five hundred sixty
Explanation
In standard form, numbers are written using only numbers. There are no words (560)
In Word form write the number by using words but no numbers ( Nine hundred fifty four)
Question 6.
700 + 20 + 1
_____
____________
Answer:721 and Seven hundred twenty one
Explanation
In standard form, numbers are written using only numbers. There are no words (721)
In Word form write the number by using words but no numbers ( Seven hundred twenty one)

Write the number in expanded form and standard form.
Question 7.
six hundred seventy-four
_____ + ______ + ______
__________
Answer: 600+70+4 and 674
Explanation
In expanded form, write the number by showing the value of each digit (600+70+4)
In standard form, numbers are written using only numbers. There are no words (674)
Question 8.
four hundred seven
_____ + ______ + ______
__________
Answer: 400+7 and 407
Explanation
In expanded form, write the number by showing the value of each digit (400+7)
In standard form, numbers are written using only numbers. There are no words (407)
Question 9.
Structure
Which number did Newton model?
Big Ideas Math Solutions Grade 2 Chapter 7 Understand Place Value to 1,000 7.4 5

Think and Grow: Modeling Real Life

There are 819 pets in a pet store. 800 are fish. 9 are cats. The rest are birds. How many birds are there?
Big Ideas Math Solutions Grade 2 Chapter 7 Understand Place Value to 1,000 7.4 6
Expanded form:
_____ + _____ + ______
_____ birds
Answer: 10 birds are there and 800+10+9
Explanation
Given that, There are 819 pets in pets store
800 are fish, 9 are cats and rest are birds.
Thus,819 the right the first digit will be at ones place 9 is in ones place and its place value is 9 ,the second digit at tens place 1 is in tens place its place value is 10 and the third digit at hundreds place.8 is in hundreds place its place value is 800.

Show and Grow

Question 10.
There are 21
7 flowers at a flower stand. 200 are roses. 7 are sunflowers. The rest are tulips. How many tulips are there?
Big Ideas Math Solutions Grade 2 Chapter 7 Understand Place Value to 1,000 7.4 7
______ tulips
Answer: 10 are tulips in flower stand.
Explanation
Given that, There are 217 flowers in flowers stand
200 are roses, 7 are sunflowers and rest are tulips (200 – 7 = 10)
Thus,10 are the tulips.
Question 11.
There are 185 books at a book fair. 80 are chapter books. 5 are comic books. The rest are picture books. How many picture books are there?
Big Ideas Math Solutions Grade 2 Chapter 7 Understand Place Value to 1,000 7.4 8
______ picture books
Answer: 100 books are picture books.
Explanation
Given that, 185 books are at book fair.
80 books are chapter books and 5 are comic books and rest books are picture books
(80 – 5 = 100)
Thus, 100 books are picture books in book fair.
Question 12.
You sell 326 candles. You sell 6 small candles. You sell 20 medium candles. The rest are large candles. How many large candles did you sell?
Big Ideas Math Solutions Grade 2 Chapter 7 Understand Place Value to 1,000 7.4 9
______ large candles
Answer: 300 are large candles
Explanation:
Given that, 326 candles are sell by you,
6 are small candles and 20 are medium candles and rest are large candles
326-6(small candles)=320
320-20(medium candles)=300
Thus,300 large candles are you sell.
Three-Digit Numbers Homework & Practice 7.4

Write the number in expanded form and word form.
Question 1.
137
______ + _____ + _____
____________
Answer: 100+30+7 and One hundred thirty seven.
Explanation:
In expanded form, write the number by showing the value of each digit (100+30+7)
In Word form write the number by using words but no numbers ( One hundred twenty four)
Question 2.
280
_____ + _____ + ______
___________
Answer: 200+80 and Two hundred eighty
Explanation
In expanded form, write the number by showing the value of each digit (200+80)
In Word form write the number by using words but no numbers ( Two hundred eighty )
Write the number in standard form and word form.
Question 3.
600 + 10 + 5 ______
___________
Answer:  615 and Six hundred fifteen
Explanation
In standard form, numbers are written using only numbers. There are no words (615)
In Word form write the number by using words but no numbers ( Six hundred fifteen )
Question 4.
900 + 70 + 6 _____
___________
Answer: 976 and Nine hundred seventy six
In standard form, numbers are written using only numbers. There are no words (976)
In Word form write the number by using words but no numbers ( Nine hundred seventy six )
Write the number in expanded form and standard form.
Question 5.
three hundred nine
_____ + ______ + _____
______
Answer: 300+9 and 309
Explanation
In expanded form, write the number by showing the value of each digit (300+9)
In standard form, numbers are written using only numbers. There are no words (309)
Question 6.
eight hundred sixty-two
_____ + ______ + ______
_______
Answer: 800+60+2 and 862
Explanation
In expanded form, write the number by showing the value of each digit (800+60+2)
In standard form, numbers are written using only numbers. There are no words (862))
Question 7.
Which One Doesn’t Belong?
Which does not belong with the other three?
Big Ideas Math Solutions Grade 2 Chapter 7 Understand Place Value to 1,000 7.4 10
Answer: 1 + 9 + 6 does not belong to the other three.

Question 8.
DIG DEEPER!
A number has 7 hundreds. The tens digit is 5 less than the hundreds digit. The ones digit is 2 more than the hundreds digit. What is the number?
______
Answer: 729
Explanation
given that, a number has 7 hundred
The tens digit is 5 less than hundreds digit

Question 9.
Modeling Real Life
There are 438 vegetables planted. 400 are carrots. 8 are beets. The rest are onions. How many onions are there?
Big Ideas Math Solutions Grade 2 Chapter 7 Understand Place Value to 1,000 7.4 11
______ onions
Answer: 30 onions are there
Explanation
As per the statement, There are 438 vegetables are planted
400 are carrot (438-400=38)
8 are beets (38 – 8=30)
Thus, the Remaining 30 are onions.

Question 10.
Modeling Real Life
There are 593 students in after-school programs. 3 students take dance class. 90 students take art class. The rest take karate class. How many students take karate class?
Big Ideas Math Solutions Grade 2 Chapter 7 Understand Place Value to 1,000 7.4 12
______ students
Answer: 500 students are in karate class.
Explanation:
As per statements, Totally there are 593 students
3 students are in dance class (593-3=590)
90 students are in art class (590-90=500)
Thus, the Remaining 500 students are in karate class.

Review & Refresh

Question 11.
Find the sum. Then change the order of the addends. Write the new equation.
4 + 7 = ______
_____ + _____ = ______
Answer: 11

Lesson 7.5 Represent Numbers in Different Ways

Explore and Grow

Circle the models that show each number.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.5 1
Answer:

Show and Grow

Question 1.
Show 261 two ways.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.5 2
Answer:

Question 2.
Show 345 two ways.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.5 3
Answer:

Apply and Grow: Practice

Question 3.
Show 432 two ways.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.5 4
Answer:

Question 4.
Show 527 two ways.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.5 5
Answer:

Question 5.
YOU BE THE TEACHER
Your friend says that 800 + 40 + 11 is the same as 800 + 50 +1. Is your friend correct? Explain.
_________________________
__________________________
Answer:

Think and Grow: Modeling Real Life

The models show how many dinosaur toys you and your friend have. Does your friend have the same number of dinosaur toys as you? Explain.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.5 6
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.5 7
_________________________
__________________________
Answer:

Show and Grow

Question 6.
The models show how many trading cards you and your friend have. Does your friend have the same number of trading cards as you? Explain.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.5 8
______________________
______________________
Answer:

Represent Numbers in Different Ways Homework & Practice 7.5

Question 1.
Show 134 two ways.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.5 9
Answer:

Question 2.
Show 319 two ways.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.5 10
Answer:

Question 3.
Number Sense
Which ways show 948?
8 hundreds, 4 tens, and 8 ones
9 hundreds, 4 tens, and 8 ones
8 hundreds, 4 tens, and 9 ones
8 hundreds, 14 tens, and 9 ones
94 tens and 8 ones
948 ones
Answer:

Question 4.
Modeling Real Life
The models show how many bouncy balls you and your friend have. Does your friend have the same number of bouncy balls as you? Explain.
Big Ideas Math Answer Key Grade 2 Chapter 7 Understand Place Value to 1,000 7.5 11
________________________
__________________________
Answer:

Review & Refresh

Question 5.
70 + 30 = ______
Answer: 100

Question 6.
53 + 19 = _____
Answer: 72

Question 7.
90 − 50 = _____
Answer: 40

Question 8.
64 − 40 = _______
Answer: 24

Understand Place Value to 1,000 Performance Task

You make trail mix using the sunflower seeds, almonds, and raisins shown.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 1
Question 1.
How many sunflower seeds, almonds, and raisins do you use?
______ + _____ + _____
_____
Answer: 400+ 30+ 5 is equal to 435.
Explanation
Given that, 400 sunflower seeds, 30 almonds and 5 raisins  for trail mix
thus, 400+30+5= 435

Question 2.
You add another bag of almonds and another bag of raisins to your trail mix. How many sunflower seeds, almonds, and raisins are there now?
_____ + _____ + _____
______
Answer: 400+40+10= 450
Explanation
Given that, 400 sunflower seeds, 30 of almonds add another bags of almonds is contains 10 totally 40 and 5 of raisins add another bags of raisins contains 5 totally 10 raisins.
400+40+10=450

Question 3.
Your friend makes trail mix with 3 bags of sunflower seeds,13 bags of almonds, and 4 bags of raisins. Does your friend use the same number of ingredients as you? Explain.
Yes No
__________________
___________________
Answer: No, friend makes a trail mix with only 3 bags of sunflower 13 bags of almonds and 4 bag of raisins. The ingredients you used is 400 sunflower seeds,40 almonds bags and 10 raisins bags. Friend and your’s are not the same ingredients.

Understand Place Value to 1,000 Activity

Naming Numbers Flip and Find
To Play: Place the Naming Numbers Flip and Find Cards face down in the boxes. Take turns flipping 2 cards. If your cards show the same number, keep the cards. If your cards show different numbers, flip the cards back over. Play until all matches are made.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 2

7.1 Hundreds

Write how many tens. Circle groups of 10 tens. Write how many hundreds. Then write the number.
Question 1.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 chp 1
_____ tens
_______ hundreds
________
Answer: 40 tens and 4 hundreds
Explanation
Given that 40 tens are there by circling 10 tens
For counting tens, count columns and for counting hundreds count all the boxes.

Question 2.

Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 chp 2
_____ tens
_______ hundreds
________
Answer:  50 tens and 5 hundred
Explanation
Given that 50 tens are there by circling 10 tens
For counting tens, count columns and for counting hundreds count all the boxes.

Question 3.

Modeling Real Life
A cafeteria has 80 bags of pretzels. Each bag has 10 pretzels. The cafeteria needs 900 pretzels. How many more bags does the cafeteria need?
______ more bags
Answer: 10 bags

Explanation:
Given that, the cafeteria has 80 bags of pretzels  each bags contains 10 pretzels, cafeteria needs 900 pretzels,
10 bags x 10 pretzels =100
Thus 10 bags of pretzels needs for the cafeteria.

7.2 Model Numbers to 1,000

Question 4.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 chp 4
______ hundreds, _____ tens, and _____ ones is ______.
Answer:5 hundreds 2 tens, 5 ones is 525.
Explanation
There are 5 unit of cubes each unit of cubes contains 10 tens which gives 500(10 tens in one unit of cubes x 50 tens in the whole unit of cubes = 500)
and there are 2 rod each contains 10 cubes that gives 2 tens is 20 and plus the ones 5 is 525.

Question 5.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 chp 5
______ hundreds, _____ tens, and _____ ones is ______.
Answer: 8 hundred,0 tens, and 3 ones is 803.
Explanation
There are 8 unit of cubes each unit of cubes contains 10 tens which gives 800(10 tens in one unit of cubes x 80 tens in the whole unit of cubes = 800)
the second digit at tens place 0 in the tens place and the right first digit is ones plus the ones 3 is 803.

Question 6.
Number Sense
What number is Descartes thinking about?
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 chp 6
______
Answer:425
Explanation
The above answer represents that 4 hundreds is 400 and the second digit at tens place. The 2 is in tens place value is
20 and the right first digit is in ones place the 5 is in ones place value 5 is 425.

7.3 Understand Place Value

Circle the value of the underlined digit
Question 7.
429
200
2
2 tens
Answer: 2 tens
Explanation
Given that there is 3 digit number which is 429. A number can have many digits and each
digit has a special place and value. the second digit at tens place. The 2 is in tens place value is 20.
Question 8.
751
70
700
7 tens
Answer: 700
Explanation
Given that there is 3 digit number which is 751. A number can have many digits and each
digit has a special place and value. the first digit at hundreds place. The 7 is in hundreds place value is 700

Question 9.
Number Sense
Write the number that has the following values.
The tens digit has a value of 60.
The ones digit has a value of 3.
The hundreds digit has a value of 900. _______
Answer:963
Explanation:
A number can have many digits and each digit has a special place and value. the first digit at hundreds place.
The 9 is in hundreds place value is 900. The second digit at tens place the 6 is in tens place value is 60 and
the right first digit is in ones place the 3 is in ones place value 3 is 963.

7.4 Write Three-Digit Numbers

Write the number in expanded form and word form.
Question 10.
605
_____ + _____ + ______
________
Answer: 600+5 and Six hundred five
Explanation
In expanded form, write the number by showing the value of each digit (600+05)
In Word form write the number by using words but no numbers ( Six hundred five)

Question 11.
541
______ + ______ + ______

___________
Answer: 500+40+1 and Five hundred forty-one
Explanation
In expanded form, write the number by showing the value of each digit (500+40+1)
In Word form write the number by using words but no numbers (Five hundred forty-one)

Write the number in standard form and word form.
Question 12.
100 + 20 + 4
______
___________
Answer: 124 and One hundred twenty-four
Explanation
In standard form, numbers are written using only numbers. There are no words (124)
In Word form write the number by using words but no numbers (One hundred twenty-four)

Question 13.
700 + 8
_______
_____________
Answer: 708 and Seven hundred eight
Explanation
In standard form, numbers are written using only numbers. There are no words (708)
In Word form write the number by using words but no numbers (Seven hundred eight)

Write the number in expanded form and standard form.
Question 14.
three hundred thirty
_____ + _____ + _____
_____
Answer: 300+30 and 330
Explanation
In expanded form, write the number by showing the value of each digit (300+30)
In standard form, numbers are written using only numbers. There are no words. (330)
Question 15.
two hundred fifty-six
_____ + ______ + _____
______
Answer: 200+50+6 and 256
Explanation
In expanded form, write the number by showing the value of each digit (200+50+6)
In standard form, numbers are written using only numbers. There are no words. (256)
7.5 Represent Numbers in Different Ways

Question 16.
Show 345 two ways.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 chp 16
Answer: Three hundred forty-five and 300+40+5
Explanation
There are 3 digit number(345)  1 digit is for hundreds which is 3, 2nd digit is for tens which is 2 and the last digit for once 5 is 345
In word form for 345 is Three hundreds forty-five,
The expanded form for 345 is 300+40+5 which gives 345.

Question 17.
Show 562 two ways.
Big Ideas Math Answers 2nd Grade Chapter 7 Understand Place Value to 1,000 chp 17
Answer: Five hundred sixty-two and 500+60+2
Explanation
There are 3 digit numbers 1 digit number is hundreds which are 5, 2nd digit number is tens which is 6 tens and the last number 2 ones is 562
In word form for 562 is Five hundred sixty-two,
The expanded form for 562 is 500+60+2 is 562.

Question 18.
Your friend says that 600 + 30 + 1 is the same as 500 + 130 + 1. Is your friend correct? Explain.
___________________
___________________
Answer: Yes correct, given that 600+30+1= 631 ( which gives) and 500+130+1 = 631( which also gives the same answer)
both equation shows the same answers.

Conclusion:

In this chapter, a brief explanation of the lessons are discussed in Answer Key of Big Ideas Math book Grade 2 Chapter 7 Understand Place Value to 1,000. Here we have provided the exercise problems and the solutions to help in practising the lessons. you can get the different and simple methods of solving problems in Big Ideas Math Grade 2 Answer Key Chapter 7 Understand Place Value to 1,000. Stay in touch with our site to get the latest edition solutions of all other Big Ideas Math Grade 2 Answers.

Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals

Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals

Download Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals PDF for free. Learn every topic of BIM Grade 5 Chapter 7 Divide Decimals Answers. Make use of our material and check out the step-by-step explanation to learn all the concepts easily. Enjoy the learning of maths with the help of our BIM Grade 5 Answer Key for Chapter 7 Divide Decimals. Our complete guide will help you to score the best marks in the exam and also in your preparation. Therefore, without any second thought prepare with Big Ideas Math Book 5th class Answer Key Chapter 7 Divide Decimals and get a good score in the exam.

Big Ideas Chapter 7 Divide Decimals 5th Grade Math Book Answer Key

Find the best tips that make your students love to practice maths and encourage them to use them for easy practicing. We have also provided different tricks to solve all the math problems. Big Ideas math 5th grade Chapter 7 Divide Decimals textbook Answer Key is the best source for the students. All the relevant links of Divide Decimals are given below. Check the links and begin your practice now.

Lesson: 1 Division Pattern with Decimals

Lesson: 2 Estimate Decimals Quotients

Lesson: 3 Use Models to Divide Decimals by Whole Numbers

Lesson: 4 Divide Decimals by One-Digit Numbers

Lesson: 5 Divide Decimals by Two-Digit Numbers

Lesson: 6 Use Models to Divide Decimals

Lesson: 7 Divide Decimals

Lesson: 8 Insert Zeros in the Dividend

Lesson: 9 Problem Solving: Decimal Operations

Chapter: 7 – Divide Decimals

Lesson 7.1 Division Pattern with Decimals

Explore and Grow

Use the relationship between positions in a place value chart to find each quotient.
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.1 1
What patterns do you notice?
Answer:

Structure

Describe the placement of the decimal point when dividing a decimal by 10, 100, 0.1, and 0.01.
Answer:

Think and Grow: Division Pattern with Decimals

Example
Find 74 ÷ 103.
Use place value concepts. Every time you multiply a number by \(\frac{1}{10}\) or divide a number by 10, each digit in the number shifts one position to the right in a place value chart.
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.1 2
Notice the pattern: In each quotient, the number of places the decimal point moves to the left is the same as the exponent.
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.1 3
Example
Find 5.8 ÷ 0.01.
Use place value concepts. Every time you multiply a number by 10 or divide a number by 0.1, each digit in the number shifts one position to the left in a place value chart.
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.1 4
Notice the pattern: When you divide by 0.1, the decimal point moves one place to the right. When you divide by 0.01, the decimal point moves two places to the right.

Show and Grow

Find the quotient.
Question 1.
62.5 ÷ 102 = ______
Answer: 0.625
Explanation:  First Simplify the 102 which means  10X10 =100 then we need to calculate the fraction to a decimal just divide the numerator(62.5) by the denominator (100): 62.5 ÷ 100 =0.625 so,  62.5/100 =0.625
Question 2.
1.84 ÷ 0.1 = ______
Answer: 18.4
Explanation: To convert this simple fraction to a decimal just divide the numerator (1.84) by the denominator (0.1): 1.84 ÷ 0.1 = 18.4 so, 1.84/0.1 = 18.4

Apply and Grow: Practice

Find the quotient.
Question 3.
76 ÷ 10 = ______
Answer:  7.6
Explanation: To convert this simple fraction to a decimal just divide the numerator (76) by the denominator (10): 76 ÷ 10 = 7.6 so, 76/10 = 7.6
Question 4.
3.65 ÷ 0.1 = _______
Answer: 36.5
Explanation: To convert this simple fraction to a decimal just divide the numerator (3.65) by the denominator (0.1): 3.65 ÷ 0.1 = 36.5. so, 3.65/0.1 = 36.5
Question 5.
2.9 ÷ 0.01 = ______
Answer: 290
Explanation: To convert this simple fraction to a decimal just divide the numerator (2.9) by the denominator (0.01): 2.9 ÷ 0.01 = 290. so, 2.9/0.01 = 290
Question 6.
18.7 ÷ 102 = ______
Answer: 0.187
Explanation: First Simplify the 102 which means  10X10 =100 then we need to calculate the fraction to a decimal just divide the numerator(18.7) by the denominator (100): 18.7 ÷ 100 =0.187 so,  18.7/100 =0.187

Find the value of k.
Question 7.
95.8 ÷ k = 958
Answer: K = 0.1
Explanation: Lets solve your equation step by step 95.8/k = 958
Multiply both side by side K.
95.8 = 958K
958k = 95.8 (Flip the equation)
958k/958 = 95.8/958(Divide both sides by 958)
K=0.1
Question 8.
k ÷ 103 = 0.35
Answer: K =350
Explanation: K÷103 =0.35
Step 1: calculate the value of the power which means 103 = 10x10x10=1000
k/1000=0.35
step 2: multiply both side by 1000
1000X K/1000 = 1000X0.35
Step 3: simplify
1000 X K/1000 = 1000X0.35
K = 350
Question 9.
245 ÷ k = 24,500
Answer: K =0.01
Explanation: variable K cannot be equal to 0 since division by zero is not defined. Multiply both side of equation by K
245 = 24500K
swap sides so that all variables terms are on the left hand side
24500K = 245
Divide both sides by 24500.
K =245/24500
Reduces the fraction 245/24500 to lowest terms by extracting and cancelling out 245
K = 1/100 ,Therefore K = 0.01
Question 10.
Newton goes on a 10-day road trip. He takes $435 with him. He spends all of his money and spends the same amount each day. How much money does he spend each day?
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.1 5
Answer: $43.5/per day
Explanation: Newton takes $435 for 10 days road trip.
435/10 = 43.5
Newton Spend the money per day is = $43.5/day
Question 11.
Number Sense
For which equations does b = 100?
49 ÷ b = 0.49
247 ÷ b = 0.247
1.3 ÷ b = 0.013
0.5 ÷ b = 0.05
Answer:

49 ÷ b = 0.49

1.3 ÷ b = 0.013

For these two equations b value should be 100.

Question 12.
YOU BE THE TEACHER
Your friend says 8,705 ÷ 103 is equivalent 8,705 × 0.001. Is your friend correct? Explain.
Answer:

First simplify the 103 which means  10 \small \times 10 \small \times 10 = 1000

8,705 ÷ 103

= 8,705 ÷ 1000
= 8,705 \small \times \small \frac{1}{1000}
= 8,705 \small \times 0.001
8,705 ÷ 103 is equivalent 8,705 × 0.001
So, my friend answer is correct.

Think and Grow: Modeling Real Life

Example
A contractor buys 2 adjacent lots of land. One lot is 0.55 acre and the other is 1.65 acres. The contractor divides the land equally for 10 new homes. How much land does each home have?
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.1 6
To find how much land each home has, divide the sum of the lot sizes by 10.
Add the sizes of the lots.
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.1 7
Divide the total number of acres by 10. Dividing 2.20 by 10, or 101, shifts the digits ______ position to the right in a place value chart. So, the decimal point moves ______ place to the left.
2.20 ÷ 10 = 2.20 ÷ 101 = ______
Each home has ________ acre.

Show and Grow

Question 13.
An art teacher has 68.5 pounds of clay and orders 56.5 more pounds. The teacher equally divides the clay among 100 students. How much clay does each student get?
Answer:
To find how much clay each student get, divide the sum of the clay by 100.
Add the quantities of the clay.
68.5 + 56.5 = 125
Divide the total clay by 100. Dividing 125 by 100, or 102
125 ÷ 100 = 125 ÷ 102 = 1.25
Each student gets 1.25 pounds clay.

Question 14.
A museum has a replica of the Space Needle that is 6.05 feet tall. It is one-hundredth of the height of the actual Space Needle. How tall is the actual Space Needle?
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.1 8
Answer:
Replica of the Space Needle height = 6.05 feet
Let actual Space Needle height = h
\small \frac{1}{100} (h) = 6.05
h = 6.05 \small \times 100 = 605
So actual Space Needle height is 605 feet.

Question 15.
DIG DEEPER!
A pile of 102 loonies weighs 627 grams and a pile of 102 toonies weighs 730 grams. How much more does a toonie weigh than a loonie? Is there more than one way to solve the problem? Explain.
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.1 9
Answer:
A pile of 102 loonies weight = 627 grams
A pile of 102 toonies weight = 730 grams
730 – 627 = 103
Toonie weighs 103 grams more than a loonie.
Method – 2
1 loonie weight = \small \frac{627}{10^{2}} = 6.27
1 toonie weight = \small \frac{730}{10^{2}} = 7.30
7.30 – 6.27 = 1.03
For 102 toonies and loonies = 1.03 x 102 = 103
Toonie weighs 103 grams more than a loonie.

Division Pattern with Decimals Homework & Practice 7.1

Find the quotient.
Question 1.
810 ÷ 10 = ______
Answer: 81

Explanation:
To convert this simple fraction to a decimal just divide the numerator (810) by the denominator (10):
When we divide by 10, the decimal point moves one place to the left.
810 ÷ 10 = 81.

Question 2.
7.4 ÷ 0.01 = ______
Answer: 740

Explanation: To convert this simple fraction to a decimal just divide the numerator (7.4) by the denominator (0.01). When we divide by 0.01, the decimal point moves two places to the right. : 7.4 ÷ 0.01 = 740.

Question 3.
903 ÷ 103 = ______
Answer: 0.903

First Simplify the 103 which means  10 x 10 x 10 =1000, then we need to calculate the fraction to a decimal just divide the numerator (903) by the denominator (1000).
When we divide by 1000, the decimal point moves three places to the left.

Question 4.
267.1 ÷ 0.01 = ______
Answer: 26710

Explanation: To convert this simple fraction to a decimal just divide the numerator (267.1) by the denominator (0.01).
When we divide by 0.01, the decimal point moves two places to the right :
267.1 ÷ 0.01 = 26710

Question 5.
5.6 ÷ 0.1 = ______
Answer: 56

Explanation: To convert this simple fraction to a decimal just divide the numerator (5.6) by the denominator (0.1).
When we divide by 0.1, the decimal point moves one place to the right :
5.6 ÷ 0.1 = 56

Question 6.
0.4 ÷ 102 = ______
Answer: 0.004

First Simplify the 102 which means  10 x 10 = 100, then we need to calculate the fraction to a decimal just divide the numerator (0.4) by the denominator (100).
When we divide by 100, the decimal point moves two places to the left :
0.4 ÷ 100 = 0.004

Find the value of k.
Question 7.
89 ÷ k = 8.9
Answer: k = 10

Explanation: Lets solve your equation step by step 89 ÷ k = 8.9
Multiply both sides by K.
89 = 8.9 K
8.9 K = 89 (Flip the equation)

\small \frac{8.9 k}{8.9}  = \small \frac{89}{8.9}  (Divide both sides by 8.9)
k = 10

Question 8.
k ÷ 0.01 = 36
Answer: k = 0.36

\small \frac{k}{0.01} = 36
Multiply both sides by 0.01
\small \frac{k}{0.01} x 0.01 = 36 x 0.01
k = 0.36

Question 9.
72.4 ÷ 0.724
Answer: 100

To convert this simple fraction to a decimal just divide the numerator (72.4) by the denominator (0.724).

Question 10.
A box of 100 sanitizing wipes costs $12. How much does one wipe cost?
Answer:
100 sanitizing wipes = $12
one wipe cost = \small \frac{12}{100} = $0.12
When we divide by 100, the decimal point moves two places to the left.

Question 11.
Patterns
How does the value of a number change when you divide by 10? 100? 1,000?
Answer:
When we divide by 10, the decimal point moves one place to the left.
When we divide by 100, the decimal point moves two places to the left.
When we divide by 1000, the decimal point moves three places to the left.

Question 12.
Writing
How can you determine where to place the decimal point when dividing 61 by 1,000?
Answer:

\small \frac{61}{1000}
When we divide by 1000, the decimal point moves three places to the left.
so, \small \frac{61}{1000} = 0.061

Question 13.
DIG DEEPER!
What is Newton’s number?
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.1 10
Answer:
3.4 is the number.
57 – 23 = 34
34 x 0.1 = 3.4

Question 14.
Modeling Real Life
A family buys 2 personal watercrafts for $3,495 each. The family makes 10 equal payments for the watercrafts. What is the amount of each payment?
Answer:
To find amount of each payment, divide the sum of the personal watercrafts by 10.
Add 2 personal watercrafts.
3,495 + 3,495 = 6990
Divide the total sum by 10. Dividing 6990 by 10, or 101
6990 ÷ 10 = 6990 ÷ 101 = 699
So, the amount of each payment = $699.

Question 15.
Modeling Real Life
A group of people attempts to bake the largest vegan cake. They use 17 kilograms of cocoa powder, which is one-tenth the amount of kilograms of dates they use. How many kilograms of cocoa power and dates do they use altogether?
Answer:
Cocoa powder = 17 kilograms
Let dates amount = d
(1/10)d = 17
dates(d) = 17 x 10 = 170 kilograms
Sum of cocoa power and dates = 17 + 170 = 187 kilograms

Review & Refresh

Find the sum or difference.
Question 16.
0.75 – 0.23 = ______
Answer: 0.52

Question 17.
1.46 + 1.97 = ______
Answer: 3.43

Lesson 7.2 Estimate Decimals Quotients

Explore and Grow

Choose an expression to estimate each quotient. Write the expression. You may use an expression more than once.
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.2 1
Compare your answers with a partner. Did you choose the same expressions?
Answer:

Construct Arguments
Which estimated quotient do you think will be closer to the quotient 8.3 ÷ 2.1? Explain your reasoning.
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.2 2
Answer:

Think and Grow: Estimate Decimals Quotients

Key Idea
You can use compatible numbers to estimate quotients involving decimals. When the divisor is greater than the dividend, rename the dividend as tenths or hundredths, then divide.
Example
Estimate 146.26 ÷ 41.2.
Round the divisor 41.2 to 40.
Think: What numbers close to 146.26 are easily divided by 40?
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.2 3
Choose 160 because 146.26 is closer to 160. So, 146.26 ÷ 41.2 is about _____.

Example
Estimate 4.2 ÷ 8.
Rename 4.2 as tenths.
4.2 is 42 tenths. 42 tenths is close to40 tenths. 40 and 8 are compatible numbers.
40 tenths ÷ 8 = _______ tenths, or ______
So, 4.2 ÷ 8 is about ______.

Show and Grow

Estimate the quotient.
Question 1.
17.4 ÷ 3.1
Answer:
Round the divisor 3.1 to 3.
Think: What numbers close to 17.4 are easily divided by 3?
Use 18.
18 ÷ 3 = 6
So, 17.4 ÷ 3.1 is about 6.

Question 2.
57.5 ÷ 6.89
Answer:
Round the divisor 6.89 to 7.
Think: What numbers close to 57.5 are easily divided by 7?
Use 56.
56 ÷ 7 = 8
So, 57.5 ÷ 6.89 is about 8.

Question 3.
3.7 ÷ 5
Answer:
Rename 3.7 as tenths
3.7 is 37 tenths. 37 is close to 35.
35 tenths ÷ 5 = 7 tenths or 0.7
So, 3.7 ÷ 5 is about 0.7

Question 4.
25.8 ÷ 30
Answer:
Rename 25.8 as tenths
25.8 is 258 tenths. 258 is close to 270.
270 tenths ÷ 30 = 9 tenths or 0.9
So, 25.8 ÷ 30 is about 0.9

Apply and Grow: Practice

Estimate the quotient.
Question 5.
3.5 ÷ 6
Answer:
Rename 3.5 as tenths
3.5 is 35 tenths. 35 is close to 36.
36 tenths ÷ 6 = 6 tenths or 0.6
So, 3.5 ÷ 6 is about 0.6

Question 6.
1.87 ÷ 9
Answer:
Rename 1.87 as tenths
1.87 is 18.7 tenths. 18.7 is close to 18.
18 tenths ÷ 9 = 2 tenths or 0.2
So, 1.87 ÷ 9 is about 0.2

Question 7.
46 ÷ 2.3
Answer:
Round the divisor 2.3 to 2.
46 ÷ 2 = 23

Question 8.
31.1 ÷ 6.5
Answer:
Round the divisor 6.5 to 6.
31.1 is closer to 30.
30 ÷ 6 = 5
So, 31.1 ÷ 6.5 is about 5.

Question 9.
91.08 ÷ 5.2
Answer:
Round the divisor 5.2 to 5.
91.08 is closer to 90.
90 ÷ 5 = 18
So, 91.08 ÷ 5.2 is about 18.

Question 10.
137.14 ÷ 12.2
Answer:
Round the divisor 12.2 to 12.
137.14 is closer to 144.
12 and 144 are compatible numbers.
144 ÷ 12 = 12
So, 137.14 ÷ 12.2 is about 12.

Question 11.
A group of 6 friends goes ice skating. They pay $43.50 altogether for admission and skate rental. The friends share the cost equally. How much does each friend pay?
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.2 4
Answer:
Total amount paid = $43.50
6 friends goes ice skating.
43.5 is closer to 42.
42 ÷ 6 = 7
So, each friend pay about $7.

Question 12.
Reasoning
Descartes estimates 43.2 ÷ 7.3 using mental math. Do you think he uses 43 ÷ 7 or 42 ÷ 7? Explain.
Answer:
Round the divisor 7.3 to 7
Think: What numbers close to 43.2 are easily divided by 7?
Use 42.
42 and 7 are compatible numbers.
42 ÷ 7 = 6
So, 42 ÷ 7 is correct.

Question 13.
DIG DEEPER!
Describe a division situation in which an estimate of two decimals is appropriate.
Answer:

Think and Grow: Modeling Real Life

Example
Your friend types 25 words each minute. About how many more words can your friend type each minute than you?
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.2 5
To find how many words you can type each minute, divide the number of words you type in 15 minutes by 15.
Think: What numbers close to 307.5 are easily divided by 15?
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.2 6
Choose 300 because 307.5 is closer to 300. So, 307.5 ÷ 15 is about _______.
So, you type about _______ words each minute.
Subtract the words you type each minute from the words your friend types each minute.
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.2 7
Your friend can type about ______ more words each minute than you.

Show and Grow

Question 14.
Newton subscribes to a television streaming service and buys a gym membership. He spends $143.99 on the streaming service for 12 months. About how much more does it cost each month for the gym membership than the streaming service?
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.2 8
Answer:
To find much more does it cost each month, divide how much he spends for 12 months by 12.
Think: What numbers close to $143.99 are easily divided by 12?
Use 144
144 ÷ 12 = 12
Gym Membership each month = $19.99 = $20
20 – 12 = $8
The gym membership costs $8 more than the streaming service.

Question 15.
A fish tank pump filters 158.5 gallons of water each hour. About how many gallons of water does the pump filter each minute?
Answer:
Fish tank pump filters 158.5 gallons of water
1 hour = 60 minutes
Think: What numbers close to 158.5 are easily divided by 60?
Use 180
180 ÷ 60 = 3
Pump filters about 3 gallons of water each minute.

Question 16.
DIG DEEPER!
A group of 32 students goes to a museum and a play. The total cost for the museum is $358.98 and the total cost for the play is $256.48. About how much does it cost for each student to go to the museum and the play?
Answer:
Cost for museum = $358.98
Cost for the play = $256.48
358.98 + 256.48 = $615.46
Think: What numbers close to 615.46 are easily divided by 32?
Use 608. It is closer to 615.46
608 ÷ 32 = $19
Each student go to the museum and the play costs about $19.

Estimate Decimals Quotients Homework & Practice 7.2

Estimate the quotient.
Question 1.
2.3 ÷ 6
Answer:
Rename 2.3 as tenths
2.3 is 23 tenths. 23 is close to 24.
24 tenths ÷ 6 = 4 tenths or 0.4
So, 2.3 ÷ 6 is about 0.4

Question 2.
1.67 ÷ 8
Answer:
Rename 1.67 as hundredths
1.67 is 167 hundredths. 167 is close to 168.
168 hundredths ÷ 8 = 21 hundredths or 0.21
So, 1.67 ÷ 8 is about 0.21

Question 3.
28 ÷ 4.7
Answer:
Round the divisor 4.7 to 5
28 is closer to 30
30 ÷ 5 = 6
So, 28 ÷ 4.7 is about 6.

Question 4.
13.8 ÷ 4.9
Answer:
Round the divisor 4.9 to 5
Think: What numbers close to 13.8 are easily divided by 5?
Use 15.
15 ÷ 5 = 3
So, 13.8 ÷ 4.9 is about 3.

Question 5.
42.1 ÷ 7.3
Answer:
Round the divisor 7.3 to 7
Think: What numbers close to 42.1 are easily divided by 7?
Use 42.
42 ÷ 7 = 6
So, 42.1 ÷ 7.3 is about 6.

Question 6.
201.94 ÷ 18.1
Answer:
Round the divisor 18.1 to 18
Think: What numbers close to 201.94 are easily divided by 18?
Use 198.
198 ÷ 18 = 11
So, 201.94 ÷ 18.1 is about 11.

Question 7.
A carpenter has a plank of wood that is 121.92 centimeters long. He cuts the plank into 4 equal pieces. About how long is each piece?
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.2 9
Answer:
Given that,
Plank of wood = 121.92 cm long
121.92 is closer to 120.
120 ÷ 4 = 30
So, each piece is 30 cm long.

Question 8.
Reasoning
A family used 9.8 gallons of gasoline to drive 275.5 miles. To determine how far they drove using one gallon of gasoline, can they use an estimate, or is an exact answer required? Explain.
Answer:
Given that,
9.8 gallons of gasoline drives = 275.5 miles
1 gallon = 275.5 ÷ 9.8
Divisor 9.8 is rounded to 10.
275.5 is closer to 276.
276 ÷ 10 is about 27.6

Question 9.
YOU BE THE TEACHER
Your friend says 9 ÷ 2.5 is about 3. Is your friend’s estimate reasonable? Explain.
Answer:
Round the divisor 2.5 to 3.
9 ÷ 3 =3
So, my friend’s estimate is reasonable.

Number Sense
Without calculating, tell whether the quotient is greater than or less than 1. Explain.
Question 10.
4.58 ÷ 0.3
Answer:
When the dividend is greater than the divisor, the quotient is greater than 1.

Question 11.
0.6 ÷ 12
Answer:
When the divisor is greater than the dividend, the quotient is less than 1.

Question 12.
Modeling Real Life
The maximum allowed flow rate for a shower head in California is 42.5 gallons of water in 17 minutes. About how much greater is this than the maximum allowed flow rate for a kitchen faucet in California?
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.2 10
Answer:
To find much much greater it is, divide how much gallons of water in 17 minutes by 17.
Think: What numbers close to 42.5 are easily divided by 17?
Use 34. 34 is closer to 42.5.
34 ÷ 17 =2
Kitchen faucet = 2.2 gallons
2.2 – 2 = 0.2
Shower head in California is about 0.2 gallons greater than the maximum allowed flow rate for a kitchen faucet in California.

Question 13.
Modeling Real Life
To compare the amounts in the table, you assume the same amount of snow fell each hour for 24 hours. About how many more inches of snow fell in Colorado each hour than in Utah?
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.2 11
Answer:
Time t = 24 hours
Colorado snowfall = 75.8 is closer to 72
Illinois snowfall = 37.8
Utah snowfall = 55.5 is closer to 48
(72 – 48)/24 = 1
Snow fall in Colorado each hour is about 1 inch more than in Utah.

Review & Refresh

Find the product. Check whether your answer is reasonable.
Question 14.
56 × 78 = _____
Answer: 4368

Question 15.
902 × 27 = ______
Answer: 24,354

Question 16.
4,602 × 35 = _______
Answer: 1,61,070

Lesson 7.3 Use Models to Divide Decimals by Whole Numbers

Explore and Grow

Complete the table.
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.3 1
Answer:

Reasoning
When you divide a decimal by a whole number, what does the quotient represent?
Answer:

Think and Grow: Use Models to Divide Decimals

Example
Use a model to find 2.16 ÷ 3.
Think: 2.16 is 2 ones, 1 tenth, and 6 hundredths.
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.3 2
• 21 tenths can be divided equally as 3 groups of _______ tenths.
• 6 hundredths can be divided equally as 3 groups of _______ hundredths.
So, 216 hundredths can be divided equally as 3 groups of _______ hundredths.
So, 2.16 ÷ 3 = _______

Show and Grow

Question 1.
Use the model to find 3.25 ÷ 5.
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.3 3
3.25 ÷ 5 = ______
Answer:
Think: 3.25 is 3 ones, 2 tenths and 5 hundredths.
32 tenths can be divided equally as 5 groups
So, 325 hundredths can be divided equally as 5 groups
So, 3.25 ÷ 5 = 0.65

Apply and Grow: Practice

Use the model to find the quotient.
Question 2.
2.4 ÷ 4
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.3 4
Answer:
Think: 2.4 is 2 ones and 4 tenths
24 tenths can be divided equally as 4 groups of 6 tenths.
So, 2.4 ÷ 4 = 6 tenths = 0.6

Question 3.
1.36 ÷ 2
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.3 5
Answer:
Think: 1.36 is 1 ones, 3 tenth and 6 hundredths.
13 tenths can be divided equally as 2 groups
So, 136 hundredths can be divided equally as 2 groups
So, 1.36 ÷ 2 = 0.68

Use a model to find the quotient.
Question 4.
1.5 ÷ 3
Answer:
Think: 1.5 is 1 ones and 5 tenths
15 tenths can be divided equally as 3 groups of 5 tenths.
So, 1.5 ÷ 3 = 5 tenths = 0.5

Question 5.
2.7 ÷ 9
Answer:
Think: 2.7 is 2 ones and 7 tenths
27 tenths can be divided equally as 9 groups of 3 tenths.
So, 2.7 ÷ 9 = 3 tenths = 0.3

Question 6.
1.44 ÷ 8
Answer:
Think: 1.44 is 1 ones, 4 tenth and 4 hundredths.
14 tenths can be divided equally as 8 groups
So, 144 hundredths can be divided equally as 8 groups
So, 1.44 ÷ 8 = 0.18

Question 7.
3.12 ÷ 6
Answer:
Think: 3.12 is 3 ones, 1 tenth and 2 hundredths.
31 tenths can be divided equally as 6 groups
So, 312 hundredths can be divided equally as 6 groups
So, 3.12 ÷ 6 = 0.52

Question 8.
Reasoning
Do you start dividing the ones first when finding 5.95 ÷ 7? Explain.
Answer:
Think: 5.95 is 5 ones, 9 tenth and 5 hundredths.
We have to start dividing the tenths first because 5 ones is less than 7.
59 tenths can be divided equally as 7 groups
So, 595 hundredths can be divided equally as 7 groups
So, 5.95 ÷ 7 = 0.85

Question 9.
Number Sense
Without dividing, determine whether the quotient of 9.85 and 5 is greater than or less than 2. Explain.
Answer: Quotient of 9.85 and 5 is less than 2, because 5 x 2 =10 and 9.85 is less than 10.

Think and Grow: Modeling Real Life

Example
A bag of 3 racquetballs weighs 4.2 ounces. What is the weight of each racquetball?
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.3 6
Divide the weight of the bag by 3 to find the weight of each racquetball.
Think: 4.2 is 4 ones and 2 tenths.
Shade 42 tenths to represent 4.2. Divide the model to show 3 equal groups.
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.3 7
42 tenths can be divided equally as 3 groups of ______ tenths.
4.2 ÷ 3 = ______
So, each racquetball weighs ______ ounces.

Show and Grow

Question 10.
You cut a 3.75-foot-long string into 5 pieces of equal length to make a beaded wind chime. What is the length of each piece of string?
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.3 8
Answer:
Divide the length of the string by 5 to find the length of each piece of string.
Think: 3.75 is 3 ones, 7 tenths and 5 hundredths.
37 tenths can be divided equally as 5 groups of 7 tenths with remainder 2. Remainder has to place before 5 hundredths.
25 hundredths can be divided equally as 5 groups of 5 hundredths.
So, 375 hundredths can be divided equally as 5 groups of 75 hundredths.
3.75 ÷ 5 = 0.75

Question 11.
DIG DEEPER!
You pay $5.49 for 3 pounds of plums and $6.36 for 4 pounds of peaches. Which fruit costs more per pound? How much more?
Answer:
Think: 5.49 is 5 ones, 4 tenths and 9 hundredths.
5 ones can be divided equally as 3 groups of 1 ones with remainder 2. Remainder has to place before 4 tenths.
24 tenths can be divided equally as 3 groups of 8 tenths
9 hundredths can be divided equally as 3 groups of 3 hundredths
So, 549 hundredths can be divided equally as 3 groups of 183 hundredths.
Plums = 5.49 ÷ 3 = 1.83
Think: 6.36 is 6 ones, 3 tenths and 6 hundredths.
6 ones can be divided equally as 4 groups of 1 ones with remainder 2. Remainder has to place before 3 tenths.
23 tenths can be divided equally as 4 groups of 5 tenths with remainder 3. Remainder has to place before 6 hundredths.
36 hundredths can be divided equally as 4 groups of 9 hundredths
So, 636 hundredths can be divided equally as 4 groups of 159 hundredths.
Peaches = 6.36 ÷ 4 = 1.59
1.83 – 1.59 = 0.24
So, plums costs 0.24 more per pound than peaches.

Use Models to Divide Decimals by Whole Numbers Homework & Practice 7.3

Use the model to find the quotient.
Question 1.
1.5 ÷ 5
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.3 9
Answer:
Think: 1.5 is 1 ones and 5 tenths
15 tenths can be divided equally as 5 groups of 3 tenths.
So, 1.5 ÷ 5 = 3 tenths = 0.3

Question 2.
2.55 ÷ 3
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.3 10
Answer:
Think: 2.55 is 2 ones, 5 tenths and 5 hundredths.
25 tenths can be divided equally as 3 groups of 8 tenths with remainder 1. Remainder has to place before 5 hundredths.
15 hundredths can be divided equally as 3 groups of 5 hundredths.
So, 255 hundredths can be divided equally as 3 groups of 85 hundredths.
2.55 ÷ 3 = 0.85

Use a model to find the quotient.
Question 3.
1.6 ÷ 8
Answer:
Think: 1.6 is 1 ones and 6 tenths
16 tenths can be divided equally as 8 groups of 2 tenths.
So, 1.6 ÷ 8 = 2 tenths = 0.2

Question 4.
2.1 ÷ 7
Answer:
Think: 2.1 is 2 ones and 1 tenths
21 tenths can be divided equally as 7 groups of 3 tenths.
So, 2.1 ÷ 7 = 3tenths = 0.3

Question 5.
1.56 ÷ 2
Answer:
Think: 1.56 is 1 ones, 5 tenths and 6 hundredths.
15 tenths can be divided equally as 2 groups of 7 tenths with remainder 1. Remainder has to place before 6 hundredths.
16 hundredths can be divided equally as 2 groups of 8 hundredths.
So, 156 hundredths can be divided equally as 2 groups of 78 hundredths.
1.56 ÷ 2 = 0.78

Question 6.
2.84 ÷ 4
Answer:
Think: 2.84 is 2 ones, 8 tenths and 4 hundredths.
28 tenths can be divided equally as 4 groups of 7 tenths.
4 hundredths can be divided equally as 4 groups of 1 hundredths.
So, 284 hundredths can be divided equally as 4 groups of 71 hundredths.
2.84 ÷ 4 = 0.71

Question 7.
Structure
Write a decimal division equation represented by the model.
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.3 11
Answer:
1.8 ÷  3

Question 8.
Writing
Explain how dividing a decimal by a whole number is similar to dividing a whole number by a whole number.
Answer:
When dividing a decimal by a whole number, first we will divide the decimal by the whole number ignoring decimal point. Now put the decimal point in the quotient same as the decimal places in the dividend.
So , dividing a decimal by a whole number is similar to dividing a whole number by a whole number.

Question 9.
Modeling Real Life
A designer learns there are 5.08 centimeters in 2 inches. How many centimeters are in 1 inch?
Answer:
5.08 ÷ 2
Think: 5.08 is 5 ones, 0 tenths and 8 hundredths.
50 tenths can be divided equally as 2 groups of 25 tenths.
8 hundredths can be divided equally as 2 groups of 4 hundredths.
So, 508 hundredths can be divided equally as 2 groups of 254 hundredths.
So, 2.54 cm are in 1 inch.

Question 10.
Modeling Real Life
Newton buys 4 gallons of gasoline. He pays $8.64. How much does 1 gallon of gasoline cost?
Answer:
8.64 ÷ 4
Think: 8.64 is 8 ones, 6 tenths and 4 hundredths.
8 ones can be divided equally as 4 groups of 2 ones.
6 tenths can be divided equally as 4 groups of 1 tenths with remainder 2. Remainder has to place before 4 hundredths.
24 hundredths can be divided equally as 4 groups of 6 hundredths.
So, 864 hundredths can be divided equally as 4 groups of 216 hundredths.
1 gallon of gasoline cost is 216 hundredths = $2.16

Review & Refresh

Find the product. Explain the strategy you used.
Question 11.
0.9 × 1.1 = ______
Answer:
First multiply 9 x 11 = 99, then put the decimal point in the answer as sum of the decimal places in the both numbers.
decimal places = 1 + 1 = 2
99 after putting decimal places = 0.99

Question 12.
1.2 × 2.7 = ______
Answer:
First multiply 12 x 27 = 324 then put the decimal point in the answer as sum of the decimal places in the both numbers.
decimal places = 1 + 1 = 2
324 after putting decimal places = 3.24

Question 13.
1.4 × 0.8 = ______
Answer: 1.12

Lesson 7.4 Divide Decimals by One-Digit Numbers

Explore and Grow

Complete the table.
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.4 1
What pattern do you notice in the placement of the decimal point?
Answer:

Reasoning
How is dividing decimals by one-digit whole numbers similar to dividing whole numbers?
Answer:

Think and Grow: Divide Decimals by One-Digit Numbers

Example
Find
Find 7.38 ÷ 6. Estimate ________
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.4 2

Show and Grow

Find the quotient. Then check your answer.
Question 1.
\(\sqrt [ 2 ]{ 9.16 } \)
Answer:
Divide the ones
9 ÷ 2
4 ones x 2 = 8
9 ones – 8 ones
There are 1 ones left over.
Divide the tenths
116 ÷ 2
58 tenths x 2
116 – 116 = 0
There are 0 tenths left over.
So, 9.16 ÷ 2 = 4.58

Question 2.
\(\sqrt [ 5 ]{ 23.5 } \)
Answer:
Divide the ones
23 ÷ 5
4 ones x 5 = 20
23 ones – 20 ones
There are 3 ones left over.
Divide the tenths
35 ÷ 5
7 tenths x 5
35 – 35 = 0
There are 0 tenths left over.
So, 23.5 ÷ 5 = 4.7

Question 3.
\(\sqrt [ 3 ]{ 6.27 } \)
Answer:
Divide the ones
6 ÷ 3
2 ones x 3 = 6
6 ones – 6 ones
There are 0 ones left over.
Divide the tenths
27 ÷ 3
9 tenths x 3
27 – 27 = 0
There are 0 tenths left over.
So, 6.27 ÷ 3 = 2.09

Apply and Grow: Practice

Find the quotient. Then check your answer.
Question 4.
\(\sqrt [ 4 ]{ 16.8 } \)
Answer:
Divide the ones
16 ÷ 4
4 ones x 4 = 16
16 ones – 16 ones
There are 0 ones left over.
Divide the tenths
8 ÷ 4
2 tenths x 4
8 – 8 = 0
There are 0 tenths left over.
So, 16.8 ÷ 4 = 4.2

Question 5.
\(\sqrt [ 9 ]{ 1.53 } \)
Answer:
Divide the tenths
15 ÷ 9
1 tenths x 9
15 – 9 = 6
There are 6 tenths left over.
Divide the hundredths
63 ÷ 9 = 7 hundredths
So, 1.53 ÷ 9 = 0.17

Question 6.
\(\sqrt [ 5 ]{ 82.5 } \)
Answer:
Divide the ones
82 ÷ 5
16 ones x 5 = 80
82 ones – 80 ones
There are 2 ones left over.
Divide the tenths
25 ÷ 5
5 tenths x 5
25 – 25 = 0
There are 0 tenths left over.
So, 82.5 ÷ 5 = 16.5

Question 7.
77.4 ÷ 3 = ______
Answer:
Divide the ones
77 ÷ 3
25 ones x 3 = 75
77 ones – 75 ones
There are 2 ones left over.
Divide the tenths
24 ÷ 3
8 tenths x 3
24 – 24 = 0
There are 0 tenths left over.
So, 77.4 ÷ 3 = 25.8

Question 8.
113.6 ÷ 8 = ______
Answer:
Divide the ones
113 ÷ 8
14 ones x 8 = 112
113 ones – 112 ones
There are 1 ones left over.
Divide the tenths
16 ÷ 8
2 tenths x 8
16 – 16 = 0
There are 0 tenths left over.
So, 113.6 ÷ 8 = 14.2

Question 9.
129.43 ÷ 7 = ______
Answer:
Divide the ones
129 ÷ 7
18 ones x 7 = 126
129 ones – 126 ones
There are 3 ones left over.
Divide the tenths
34 ÷ 7
4 tenths x 7
34 – 28 = 6
There are 6 tenths left over.
Divide the hundredths
63 ÷ 7 = 9 hundredths
So, 129.43 ÷ 7 = 18.49

Find the value of y.
Question 10.
y ÷ 2 = 4.8
Answer:
y = 4.8 x 2
y = 9.6

Question 11.
6.05 ÷ 5 = y
Answer:
6.05 ÷ 5
Divide the ones
1 ones x 5 = 5
6 ones – 5 ones
There are 1 ones left over.
Divide the tenths
105 ÷ 5
21 tenths x 5
105 – 105 = 0
There are 0 tenths left over.
So, 6.05 ÷ 5 = 1.21
y = 1.21

Question 12.
y ÷ 8 = 4.29
Answer:
y = 4.29 x 8
y = 34.32

Question 13.
Reasoning
Newton finds 75.15 ÷ 9. In what place is the first digit of the quotient? Explain.
Answer:
75.15 ÷ 9
Divide the ones
75 ÷ 9
8 ones x 9 = 72
75 ones – 72 ones
There are 3 ones left over.
Divide the tenths
31 ÷ 9
3 tenths x 9
31 – 27= 4
There are 4 tenths left over.
Divide the hundredths
45 ÷ 9 = 5 hundredths
75.15 ÷ 9 = 8.35, here quotient is in ones place.

Question 14.
DIG DEEPER!
Find the missing digits.
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.4 3
Answer:
Divide the ones
47 ÷ 6
7 ones x 6 = 42
47 ones – 42 ones = 3 ones
So, first digit of the quotient is 7.
We know that divisor x quotient = dividend
6 x 7.89 = 47.34
So, missing digits are 7 and 4.

Think and Grow: Modeling Real Life

Example
A group of 5 gold miners finds the amounts of gold shown. They divide the gold equally. How many ounces does each miner get?
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.4 4
To find how many ounces each miner gets, divide the total amount of gold by 5.
Add the amounts of gold.
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.4 5
Each miner gets _______ ounces of gold.

Show and Grow

Question 15.
A pharmacist combines the medicine from both vials and divides it equally into 7 doses. How much medicine is in each dose?
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.4 6
Answer:
To find how much medicine is in each dose, divide the total amount of medicine by 7.
Add the amounts of medicine.
4.5 + 20 = 24.5
24.5 ÷ 7
Divide the ones
24 ÷ 7
3 ones x 7 = 21
24 ones – 21 ones
There are 3 ones left over.
Divide the tenths
35 ÷ 7
5 tenths x 7
35 – 35 = 0
There are 0 tenths left over.
24.5 ÷ 7 = 3.5
So, 3.5 milliliters medicine is in each dose.

Question 16.
Identical rectangular stepping stones form a path in a garden. What are the dimensions of each stone?
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.4 7
Answer:

Question 17.
DIG DEEPER!
A customer saves $9.24 by buying the set rather than buying them individually. What is one flying disc priced individually?
Answer:

Divide Decimals by One-Digit Numbers Homework & Practice 7.4

Find the quotient. Then check your answer.
Question 1.
\(\sqrt [ 3 ]{ 9.6 } \)
Answer:
Divide the ones
9 ÷ 3
3 ones x 3 = 9
9 ones – 9 ones
There are 0 ones left over.
Divide the tenths
6 ÷ 3
2 tenths x 3
6 – 6 = 0
There are 0 tenths left over.
So, 9.6 ÷ 3 = 3.2.

Question 2.
\(\sqrt [ 6 ]{ 7.56 } \)
Answer:
Divide the ones
7 ÷ 6
1 ones x 6 = 6
7 ones – 6 ones
There are 1 ones left over.
Divide the tenths
15 ÷ 6
2 tenths x 6
15 – 12 = 3
There are 3 tenths left over.
Divide the hundredths
36 ÷ 6 = 6 hundredths.
So, 7.56 ÷ 6 = 1.26.

Question 3.
\(\sqrt [ 8 ]{ 42.4 } \)
Answer:
Divide the ones
42 ÷ 8
5 ones x 8 = 40
42 ones – 40 ones
There are 2 ones left over.
Divide the tenths
24 ÷ 8
3 tenths x 8
24 – 24 = 0
There are 0 tenths left over.
So, 42.4 ÷ 8 = 5.3.

Question 4.
63.6 ÷ 4 = ______
Answer:
Divide the ones
63 ÷ 4
15 ones x 4 = 60
63 ones – 60 ones
There are 3 ones left over.
Divide the tenths
36 ÷ 4
9 tenths x 4
36 – 36 = 0
There are 0 tenths left over.
63.6 ÷ 4 = 15.9

Question 5.
15.68 ÷ 7 = ______
Answer:
Divide the ones
15 ÷ 7
2 ones x 7 = 14
15 ones – 14 ones
There are 1 ones left over.
Divide the tenths
16 ÷ 7
2 tenths x 7
16 – 14 = 2
There are 2 tenths left over.
Divide the hundredths
28 ÷ 7 = 4 hundredths
15.68 ÷ 7 = 2.24

Question 6.
143.82 ÷ 9 = _______
Answer:
Divide the ones
143 ÷ 9
15 ones x 9 = 135
143 ones – 135 ones
There are 8 ones left over.
Divide the tenths
88 ÷ 9
9 tenths x 9
88 – 81 = 7
There are 7 tenths left over.
Divide the hundredths
72 ÷ 9 = 8 hundredths
143.82 ÷ 9 = 15.98

Find the value of y.
Question 7.
y ÷ 6 = 7.8
Answer:
y = 7.8 x 6
y= 46.8

Question 8.
14.9 ÷ 5 = y
Answer:
Divide the ones
14 ÷ 5
2 ones x 5 = 10
14 ones – 10 ones
There are 4 ones left over.
Divide the tenths
49 ÷ 5
9 tenths x 5
49 – 45 = 4
There are 4 tenths left over.
Divide the hundredths
40 ÷ 5 = 8 hundredths
14.9 ÷ 5 = 2.98
y = 2.98

Question 9.
y ÷ 2 = 4.7
Answer:
y = 4.7 x 2
y = 9.4

Question 10.
Number Sense
Evaluate the expression.
(213.3 – 95.7) ÷ 8
Answer:
(213.3 – 95.7) ÷ 8 = 117.6 ÷ 8
Divide the ones
117 ÷ 8
14 ones x 8 = 112
117 ones – 112 ones
There are 5 ones left over.
Divide the tenths
56 ÷ 8
7 tenths x 8
56 – 56 = 0
There are 0 tenths left over.
(213.3 – 95.7) ÷ 8 = 117.6 ÷ 8 = 14.7

Question 11.
Writing
Write and solve a real-life problem that involves dividing a decimal by a whole number.
Answer:
In 5 minutes John eats 7.5 chocolates.  how many chocolates can he eat in one minute?
7.5 ÷ 5
Divide the ones
7 ÷ 5
1 ones x 5 = 5
7 ones – 5 ones
There are 2 ones left over.
Divide the tenths
25 ÷ 5 = 5 tenths
7.5 ÷ 5 = 1.5
In 1 minute, he can eat 1.5 chocolates.

Question 12.
YOU BE THE TEACHER
Your friend finds 197.2 ÷ 4. Is your friend correct? Explain.
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.4 8
Answer:
Divide the ones
197 ÷ 4
49 ones x 4 = 196
197 ones – 196 ones
There are 1 ones left over.
Divide the tenths
12 ÷ 4
3 tenths x 4 = 12
12 – 12 = 0
There are 0 tenths left over.
197.2 ÷ 4 = 49.3
So, my friend answer is not correct.

Question 13.
Modeling Real Life
You buy 2 packages of ground beef. One package contains 4.5 pounds and the other contains 2.25 pounds. You put equal amounts of meat into 9 freezer bags. How many pounds of meat are in each bag?
Answer:
To find many pounds of meat are in each bag, divide the total meat by 9.
Add the two packages of meat.
4.5 + 2.25 = 6.75
6.75 ÷ 9
Divide the tenths
67 ÷ 9
7 tenths x 9 = 63
67 tenths – 63 tenths
There are 4 tenths left over.
Divide the hundredths
45 ÷ 9 = 5 hundredths
6.75 ÷ 9 = 0.75

Question 14.
DIG DEEPER!
A homeowner hangs wallpaper on the walls of her bathroom. What is the width of the bathroom?
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.4 9
Answer:
We know that perimeter of a rectangle = 2(l + w)
8.52 = 2(2.74 + w)
2.74 + w = 8.52 ÷ 2
8.52 ÷ 2
Divide the ones
8 ÷ 2 = 4 ones
Divide the tenths
52 ÷ 2 = 26 tenths
8.52 ÷ 2 = 4.26
2.74 + w = 4.26
Width w = 4.26 – 2.74 = 1.52
So, width of the bathroom = 1.52 m

Review & Refresh

Use partial quotients to divide.
Question 15.
607 ÷ 15 = ______
Answer:
15 x 40 = 600 with remainder 7.

Question 16.
4,591 ÷ 33 = ______
Answer:

Question 17.
6,699 ÷ 87 = ______
Answer:
87 x 50 = 4350
6,699 – 4350 = 2349
87 x 20 = 1740
2349 – 1740 = 609
87 x 5 = 435
609 – 435 = 174
87 x 2 = 174
6,699 ÷ 87 = 50 + 20 + 5 + 2 = 77.

Lesson 7.5 Divide Decimals by Two-Digit Numbers

Explore and Grow

Write a division problem you can use to find the width of each rectangle. Then find the width of each rectangle.
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.5 1
Answer:

Precision
Explain how you can use estimation to check your answers.
Answer:

Think and Grow: Divide Decimals by Two-Digit Numbers

Example
Find 79.8 ÷ 14. Estimate _________
Regroup 7 tens as 70 ones and combine with 9 ones.
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.5 2

Example
Find 20.54 ÷ 26.
Step 1: Estimate the quotient.
2,000 hundredths ÷ 25 = _______ hundredths
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.5 3
Step 2: Divide as you do with whole numbers.
Step 3: Use the estimate to place the decimal point.
So, 20.54 ÷ 26 = _______.

Show and Grow

Find the quotient. Then check your answer.
Question 1.
\(\sqrt [ 12 ]{ 51.6 } \)
Answer:
Divide the ones
51 ÷ 12
4 ones x 12 = 48
51 ones – 48 ones
There are 3 ones left over.
Divide the tenths
36 ÷ 12
3 tenths x 12 = 36
36 – 36 = 0
There are 0 tenths left over.
So, 51.6 ÷ 12 = 4.3

Question 2.
\(\sqrt [ 17 ]{ 140.25 } \)
Answer:
Divide the ones
140 ÷ 17
8 ones x 17 = 136
140 ones – 136 ones
There are 4 ones left over.
Divide the tenths
42 ÷ 17
2 tenths x 17 = 34
42 – 34 = 8
There are 8 tenths left over.
Divide the hundredths
85 ÷ 17 = 5 hundredths.
So, 140.25 ÷ 17 = 8.25

Question 3.
\(\sqrt [ 61 ]{ 32.33 } \)
Answer:
Divide the tenths
323 ÷ 61
5 ones x 61 = 305
323 tenths – 305 tenths
There are 18 tenths left over.
Divide the hundredths
183 ÷ 61 = 3 hundredths
So, 32.33 ÷ 61 = 0.53

Apply and Grow: Practice

Place a decimal point where it belongs in the quotient.
Question 4.
251.75 ÷ 19 = 1 3 . 2 5
Answer:
When dividing a decimal by a whole number, first we will divide the decimal by the whole number ignoring decimal point. Now put the decimal point in the quotient same as the decimal places in the dividend.

Question 5.
88.04 ÷ 62 = 1 . 4 2
Answer:

Question 6.
3.22 ÷ 23 = 0 .1 4
Answer:

Find the quotient. Then check your answer.
Question 7.
\(\sqrt [ 54 ]{ 97.2 } \)
Answer:
Divide the ones
97 ÷ 54
1 ones x 54 = 54
97 ones – 54 ones
There are 43 ones left over.
Divide the tenths
432 ÷ 54 = 8 tenths
So, 97.2 ÷ 54 = 1.8

Question 8.
\(\sqrt [ 91 ]{ 200.2 } \)
Answer:
Divide the ones
200 ÷ 91
2 ones x 91 = 182
200 ones – 182 ones
There are 18 ones left over.
Divide the tenths
182 ÷ 91 = 2 tenths
So, 200.2 ÷ 91 = 2.2

Question 9.
\(\sqrt [ 2 ]{ 56.2 } \)
Answer:
Divide the ones
56 ÷ 2
28 ones x 2 = 56
56 ones – 56 ones
There are 0 ones left over.
Divide the tenths
2 ÷ 2 = 1 tenths
So, 56.2 ÷ 2 = 28.1

Question 10.
6.08 ÷ 16 = _____
Answer:
Divide the tenths
60 ÷ 16
3 tenths x 16 = 48
60 tenths – 48 tenths
There are 12 tenths left over.
Divide the hundredths
128 ÷ 16
8 hundredths x 16
128 – 128 = 0
There are 0 hundredths left over.
So, 6.08 ÷ 16 = 0.38

Question 11.
7.45 ÷ 5 = _______
Answer:
Divide the tenths
74 ÷ 5
14 tenths x 5 = 70
74 tenths – 70 tenths
There are 4 tenths left over.
Divide the hundredths
45 ÷ 5
9 hundredths x 5 = 45
45 – 45 = 0
There are 0 hundredths left over.
So, 7.45 ÷ 5 = 1.49

Question 12.
147.63 ÷ 37 = _______
Answer:
Divide the ones
147 ÷ 37
3 ones x 37 = 111
147 ones – 111 ones
There are 36 ones left over.
Divide the tenths
366 ÷ 37
9 tenths x 37 = 333
366 – 333 = 33
Divide the hundredths
333 ÷ 37 = 9 hundredths
So, 147.63 ÷ 37 = 3.99

Find the value of y.

Question 13.
y ÷ 44 = 1.82
Answer:
y = 44 x 1.82
y = 80.08

Question 14.
106.6 ÷ 82 = y
Answer:
Divide the ones
106 ÷ 82
1 ones x 82 = 82
106 ones – 82 ones
There are 24 ones left over.
Divide the tenths
246 ÷ 82
3 tenths x 82 = 246
246 – 246 = 0
106.6 ÷ 82 = 1.3, y = 1.3

Question 15.
y ÷ 13 = 2.6
Answer:
y = 13 x 2.6
y = 33.8

Question 16.
Logic
Newton and Descartes find 44.82 ÷ 18. Only one of them is correct. Without solving, who is correct? Explain.
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.5 4
Answer:
Descartes answer is correct, 44.82 ÷ 18 = 2.49
When dividing a decimal by a whole number, first we will divide the decimal by the whole number ignoring decimal point. Now put the decimal point in the quotient same as the decimal places in the dividend.

Question 17.
DIG DEEPER!
Find a decimal that you can divide by a two-digit whole number to get the quotient shown. Fill in the boxes with your dividend and divisor.
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.5 5

Dividend is 20 and divisor is 12.

Think and Grow: Modeling Real Life

Example
You practice paddle boarding for 3 weeks. You paddle the same amount each day for 5 days each week. You paddle 22.5 miles altogether. How many miles do you paddle each day?
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.5 6
To find the total number of days you paddle in 3 weeks, multiply the days you paddle each week by 3.
5 × 3 = 15 So, you paddle board _______ days in 3 weeks.
To find the number of miles you paddle each day, divide the total number of miles by the number of days you paddle in 3 weeks.
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.5 7
You paddle _______ miles each day.

Show and Grow

Question 18.
Descartes borrows $6,314.76 for an all-terrain vehicle. He pays back the money in equal amounts each month for 3 years. What is his monthly payment?
Answer:
Time t = 3 years = 3 x 12 = 36 months
Descartes borrowed amount = $6,314.76
6,314.76 ÷ 36
63 ÷ 36 = 1 and 27 is left over
271 ÷ 36 = 7 and 19 is left over
194 ÷ 36 = 5 and 14 is left over
147 ÷ 36 = 4 and 3 is left over
36 ÷ 36 = 1 and 0 left over.
6,314.76 ÷ 36 = 175.41
Descartes monthly payment is $175.41

Question 19.
A blue car travels 297.6 miles using 12 gallons of gasoline and a red car travels 358.8 miles using 13 gallons of gasoline. Which car travels farther using 1 gallon of gasoline? How much farther?
Answer:
297 ones ÷ 12 = 24 ones x 12 = 288
297 ones – 288 ones
There are 9 ones left over.
96 ÷ 12 = 8 tenths x 12 = 96
96 – 96 = 0
There are 0 hundredths left over.
So, 297.6 ÷ 12 = 24.8
358 ones ÷ 13 = 27 ones x 13 = 351
358 ones – 351 ones
There are 7 ones left over.
78 ÷ 13 = 6 tenths x 13 = 78
78 – 78 = 0
There are 0 hundredths left over.
So, 358.8 ÷ 13 = 27.6
Red car – blue car = 27.6 – 24.8 = 2.8
Red car travels 2.8 miles farther than blue car using 1 gallon of gasoline.

Question 20.
DIG DEEPER!
The rectangular dog park has an area of 2,616.25 square feet. How much fencing does an employee need to enclose the dog park?
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.5 8
Answer:

Divide Decimals by Two-Digit Numbers Homework & Practice 7.5

Place a decimal point where it belongs in the quotient.
Question 1.
127.2 ÷ 24 = 5 . 3
Answer:

Question 2.
48.64 ÷ 32 = 1 . 5 2
Answer:

Question 3.
514.18 ÷ 47 = 1 0 . 9 4
Answer:

Find the quotient. Then check your answer.
Question 4.
\(\sqrt [ 72 ]{ 93.6 } \)
Answer:
Divide the ones
93 ÷ 72
1 ones x 72 = 72
93 ones – 72 ones
There are 21 ones left over.
Divide the tenths
216 ÷ 72 = 3 tenths.
So, 93.6 ÷ 72 = 1.3

Question 5.
\(\sqrt [ 7 ]{ 3.92 } \)
Answer:
Divide the tenths
39 ÷ 7
5 ones x 7 = 35
39 ones – 35 ones
There are 4 ones left over.
Divide the hundredths
42 ÷ 7 = 6 tenths.
So, 3.92 ÷ 7 = 0.56

Question 6.
\(\sqrt [ 29 ]{ 1.74 } \)
Answer:
Divide the hundredths
174 ÷ 29
6 ones x 29 = 174
174 hundredths – 174 hundredths
There are 0 hundredths left over.
So, 1.74 ÷ 29 = 0.06

Question 7.
24.3 ÷ 9 = _______
Answer:
Divide the ones
24 ÷ 9
2 ones x 9 = 18
24 ones – 18 ones
There are 6 ones left over.
Divide the tenths
63 ÷ 9
7 tenths x 9 = 63
63 – 63 = 0
There are 0 tenths left over.
So, 24.3 ÷ 9 = 2.7

Question 8.
244.9 ÷ 31 = ______
Answer:
Divide the ones
244 ÷ 31
7 ones x 31 = 217
244 ones – 217 ones
There are 27 ones left over.
Divide the tenths
279 ÷ 31
9 tenths x 31
279 – 279 = 0
There are 0 tenths left over.
So, 244.9 ÷ 31 = 7.9

Question 9.
55.62 ÷ 27 = ______
Answer:
Divide the ones
55 ÷ 27
2 ones x 27 = 54
55 ones – 54 ones
There is 1 ones left over.
Divide the tenths
162 ÷ 27
6 tenths x 27
162 – 162 = 0
There are 0 tenths left over.
So, 55.62 ÷ 27 = 2.06

Find the value of y.
Question 10.
y ÷ 16 = 0.23
Answer:
y = 16 x 0.23
y = 3.68

Question 11.
44.1 ÷ 21 = y
Answer:
Divide the ones
44 ÷ 21
2 ones x 21 = 42
44 ones – 42 ones

There are 2 ones left over.
Divide the tenths
21 ÷ 21
1 tenths x 21
21 – 21 = 0
There are 0 tenths left over.
So, 44.1 ÷ 21 = 2.1

Question 12.
y ÷ 28 = 11.04
Answer:
y = 28 x 11.04
y = 309.12

Question 13.
YOU BE THE TEACHER
Your friend finds 21.44 ÷ 16. Is your friend correct? Explain.
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.5 9
Answer:
My friend answer is not correct.
When dividing a decimal by a whole number, first we will divide the decimal by the whole number ignoring decimal point. Now put the decimal point in the quotient same as the decimal places in the dividend.
Divide the ones
21 ÷ 16
1 ones x 16 = 16
21 ones – 16 ones
There are 5 ones left over.
Divide the tenths
54 ÷ 16
3 tenths x 16
54 tenths – 48 tenths
There are 6 tenths left over.
Divide the hundredths
64 ÷ 16
4 hundredths x 16
64 hundredths- 64 hundredths
There are 0 hundredths left over.
So, 21.44 ÷ 16 = 1.34

Question 14.
DIG DEEPER!
A banker divides the amount shown among 12 people. How can she regroup the money? How much money does each person get?
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.5 10
Answer:

Question 15.
Modeling Real Life
You have hip-hop dance practice for 5 weeks. You attend practice 5 days each week. Each practice is the same length of time. You practice for 37.5 hours altogether. How many hours do you practice each day?
Answer:
To find the total number of days you practice in 5 weeks, multiply the days you practice each week by 5.
5 × 5 = 25 So, you practice 25 days in 5 weeks.
To find the number of hours you practice each day, divide the total number of hours by the number of days you practice in 5 weeks.
37.5 ÷ 25
Divide the ones
37 ÷ 25
1 ones x 25 = 25
37 ones – 25 ones
There are 12 ones left over.
Divide the tenths
125 ÷ 25
5 tenths x 25
125 tenths – 125 tenths
There are 0 tenths left over.
So, 37.5 ÷ 25 = 1.5
So, I practice dance 1.5 hours each day.

Question 16.
DIG DEEPER!
Your rectangular classroom rug has an area of 110.5 square feet. What is the perimeter of the rug?
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.5 11
Answer:

Review & Refresh

Find the product.
Question 17.
0.52 × 0.4 = _______
Answer: 0.208

Question 18.
0.7 × 21.3 = _______
Answer: 14.91

Question 19.
1.52 × 8.6 = ______
Answer: 13.072

Lesson 7.6 Use Models to Divide Decimals

Explore and Grow

Use the model to find each quotient.
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 1
Answer:

Structure
When using a model to divide decimals, how do you determine the number of rows and columns to shade? How do you divide the shaded region?
Answer:

Think and Grow: Use Models to Divide Decimals

Example
Use a model to find 1.2 ÷ 0.3.
Shade 12 columns to represent 1.2.
Divide the model to show groups of 0.3.
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 2
There are ______ groups of ______ tenths.
So, 1.2 ÷ 0.3 = ________.

Example
Use a model to find 0.7 ÷ 0.14.
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 3
Shade 7 columns to represent 0.7.
Divide the model to show groups of 0.14.
There are ______ groups of _______ hundredths.
So, 0.7 ÷ 0.14 = ______.

Show and Grow

Use the model to find the quotient.
Question 1.
1.5 ÷ 0.5 = _____
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 4
Answer:
Shade 15 columns to represent 1.5.
Divide the model to show groups of 0.5.
There are 3 groups of 5 tenths.
So, 1.5 ÷ 0.5 = 3

Question 2.
1.72 ÷ 0.86 = ______
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 5
Answer:
Shade 17.2 columns to represent 1.72.
Divide the model to show groups of 0.86.
There are 2 groups of 86 hundredths.
So, 1.72 ÷ 0.86 = 2

Apply and Grow: Practice

Use the model to find the quotient.
Question 3.
0.32 ÷ 0.04 = ______
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 6
Answer:
Shade 3.2 columns to represent 0.32.
Divide the model to show groups of 0.04.
There are 8 groups of 4 hundredths.
So, 0.32 ÷ 0.04 = 8

Question 4.
0.9 ÷ 0.15 = ______
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 7
Answer:
Shade 9 columns to represent 0.9.
Divide the model to show groups of 0.15.
There are 6 groups of 15 hundredths.
So, 0.9 ÷ 0.15 = 6

Question 5.
1.4 ÷ 0.07 = _____
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 8
Answer:
Shade 14 columns to represent 1.4.
Divide the model to show groups of 0.07.
There are 20 groups of 7 hundredths.
So, 1.4 ÷ 0.07 = 20

Question 6.
1.08 ÷ 0.09 = _____
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 9
Answer:
Shade 10.8 columns to represent 1.08.
Divide the model to show groups of 0.09.
There are 12 groups of 9 hundredths.
So, 1.08 ÷ 0.09 = 12

Question 7.
You have$1.50 in dimes. You exchange all of your dimes for quarters. How many quarters do you get?
Answer:
Quarter = 0.25
1.50 ÷ 0.25
Shade 15 columns to represent 1.50.
Divide the model to show groups of 0.25.
There are 6 groups of 25 hundredths.
So, 1.50 ÷ 0.25 = 6 quarters.

Question 8.
YOU BE THE TEACHER
Your friend uses the model below and says 1.6 ÷ 0.08 = 2. Is your friend correct? Explain.
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 10
Answer:
1.6 ÷ 0.08
Shade 16 columns to represent 1.6.
Divide the model to show groups of 0.08.
There are 20 groups of 8 hundredths.
So, 1.6 ÷ 0.08 = 20
So, my friend answer is wrong.

Question 9.
Structure
Use the model to find the missing number.
0.72 ÷ ____ = 8
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 11
Answer:
Shade 7.2 columns to represent 0.72.
Divide the model to show groups of 8.
There are 0.09 groups of 800 hundredths.
So, 0.72 ÷ 0.09 = 8
Missing number is 0.09.

Think and Grow: Modeling Real Life

Example
Is aluminum more than 5 times as dense as neon?
Divide the density of aluminum by the density of neon to find how many times as dense it is.
Use a model. Shade 27 columns to represent 2.7.
Divide the model to show groups of 0.9.
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 12
There are ______ groups of ______ tenths.
So, 2.7 ÷ 0.9 = _______.
Compare the quotient to 5.
So, aluminum ________ more than 5 times as dense as neon.

Show and Grow

Question 10.
Use the table above. Is neon more than 9 times as dense as hydrogen?
Answer:
Divide the density of neon by the density of hydrogen to find how many times as dense it is.
Use a model. Shade 9 columns to represent 0.9.
Divide the model to show groups of 0.09.
There are 10 groups of 9 hundredths.
So, 0.9 ÷ 0.09 = 10
Compare the quotient to 9.
So, neon is more than 9 times as dense as hydrogen.

Question 11.
You fill a bag with peanuts, give the cashier $5, and receive $3.16 in change. How many pounds of peanuts do you buy?
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 13
Answer:
Amount to buy peanuts = 5 – 3.16 = 1.84
peanuts per pound = $0.23
1.84 ÷ 0.23
Shade 18.4 columns to represent 1.84.
Divide the model to show groups of 0.23.
There are 8 groups of 23 hundredths.
So, 1.84 ÷ 0.23 = 8
I can buy 8 pounds of peanuts.

Question 12.
DIG DEEPER!
You have 2.88 meters of copper wire and 5.85 meters of aluminum wire. You need 0.24 meter of copper wire to make one bracelet and 0.65 meter of aluminum wire to make one necklace. Can you make more bracelets or more necklaces? Explain.
Answer:
Copper wire = 2.88 ÷ 0.24
Shade 28.8 columns to represent 2.88.
Divide the model to show groups of 0.24.
There are 12 groups of 24 hundredths.
So, 2.88 ÷ 0.24 = 12
Aluminum wire = 5.85 ÷ 0.65
Shade 58.5 columns to represent 5.85.
Divide the model to show groups of 0.65.
There are 9 groups of 65 hundredths.
So, 5.85 ÷ 0.65 = 9
So, we can make more bracelets.

Use Models to Divide Decimals Homework & Practice 7.6

Use the model to find the quotient.
Question 1.
0.08 ÷ 0.02 = _____
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 14
Answer:
Shade 8 columns to represent 0.08.
Divide the model to show groups of 0.02.
There are 4 groups of 2 hundredths.
So, 0.08 ÷ 0.02 = 4

Question 2.
0.4 ÷ 0.05 = ______
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 15
Answer:
Shade 5 columns to represent 0.4.
Divide the model to show groups of 0.05.
There are 8 groups of 5 hundredths.
So, 0.4 ÷ 0.05 = 8

Question 3.
1.7 ÷ 0.85 = ______
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 16
Answer:
Shade 17 columns to represent 1.7.
Divide the model to show groups of 0.85.
There are 2 groups of 85 hundredths.
So, 1.7 ÷ 0.85 = 2

Question 4.
1.5 ÷ 0.3 = _______
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 17
Answer:
Shade 15 columns to represent 1.5.
Divide the model to show groups of 0.3.
There are 5 groups of 3 tenths.
So, 1.5 ÷ 0.3 = 5

Question 5.
You have a piece of scrapbook paper that is 1.5 feet long. You cut it into pieces that are each 0.5 foot long. How many pieces of scrap book paper do you have now?
Answer:
1.5 ÷ 0.5
Shade 15 columns to represent 1.5.
Divide the model to show groups of 0.5.
There are 3 groups of 5 tenths.
So, 1.5 ÷ 0.5 = 3
So, I have 3 pieces of scrap book paper.

Question 6.
YOU BE THE TEACHER
Your friend uses the model below and says 0.12 ÷ 0.04 = 0.03. Is your friend correct? Explain.
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 18
Answer:
0.12 ÷ 0.04
Shade 1.2 columns to represent 0.12.
Divide the model to show groups of 0.04.
There are 3 groups of 4 hundredths.
So, 0.12 ÷ 0.04 = 3
My friend is not correct.

Question 7.
Writing
Write a real-life problem that involves dividing a decimal by another decimal.
Answer:

Question 8.
Modeling Real Life
Does the watercolor paint cost more than 3 times as much as the paintbrush? Explain.
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 19
Answer:
Divide the price of watercolor paint by the price of paintbrush to find how many times as cost it is.
Use a model. Shade 29.6 columns to represent 2.96.
Divide the model to show groups of 0.74.
There are 4 groups of 74 hundredths.
So, 2.96 ÷ 0.74
Compare the quotient to 3.
So, watercolor paint costs more than 3 times as much as the paintbrush.

Question 9.
DIG DEEPER!
You have 3.75 cups of popcorn kernels. You fill a machine with 0.25 cup of kernels 3 times each hour. How many hours pass before you run out of kernels?
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 7.6 20
Answer:
Filling kernels each hour = 0.25 x 3 = 0.75
Total cups of popcorn kernels = 3.75
3.75 ÷ 0.75
Shade 37.5 columns to represent 3.75.
Divide the model to show groups of 0.75.
There are 5 groups of 75 hundredths.
So, 3.75 ÷ 0.75 = 5 hours

Review & Refresh

Complete the equation. Identify the property shown.
Question 10.
3 × 14 = 14 × 3
Answer: Commutative Property of Multiplication

Question 11.
8 × (3 + 10) = (8 × 3) + (8 × 10)
Answer: Distributive Property

Lesson 7.7 Divide Decimals

Explore and Grow

Use the model to find 0.96 ÷ 0.32.
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.7 1
Find 96 ÷ 32.
Answer:

Structure
How can multiplying by a power of 10 help you divide decimals?
Answer:

Think and Grow: Divide Decimals by Decimals

Key Idea
To divide by a decimal, multiply the divisor by a power of 10 to make it a whole number. Multiply the dividend by the same power of 10. Then divide as you would with whole numbers.

Example
Find 6.12 ÷ 1.8. Estimate _______
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.7 2

Example
Find 2.43 ÷ 0.09.
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.7 3
So, 2.43 ÷ 0.09 = ______.

Show and Grow

Multiply the divisor by a power of 10 to make it a whole number. Then write the equivalent expression.
Question 1.
3.5 ÷ 0.5
Answer:
Step 1: Multiply 0.5 by a power of 10 to make it a whole number. Then multiply 3.5 by the same power of 10.
0.5 x 10 = 5
3.5 x 10 = 35
35 ÷ 5 = 7
So, 3.5 ÷ 0.5 = 7

Question 2.
9.84 ÷ 2.4
Answer:
Step 1: Multiply 2.4 by a power of 10 to make it a whole number. Then multiply 9.84 by the same power of 10.
2.4 x 10 = 24
9.84 x 10 = 98.4
Step 2: Divide 98.4 ÷ 24
98 ÷ 24 = 4 with remainder 2.
24 ÷ 24 = 1 with remainder 0.
So, 9.84 ÷ 2.4 = 4.1

Question 3.
4.68 ÷ 0.78
Answer:
Step 1: Multiply 0.78 by a power of 10 to make it a whole number. Then multiply 4.68 by the same power of 10.
0.78 x 100 = 78
4.68 x 100 = 468
Step 2: Divide 468 ÷ 78 = 6
So, 4.68 ÷ 0.78 = 6

Apply and Grow: Practice

Place a decimal point where it belongs in the quotient.
Question 4.
28.47 ÷ 0.39 = 7 3 . 0
Answer:

Question 5.
75.85 ÷ 3.7 = 2 0 . 5
Answer:

Question 6.
4.51 ÷ 4.1 = 1 . 1
Answer:

Find the quotient. Then check your answer.
Question 7.
\(\sqrt [ 1.5 ]{ 7.5 } \)
Answer:
Step 1: Multiply 7.5 by a power of 10 to make it a whole number. Then multiply 1.5 by the same power of 10.
7.5 x 10 = 75
1.5 x 10 = 15
75 ÷ 15 = 5
So, 7.5 ÷ 1.5 = 5

Question 8.
\(\sqrt [ 0.13 ]{ 0.91 } \)
Answer:
Step 1: Multiply 0.91 by a power of 100 to make it a whole number. Then multiply 0.13 by the same power of 100.
0.91 x 100 = 91
0.13 x 100 = 13
91 ÷ 13 = 7
So, 0.91 ÷ 0.13 = 7

Question 9.
\(\sqrt [ 2.4 ]{ 2.88 } \)
Answer:
Step 1: Multiply 2.88 by a power of 10 to make it a whole number. Then multiply 2.4 by the same power of 10.
2.88 x 10 = 28.8
2.4 x 10 = 24
Step 2: Divide 28.8 ÷ 24
28 ÷ 24 = 1 with remainder 4.
48 ÷ 24 = 2 with remainder 0.
So, 2.88 ÷ 2.4 = 1.2

Question 10.
\(\sqrt [ 0.6 ]{ 7.8 } \)
Answer:
Step 1: Multiply 7.8 by a power of 10 to make it a whole number. Then multiply 0.6 by the same power of 10.
7.8 x 10 = 78
0.6 x 10 = 6
78 ÷ 6 = 13
So, 7.8 ÷ 0.6 = 13

Question 11.
\(\sqrt [ 3.6 ]{ 4.32 } \)
Answer:
Step 1: Multiply 4.32 by a power of 10 to make it a whole number. Then multiply 3.6 by the same power of 10.
4.32 x 10 = 43.2
3.6 x 10 = 36
Step 2: Divide 43.2 ÷ 36
43 ÷ 36 = 1 with remainder 7.
72 ÷ 36 = 2 with remainder 0.
So, 4.32 ÷ 3.6 = 1.2

Question 12.
\(\sqrt [ 0.1 ]{ 11.2 } \)
Answer:
Step 1: Multiply 11.2 by a power of 10 to make it a whole number. Then multiply 0.1 by the same power of 10.
11.2 x 10 = 112
0.1 x 10 = 1
112 ÷ 1 = 112
So, 11.2 ÷ 0.1 = 112

Question 13.
40.42 ÷ 8.6 = ______
Answer:
Step 1: Multiply 8.6 by a power of 10 to make it a whole number. Then multiply 40.42 by the same power of 10.
8.6 x 10 = 86
40.42 x 10 = 404.2
Step 2: Divide 404.2 ÷ 86
404 ÷ 86 = 4 with remainder 60.
602 ÷ 86 = 7 with remainder 0.
So, 40.42 ÷ 8.6 = 4.7

Question 14.
7.2 ÷ 2.4 = _______
Answer:
Step 1: Multiply 2.4 by a power of 10 to make it a whole number. Then multiply 7.2 by the same power of 10.
2.4 x 10 = 24
7.2 x 10 = 72
Step 2: Divide 72 ÷ 24 = 3
So, 7.2 ÷ 2.4 = 3

Question 15.
5.76 ÷ 1.8 = _______
Answer:
Step 1: Multiply 1.8 by a power of 10 to make it a whole number. Then multiply 5.76 by the same power of 10.
1.8 x 10 = 18
5.76 x 10 = 57.6
Step 2: Divide 57.6 ÷ 18
57 ÷ 18 = 3 with remainder 3.
36 ÷ 18 = 2 with remainder 0.
So, 5.76 ÷ 1.8 = 3.2

Question 16.
YOU BE THE TEACHER
Descartes says 4.14 ÷ 2.3 = 1.8. Is he correct? Explain.
Answer:
Step 1: Multiply 2.3 by a power of 10 to make it a whole number. Then multiply 4.14 by the same power of 10.
2.3 x 10 = 23
4.14 x 10 = 41.4
Step 2: Divide 41.4 ÷ 23
41 ÷ 23 = 1 with remainder 18.
184 ÷ 23 = 8 with remainder 0.
So, 4.14 ÷ 2.3 = 1.8.
Descartes answer is correct.

Question 17.
Logic
What can you conclude about Newton’s quotient?
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.7 4
Answer:
The quotient will be above 5.72.
Because if the divisor is less than 1 then the quotient must be greater than the dividend.

Think and Grow: Modeling Real Life

Example
A farmer sells a bag of papayas for $5.46. How much does the bag of papayas weigh?
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.7 5
Divide the price of the papayas by the price per pound to find how much the bag of papayas weighs.
5.46 ÷ 1.3 = ? Estimate _______
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.7 6
So, the bag of papayas weighs _______ pounds.

Show and Grow

Use the table above.
Question 18.
You buy a honeydew for $6.08. What is the weight of the honeydew?
Answer:
Honeydew price = $0.8
6.08 ÷ 0.8
Step 1: Multiply 0.8 by a power of 10 to make it a whole number. Then multiply 6.08 by the same power of 10.
0.8 x 10 = 8
6.08 x 10 = 60.8
Step 2: Divide 60.8 ÷ 8
60 ÷ 8 = 7 with remainder 4.
48 ÷ 8 = 6 with remainder 0.
So, 6.08 ÷ 0.8 = 7.6
Weight of the honeydew = 7.6 pounds

Question 19.
You buy a pumpkin for $7.20 and a watermelon for $5.94. Does the watermelon or the pumpkin weigh more? How much more?
Answer:
Pumpkin = 7.20 ÷ 0.45
Watermelon = 5.94 ÷ 0.33
7.20 ÷ 0.45
Step 1: Multiply 0.45 by a power of 10 to make it a whole number. Then multiply 7.20 by the same power of 10.
0.45 x 100 = 45
7.20 x 100 = 720
Step 2: Divide 720 ÷ 45 = 16
Pumpkin weight = 16 pounds
5.94 ÷ 0.33
Step 1: Multiply 0.33 by a power of 10 to make it a whole number. Then multiply 5.94 by the same power of 10.
0.33 x 100 = 33
5.94 x 100 = 594
Step 2: Divide 594 ÷ 33 = 18
Watermelon weight = 18 pounds
Watermelon weighs 2 pounds more than the pumpkin.

Question 20.
DIG DEEPER!
You pay $5 for a pineapple and receive $2.48 in change. The inedible parts of the pineapple weigh 1.75 pounds. How many pounds of edible pineapple do you have? Explain.
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.7 7
Answer:
Amount paid = 5 – 2.48 = $2.52
pineapple price per pound = $0.63
2.52 ÷ 0.63
Step 1: Multiply 0.63 by a power of 10 to make it a whole number. Then multiply 2.52 by the same power of 10.
0.63 x 100 = 63
2.52 x 100 = 252
Step 2: Divide 252 ÷ 63 = 4
Total weight = 4 pounds
Edible pineapple = total weight – inedible pineapple weight
= 4 – 1.75
= 2.25
Edible pineapple weight = 2.25 pounds.

Divide Decimals Homework & Practice 7.7

Multiply the divisor by a power of 10 to make it a whole number. Then write the equivalent expression.
Question 1.
16.15 ÷ 1.9
Answer:
Step 1: Multiply 1.9 by a power of 10 to make it a whole number. Then multiply 16.15 by the same power of 10.
1.9 x 10 = 19
16.15 x 10 = 161.5
Step 2: Divide 161.5 ÷ 19
161 ÷ 19 = 8 with remainder 9.
95 ÷ 19 = 5 with remainder 0.
So, 16.15 ÷ 1.9 = 8.5

Question 2.
0.36 ÷ 0.09
Answer:
Step 1: Multiply 0.09 by a power of 10 to make it a whole number. Then multiply 0.36 by the same power of 10.
0.09 x 100 = 9
0.36 x 100 = 36
Step 2: Divide 36 ÷ 9 = 4
So, 0.36 ÷ 0.09 = 4

Question 3.
2.04 ÷ 1.7
Answer:
Step 1: Multiply 1.7 by a power of 10 to make it a whole number. Then multiply 2.04 by the same power of 10.
1.7 x 10 = 17
2.04 x 10 = 20.4
Step 2: Divide 20.4 ÷ 17
20 ÷ 17 = 1 with remainder 3.
34 ÷ 17 = 2 with remainder 0.
So, 2.04 ÷ 1.7 = 1.2

Place a decimal point where it belongs in the quotient.
Question 4.
81.27 ÷ 13.5 = 6 . 0 2
Answer:

Question 5.
5.76 ÷ 3.2 = 1 . 8
Answer:

Question 6.
47.15 ÷ 2.3 = 2 0 . 5
Answer:

Find the quotient. Then check your answer.
Question 7.
\(\sqrt [ 5.3 ]{ 21.2 } \)
Answer:
Step 1: Multiply 5.3 by a power of 10 to make it a whole number. Then multiply 21.2 by the same power of 10.
5.3 x 10 = 53
21.2 x 10 = 212
212 ÷ 53 = 4
So, 21.2 ÷ 5.3 = 4

Question 8.
\(\sqrt [ 0.03 ]{ 76.38 } \)
Answer:
Step 1: Multiply 0.03 by a power of 10 to make it a whole number. Then multiply 76.38 by the same power of 10.
0.03 x 100 = 3
76.38 x 100 = 7,638
Step 2: Divide 7638 ÷ 3
76 ÷ 3 = 25 with remainder 1.
138 ÷ 3 = 46 with remainder 0.
So, 76.38 ÷ 0.03 = 25.46

Question 9.

\(\sqrt [ 6.2 ]{ 33.48 } \)
Answer:
Step 1: Multiply 6.2 by a power of 10 to make it a whole number. Then multiply 33.48 by the same power of 10.
6.2 x 10 = 62
33.48 x 10 = 334.8
Step 2: Divide 334.8 ÷ 62
334 ÷ 62 = 5 with remainder 24.
248 ÷ 62 = 4 with remainder 0.
So, 33.48 ÷ 6.2 = 5.4

Find the quotient. Then check your answer.
Question 10.
0.63 ÷ 0.09 = ______
Answer:
Step 1: Multiply 0.09 by a power of 10 to make it a whole number. Then multiply 0.63 by the same power of 10.
0.09 x 100 = 9
0.63 x 100 = 63
Step 2: Divide 63 ÷ 9 = 7
So, 0.63 ÷ 0.09 = 7

Question 11.
10.53 ÷ 3.9 = ______
Answer:
Step 1: Multiply 3.9 by a power of 10 to make it a whole number. Then multiply 10.53 by the same power of 10.
3.9 x 10 = 39
10.53 x 10 = 105.3
Step 2: Divide 105.3 ÷ 39
105 ÷ 39 = 2 with remainder 27.
273 ÷ 39 = 7 with remainder 0.
So, 10.53 ÷ 3.9 = 2.7

Question 12.
33.8 ÷ 2.6 = ______
Answer:
Step 1: Multiply 2.6 by a power of 10 to make it a whole number. Then multiply 33.8 by the same power of 10.
2.6 x 10 = 26
33.8 x 10 = 338
Step 2: Divide 338 ÷ 26 = 13
So, 33.8 ÷ 2.6 = 13

Question 13.
Logic
Without calculating, determine whether 5.4 ÷ 0.9 is greater than or less than 5.4. Explain.
Answer:
5.4 ÷ 0.9 is greater than 5.4
If the divisor is less than 1 then the quotient must be greater than the dividend.

Question 14.
Structure
Explain how 35.64 ÷ 2.97 compares to 3,564 ÷ 297.
Answer:
Both 35.64 ÷ 2.97 and 3,564 ÷ 297 are same.
Both dividend and divisor are multiplied by same power of 10.
35.64 x 100 = 3564
2.97 x 100 = 297.

Question 15.
Modeling Real Life
A farmer sells a bag of grapes for $5.88. How much do the grapes weigh?
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.7 8
Answer:
Bag of grapes price = $5.88
Grapes price per pound = $2.80
5.88 ÷ 2.8
Step 1: Multiply 2.8 by a power of 10 to make it a whole number. Then multiply 5.88 by the same power of 10.
2.8 x 10 = 28
5.88 x 10 = 58.8
Step 2: Divide 58.8 ÷ 28
58 ÷ 28 = 2 with remainder 2.
28 ÷ 28 = 1 with remainder 0.
So, 5.88 ÷ 2.8 = 2.1
Grapes weight = 2.1 pounds

Question 16.
DIG DEEPER!
Descartes makes 2.5 times as many ounces of applesauce as Newton. Newton eats 8 ounces of his applesauce, and then divides the rest equally into 3 containers. How much applesauce is in each of Newton’s containers?
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals 7.7 9
Answer:
From the given information, Newton makes applesauce = 72.5 ÷ 2.5
Step 1: Multiply 2.5 by a power of 10 to make it a whole number. Then multiply 72.5 by the same power of 10.
2.5 x 10 = 25
72.5 x 10 = 725
Step 2: Divide 725 ÷ 25 = 29
So, newton makes 29 ounces of applesauce
He eats 8 ounces = 29 – 8 = 21
21 ÷ 3 = 7 ounces.
7 ounces of applesauce is in each of Newton’s containers.

Review & Refresh

Question 17.
Write the number in two other forms.
Standard form:
Word form: two hundred thirty thousand, eighty-two
Expanded form:
Answer:
Standard form is 230,082
Expanded form is 200000 + 30000 + 80 + 2.

Lesson 7.8 Insert Zeros in the Dividend

Explore and Grow

Use the model to find each quotient.
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.8 1
Answer:

Reasoning
Why is the number of digits in the quotients you found above different than the number of digits in the dividends?
Answer:

Think and Grow: Inserting Zeros in the Dividend

Example
Find 52.6 ÷ 4. Estimate ________
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.8 2

Example
Find 1 ÷ 0.08.
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.8 3

Show and Grow

Find the quotient. Then check your answer.
Question 1.
\(\sqrt [ 0.5 ]{ 85 } \)
Answer:
Multiply 0.5 by a power of 10 to make it a whole number. Then multiply 85 by the same power of 10.
0.5 x 10 = 5
85 x 10 = 850
850 ÷ 5 = 170
So, 85 ÷ 0.5 = 170.

Question 2.
\(\sqrt [ 15 ]{ 9.6 } \)
Answer:
Insert a zero in the dividend and continue to divide.
96 ÷ 15 = 6 with remainder 6.
60 ÷ 15 = 4 with remainder 0.
So, 9.6 ÷ 15 = 0.64

Question 3.
\(\sqrt [ 0.24 ]{ 2.52 } \)
Answer:
Multiply 0.24 by a power of 10 to make it a whole number. Then multiply 2.52 by the same power of 10.
0.24 x 100 = 24
2.52 x 100 = 252
252 ÷ 24
252 ÷ 24 = 10 with remainder 12.
Insert a zero in the dividend and continue to divide.
120 ÷ 24 = 5 with remainder 0.
So, 2.52 ÷ 0.24 = 10.5.

Apply and Grow: Practice

Place a decimal point where it belongs in the quotient.
Question 4.
3.24 ÷ 0.48 = 6 . 7 5
Answer:

Question 5.
35 ÷ 0.5 = 7 0.
Answer:

Question 6.
12.8 ÷ 2.5 = 5 .1 2
Answer:

Find the quotient. Then check your answer.
Question 7.
\(\sqrt [ 2.4 ]{ 0.84 } \)
Answer:
Multiply 2.4 by a power of 10 to make it a whole number. Then multiply 0.84 by the same power of 10.
2.4 x 10 = 24
0.84 x 10 = 8.4
Insert a zero in the dividend and continue to divide.
84 ÷ 24 = 3 with remainder 12.
120 ÷ 24 = 5 with remainder 0.
So, 0.84 ÷ 2.4 = 0.35

Question 8.
\(\sqrt [ 0.32 ]{ 2.08 } \)
Answer:
Multiply 0.32 by a power of 10 to make it a whole number. Then multiply 2.08 by the same power of 10.
0.32 x 100 = 32
2.08 x 100 = 208
208 ÷ 32 = 6 with remainder 16.
Insert a zero in the dividend and continue to divide.
160 ÷ 32 = 5 with remainder 0.
So, 2.08 ÷ 0.32 = 6.5

Question 9.
\(\sqrt [ 4 ]{ 45.8 } \)
Answer:
45.8 ÷ 4
45 ÷ 4 = 11 with remainder 1.
18 ÷ 4 = 4 with remainder 2.
Insert a zero in the dividend and continue to divide.
20 ÷ 4 = 5 with remainder 0.
So, 45.8 ÷ 4 = 11.45.

Question 10.
9 ÷ 1.2 = ______
Answer:
Multiply 1.2 by a power of 10 to make it a whole number. Then multiply 9 by the same power of 10.
1.2 x 10 = 12
9 x 10 = 90
90 ÷ 12
Insert a zero in the dividend and continue to divide.

12 ) 90 ( 7.5

84

——-

60

– 60

——-

0
So, 9 ÷ 1.2 = 7.5

Question 11.
3.5 ÷ 2.5 = ______
Answer:
Multiply 2.5 by a power of 10 to make it a whole number. Then multiply 3.5 by the same power of 10.
2.5 x 10 = 25
3.5 x 10 = 35
35 ÷ 25
Insert a zero in the dividend and continue to divide.
25 ) 35 ( 1.4

25

——-

100

-100

——-

0
So, 3.5 ÷ 2.5 = 1.4

Question 12.
1.8 ÷ 12 = ______
Answer:
Insert a zero in the dividend and continue to divide.
12 ) 18 ( 1.5

12

——-

60

– 60

——-

0
So, 1.8 ÷ 12 = 0.15

Question 13.
You read 2.5 chapters of the book each night. How many nights does it take you to finish the book?
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.8 4

Answer:
Total chapters in the book = 15
15 ÷ 2.5
Multiply 2.5 by a power of 10 to make it a whole number. Then multiply 15 by the same power of 10.
2.5 x 10 = 25
15 x 10 = 150
150 ÷ 25 = 6 nights to finish the book.

Question 14.
Precision
Why does Newton place zeros to the right of the dividend but Descartes does not?
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.8 5
Answer:
Newton’s dividend does not have enough digits to divide completely, so he placed zeros to the right of the dividend.
Descartes dividend is a multiple of divisor and it is divided completely, so no need of placing zeros.

Think and Grow: Modeling Real Life

Example
The John Muir Trail in Yosemite National Park is 210 miles long. A hiker completes the trail in 20 days by hiking the same distance each day. How many miles does the hiker travel each day?
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.8 6
Divide 210 miles by 20 to find how many miles the hiker travels each day.
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.8 7
So, the hiker travels _______ miles each day.

Show and Grow

Question 15.
A box of 15 tablets weighs 288 ounces. Each tablet weighs the same number of ounces. What is the weight of each tablet?
Answer:
Divide 288 ounces by 15 to find the weight of each tablet.
288 ÷ 15

15 ) 288 ( 19.2

15

——-

138

-135

——-

30

– 30

——-

0
288 ÷ 15 = 19.2
The weight of each tablet = 19.2 ounces.

Question 16.
Which bag of dog food costs less per pound? Explain why it makes sense to write each quotient as a decimal in this situation.
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.8 8
Answer:

Question 17.
DIG DEEPER!
A farmer sells a pound of rice for $0.12 and a pound of oats for $0.08. Can you buy more pounds of rice or oats with $3? How much more? Explain.
Answer:
Rice = 3 ÷ 0.12
Multiply 0.12 by a power of 10 to make it a whole number. Then multiply 3 by the same power of 10.
0.12 x 100 = 12
3 x 100 = 300
300 ÷ 12 = 25
Oats = 3 ÷ 0.08
Multiply 0.08 by a power of 10 to make it a whole number. Then multiply 3 by the same power of 10.
0.08 x 100 = 8
3 x 100 = 300
300 ÷ 8 = 37.5
I can buy 12.5 pounds oats more than the rice.

Insert Zeros in the Dividend Homework & Practice 7.8

Place a decimal point where it belongs in the quotient.
Question 1.
9.3 ÷ 0.31 = 3 0.
Answer:

Question 2.
10 ÷ 0.8 = 1 2 . 5
Answer:

Question 3.
0.76 ÷ 0.25 = 3 . 0 4
Answer:

Find the quotient. Then check your answer.
Question 4.
\(\sqrt [ 0.8 ]{ 30 } \)
Answer:
Multiply 0.8 by a power of 10 to make it a whole number. Then multiply 30 by the same power of 10.
0.8 x 10 = 8
30 x 10 = 300
300 ÷ 8
30 ÷ 8 = 3 with remainder 6.
60 ÷ 8 = 7 with remainder 4.
Insert a zero in the dividend and continue to divide.
40 ÷ 8 = 5 with remainder 0.
So, 30 ÷ 0.8 = 37.5.

Question 5.
\(\sqrt [ 15 ]{ 91.2 } \)
Answer:
91.2 ÷ 15
91 ÷ 15 = 6 with remainder 1.
Insert a zero in the dividend and continue to divide.
120 ÷ 15 = 8 with remainder 0.
So, 91.2 ÷ 15 = 6.08

Question 6.
\(\sqrt [ 35 ]{ 97.3 } \)
Answer:
97.3 ÷ 35
97 ÷ 35 = 2 with remainder 27.
273 ÷ 35 = 7 with remainder 28.
Insert a zero in the dividend and continue to divide.
280 ÷ 35 = 8 with remainder 0.
So, 97.3 ÷ 35 = 2.78.

Question 7.
3.57 ÷ 0.84 = ______
Answer:
Multiply 0.84 by a power of 10 to make it a whole number. Then multiply 3.57 by the same power of 10.
0.84 x 100 = 84
3.57 x 100 = 357
357 ÷ 84
Insert a zero in the dividend and continue to divide.

84 ) 357 ( 4.25

336

——-

210

-168

——-

420

– 420

——-

0
3.57 ÷ 0.84 = 4.25

Question 8.
20.2 ÷ 4 = _____
Answer:
Insert a zero in the dividend and continue to divide.

4 ) 20.2 ( 5.05

20

——

20

20

——

0
20.2 ÷ 4 = 5.05

Question 9.
1.74 ÷ 0.25 = _______
Answer:
Multiply 0.25 by a power of 10 to make it a whole number. Then multiply 1.74 by the same power of 10.
0.25 x 100 = 25
1.74 x 100 = 174
174 ÷ 25
Insert a zero in the dividend and continue to divide.

25 ) 174 ( 6.96

150

——-

240

-225

——-

150

-150

——-

0
1.74 ÷ 0.25 = 6.96

Question 10.
A painter has 5 gallons of paint to use in a room. He uses 2.5 gallons of paint for 1 coat. How many coats can he paint?
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.8 9
Answer:
Multiply 2.5 by a power of 10 to make it a whole number. Then multiply 5 by the same power of 10.
2.5 x 10 = 25
5 x 10 = 50
50 ÷ 25 = 2
He can paint 2 coats.

Question 11.
YOU BE THE TEACHER
Your friend say she can find 5.44 ÷ 0.64 by dividing both the divisor and dividend by 0.01 to make an equivalent problem with a whole-number divisor. Is he correct? Explain.
Answer:
To divide this 5.44 ÷ 0.64, multiply 0.64 by a power of 10 to make it a whole number. Then multiply 5.44 by the same power of 10.
Multiplying by 100 and dividing by 0.01 both are same.
So, my friend is correct.

Question 12.
Writing
Explain when you need to insert a zero in the dividend when dividing.
Answer:
When dividend does not have enough digits to divide completely, then we need to insert a zero in the dividend.
For example, 35 ÷ 25
Here 35 is not a multiple of 25, so we have to add a zero to 35.

Question 13.
Modeling Real Life
You cut a 12-foot-long streamer into 8 pieces of equal length. How long is each piece?
Answer:
Length of each piece = 12 ÷ 8

8 ) 12 ( 1.5

8

—–

40

40

—–

0
So, length of each piece = 1.5

Question 14.
DIG DEEPER!
How many days longer does the bag of dog food last for the 20-pound dog than the 40-pound dog? Explain.
Big Ideas Math Solutions Grade 5 Chapter 7 Divide Decimals 7.8 10
Answer:
Total cups of dog food = 200
20-pound dog eats per day = 1.25 cups
40-pound dog eats per day = 1.25 x 2 = 2.5 cups
200 ÷ 1.25
Multiply 1.25 by a power of 10 to make it a whole number. Then multiply 200 by the same power of 10.
1.25 x 100 = 125
200 x 100 = 20,000
20,000 ÷ 125
200 ÷ 125 = 1 with remainder 75
7500 ÷ 125 = 60 with remainder 0.
So, 200 ÷ 1.25 = 160
Food lasts for the 20-pound dog = 160 days
40-pound dog = 200 ÷ 2.5
Multiply 2.5 by a power of 10 to make it a whole number. Then multiply 200 by the same power of 10.
2.5 x 10 = 25
200 x 10 = 2000
2000 ÷ 25 = 80
Food lasts for the 40-pound dog = 80 days

Review & Refresh

Find the sum. Check whether your answer is reasonable.
Question 15.
1.7 + 6.8 = ________
Answer: 8.5

Question 16.
150.23 + 401.79 = _______
Answer: 552.02

Lesson 7.9 Problem Solving: Decimal Operations

Explore and Grow

Make a plan to solve the problem.
Three friends take a taxi ride that costs $4.75 per mile. They travel 10.2 miles and tip the driver $8. They share the total cost equally. How much does each friend pay?
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.9 1
Answer:

Reasoning
Explain how you can work backward to check your answer.
Answer:

Think and Grow: Problem Solving: Decimal Operations

Example
You spend $67.45 on the video game controller, the gaming headset, and 3 video games. The video games each cos the same amount. How much does each video game cost?
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.9 2
Understand the Problem
What do you know?
• You spend a total of $67.45.
• The controller costs $15.49 and the headset costs $21.99.
• You buy 3 video games that each cost the same amount.

What do you need to find?
• You need to find the cost of each video game.

Make a Plan
How will you solve?
Write and solve an equation to find the cost of each video game.

Solve
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.9 3
So, each video game costs ______.

Show and Grow

Question 1.
Explain how you can check whether your answer above is reasonable.
Answer:
v = (67.45 – 15.49 – 21.99) ÷ 3
= 29.97 ÷ 3
v = 9.99
So, each video game costs $9.99.

Apply and Grow: Practice

Understand the problem. What do you know? What do you need to find? Explain.
Question 2.
Your friend pays $84.29 for a sewing machine and 6 yards of fabric. The sewing machine costs $59.99. How much does each yard of fabric cost?
Answer:

What do you know?
• You spend a total of $84.29 for a sewing machine and 6 yards of fabric.
• The sewing machine costs $59.99 and the 6 yards of fabric costs $24.3.

What do you need to find?

We have to find each yard of fabric cost.
1 yard of fabric cost = 24.3 ÷ 6
So, each yard of fabric costs = $4.05

Question 3.
There are 25.8 grams of fiber in 3 cups of cooked peas. There are 52.5 grams of fiber in 5 cups of avocados. Which contains more fiber in 1 cup, cooked peas or avocados?
Answer:
Cooked peas = 25.8 ÷ 3 = 8.6 grams
Avocados = 52.5 ÷ 3 = 10.5 grams
So, avocados contains more fiber in 1 cup.

Understand the problem. Then make a plan. How will you solve? Explain.
Question 4.
Your friend makes a hexagonal frame with a perimeter of 7.5 feet. You make a triangular frame with a perimeter of 5.25 feet. Whose frame has longer side lengths? How much longer?
Answer:
Hexagonal perimeter = 6a = 7.5 feet
Triangular perimeter = 3sides(3a) = 5.25 feet
So, 6a ÷ 2 = 3a
7.5 ÷ 2 = 3.75 feet
5.25 – 3.75 = 1.5 feet
So, triangular frame has 1.5 feet longer side lengths.

Question 5.
You spend $119.92 on the wet suit, the snorkeling equipment, and 2 research books. The books each cost the same amount. How much does each book cost?
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.9 4
Answer:
Write and solve an equation to find the cost of each book.
cost of each book = (Amount spend – wet suit cost – snorkeling equipment cost) ÷ 2
= (119.92 – 64.95 – 14.99) ÷ 2
= 39.98 ÷ 2
= 19.99
So, each book costs $19.99.

Question 6.
DIG DEEPER!
You pour goop into molds and bake them to make plastic lizards. You run out of goop and go shopping for more. Which package costs less per ounce of goop? Explain.
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.9 5.1
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.9 5
Answer:
Fluorescent package = 40.5 ÷ 2.25 = $18
Color-Changing package = 16.2 ÷ 1.8 = $9
So, Color-Changing package costs less per ounce of goop.

Think and Grow: Modeling Real Life

Example
Descartes spends $16.40 on the game app, an e-book, and 5 songs. The e-book costs 4 times as much as the game app. The songs each cost the same amount. How much does each song cost?
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.9 6
Think: What do you know? What do you need to find? How will you solve?
Step 1: Multiply the cost of the app by4 to find the cost of the e-book.
1.99 × 4 = 7.96 The e-book costs _______.
Step 2: Write and solve an equation to find the cost of each song.
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.9 7
Let c represent the cost of each song.
c = (16.40 – 1.99 – 7.96) ÷ 5c
= _____ ÷ 5
= _____
So, each song costs $ ______.

Show and Grow

Question 7.
You spend $2.24 on a key chain, a bookmark, and 2 pencils. The key chain costs 3 times as much as the bookmark. The pencils each cost the same amount. How much does each pencil cost?
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.9 8
Answer:
Given that,
Bookmark cost = $0.45
Key chain cost = 3 x 0.45 = $1.35
Write and solve an equation to find the cost of each pencil.
cost of each pencil = (Amount spend – keychain cost – bookmark cost) ÷ 2
= (2.24 – 1.35 – 0.45) ÷ 2
= 0.44 ÷ 2
= $0.22
So, cost of each pencil = $0.22.

Question 8.
Newton buys an instant-print camera, a camera bag, and 2 packs of film. He pays $113.96 after using a $5 coupon. The camera costs $69.40, which is 5 times as much as the camera case. How much does each pack of film cost?
Answer:
Total cost = 113.96 + 5 = $118.96
Camera cost = $69.40
Camera case cost = 69.40 ÷ 5 = $13.88
Write and solve an equation to find the cost of each pack of film cost.
cost of each pack of film = (amount spend – camera cost – camera case cost) ÷ 2
= (118.96 – 69.40 – 13.88) ÷ 2
= 35.68 ÷ 2
= 17.84
So, cost of each pack of film = $17.84

Problem Solving: Decimal Operations Homework & Practice 7.9

Understand the problem. What do you know? What do you need to find? Explain.
Question 1.
A 20-ounce bottle of ketchup costs $2.80. A 14-ounce bottle of mustard costs $2.38. Which item costs less per ounce? How much less?
Answer:
20-ounce bottle of ketchup costs = $2.80
14-ounce bottle of mustard costs = $2.38
1 ounce ketchup = 2.8 ÷ 20 = $0.14
1 ounce mustard = 2.38 ÷ 14 = $0.17
Ketchup costs $0.03 less per ounce than mustard.

Question 2.
Gymnast A scores the same amount in each of his 4 events. Gymnast B scores the same amount in each of his 3 events. Which gymnast scores more in each of his events? How much more?
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.9 9
Answer:
Gymnast A in each of his events = 33.56 ÷ 4 = 8.39 points
Gymnast B in each of his events = 25.05 ÷ 3 = 8.35 points
Gymnast A scores 0.04 points more in each of his events than gymnast B.

Understand the problem. Then make a plan. How will you solve? Explain.
Question 3.
Three children’s tickets to the circus cost $53.85. Two adult tickets to the circus cost $63.90. How much more does 1 adult ticket cost than 1 children’s ticket? Which item costs more per ounce? How much more?
Answer:
3 children’s tickets cost = $53.85
2 adult tickets cost = $63.90
1 adult ticket cost = 63.90 ÷ 2 = $31.95
1 children’s ticket cost = 53.85 ÷ 3 = $17.95
One adult ticket cost is $14 more than 1 children’s ticket.

Question 4.
A chef at a restaurant buys 50 pounds of red potatoes for $27.50 and 30 pounds of sweet potatoes for $22.50. Which kind of potato costs more per pound? How much more?
Answer:
Red potatoes per pound = 27.5 ÷ 50 = $0.55
Sweet potatoes per pound = 22.5 ÷ 30 = $0.75
Sweet potatoes costs $0.2 more per pound than red potatoes.

Question 5.
Modeling Real Life
You download 2 music videos, a TV series, and a movie for $42.95 total. The TV series costs 2 times as much as the movie. How much does each music video cost?
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.9 10
Answer:
Total cost = $42.95
Movie cost = $12.99
TV series cost = $25.98
Write and solve an equation to find the cost of each music video cost.
cost of each music video = (total cost – movie cost – TV series cost) ÷ 2
= (42.95 – 12.99 – 25.98) ÷ 2
= 3.98 ÷ 2
= 1.99
So, cost of each music video = $1.99.

Question 6.
DIG DEEPER!
Which item costs more per ounce? How much more?
Big Ideas Math Answer Key Grade 5 Chapter 7 Divide Decimals 7.9 11
Answer:
Glue cost = 23.04 ÷ 1 = 23.04
Paste cost = 4.00 ÷ 2 = 2
Glue costs $21.04 more than paste.

Review & Refresh

Find the quotient.
Question 7.
4,000 ÷ 20 = ______
Answer: 200

Question 8.
900 ÷ 300 = _______
Answer: 3

Question 9.
5,600 ÷ 800 = _______
Answer: 7

Divide Decimals Performance Task

Question 1.
Multiple teams adopt different sections of a state highway to clean. The teams must clean both sides of their adopted section of the highway.
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 1
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 2
a. The teams clean their section of the highway over 4 days. They clean the same distance each day.How many miles of the highway does each team clean each day?
b. Each team divides their daily distance equally among each team member. Which team’s members clean the greatest distance each day?
c. The team that collects the greatest amount of litter per team member wins a prize.Which team wins the prize?
Answer:

Question 2.
In a community, 25 people volunteer to clean the rectangular park shown. The park is divided into sections of equal area. One section is assigned to each volunteer. What is the area of the section that each volunteer cleans? What is one possible set of dimensions for 24.5 m each section?
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 3
Answer:

Divide Decimals Activity

Race Around the World: Division
Directions:
1. Players take turns.
2. On your turn, flip a Race Around the World: Division Card and find the quotient.
3. Move your piece to the next number on the board that is highlighted in the quotient.
4. The first player to make it back to North America wins!
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals 4
Answer:

Divide Decimals Chapter Practice

7.1 Division Patterns with Decimals

Find the quotient.
Question 1.
25 ÷ 102 = ______
Answer:
First Simplify the 102 which means  10 x 10  =100, then we need to calculate the fraction to a decimal just divide the numerator (25) by the denominator (100).
When we divide by 100, the decimal point moves two places to the left.
25 ÷ 102 = 0.25.

Question 2.
1.69 ÷ 0.01 = ______
Answer: To convert this simple fraction to a decimal just divide the numerator (1.69) by the denominator (0.01). When we divide by 0.01, the decimal point moves two places to the right.

1.69 ÷ 0.01 = 169.

Question 3.
681 ÷ 103 = ______
Answer:
First Simplify the 103 which means  10 x 10 x 10 =1000, then we need to calculate the fraction to a decimal just divide the numerator (681) by the denominator (1000).
When we divide by 1000, the decimal point moves three places to the left.
681 ÷ 103 = 0.681.

Question 4.
5.7 ÷ 0.1 = _____
Answer:
To convert this simple fraction to a decimal just divide the numerator (5.7) by the denominator (0.1). When we divide by 0.1, the decimal point moves one places to the right.
5.7 ÷ 0.1 = 57

Question 5.
200 ÷ 0.01 = _____
Answer:
To convert this simple fraction to a decimal just divide the numerator 200 by the denominator (0.01). When we divide by 0.01, the decimal point moves one places to the right.

Question 6.
41.3 ÷ 10 = _____
Answer: To convert this simple fraction to a decimal just divide the numerator (41.3) by the denominator (10). When we divide by 10, the decimal point moves one places to the left.
41.3 ÷ 10 = 4.13

Find the value of k.
Question 7.
74 ÷ k = 7,400
Answer:
74 ÷ 7400 = k

Explanation: To convert this simple fraction to a decimal just divide the numerator (74) by the denominator (7400). When we divide by 100, the decimal point moves two places to the left.
74 ÷ 7400 = 0.01
k = 0.01.

Question 8.
k ÷ 0.1 = 8.1
Answer:
k = 8.1 x 0.1
k = 0.81.

Question 9.
0.35 ÷ k = 0.035
Answer:
0.35 ÷ 0.035 = k
Explanation: To convert this simple fraction to a decimal just divide the numerator (0.35) by the denominator (0.035). When we divide by 0.01, the decimal point moves two places to the right.
0.35 ÷ 0.035 = 10
k = 10.

7.2 Estimate Decimal Quotients

Estimate the quotient.
Question 10.
9.6 ÷ 2
Answer:
9.6 is closer to 10.
10 ÷ 2 = 5
9.6 ÷ 2 is about 5.

Question 11.
37.2 ÷ 6.4
Answer:
Round the divisor 6.4 to 6.
Think: What numbers close to 37.2 are easily divided by 6?
Use 36.
36 ÷ 6 = 6
So, 37.2 ÷ 6.4 is about 6.

Question 12.
44.8 ÷ 4.7
Answer:
Round the divisor 4.7 to 5.
Think: What numbers close to 44.8 are easily divided by 5?
Use 45.
45 ÷ 5 = 9
So, 44.8 ÷ 4.7 is about 9.

Question 13.
78.2 ÷ 10.8
Answer:
Round the divisor 10.8 to 11.
Think: What numbers close to 78.2 are easily divided by 11?
Use 77.
77 ÷ 11 = 7
So, 78.2 ÷ 10.8 is about 7.

7.3 Use Models to Divide Decimals by Whole Numbers

Use the model to find the quotient.
Question 14.
1.4 ÷ 2
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals chp 14
Answer:
Think: 1.4 is 1 ones and 4 tenths.
14 tenths can be divided equally as 2 groups of 7 tenths.
1.4 ÷ 2 = 0.7

Question 15.
2.85 ÷ 3
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals chp 15
Answer:
Think: 2.85 is 2 ones, 8 tenths and 5 hundredths.
28 tenths can be divided equally as 3 groups of 9 tenths with remainder 1. Remainder has to place before 5 hundredths.
15 hundredths can be divided equally as 3 groups of 5 hundredths.
So, 285 hundredths can be divided equally as 3 groups of 95 hundredths.
2.85 ÷ 3 = 0.95

Use a model to find the quotient.
Question 16.
1.28 ÷ 4
Answer:
Think: 1.28 is 1 ones, 2 tenths and 8 hundredths.
12 tenths can be divided equally as 4 groups of 3 tenths
8 hundredths can be divided equally as 4 groups of 2 hundredths.
So, 128 hundredths can be divided equally as 4 groups of 32 hundredths.
1.28 ÷ 4 = 0.32

Question 17.
3.5 ÷ 5
Answer:
Think: 3.5 is 3 ones and 5 tenths.
35 tenths can be divided equally as 5 groups of 7 tenths.
3.5 ÷ 5 = 0.7

7.4 Divide Decimals by One-Digit Numbers

Find the quotient. Then check your answer.
Question 18.
\(\sqrt [ 3 ]{ 14.1 } \)
Answer:
Divide the ones
14 ÷ 3
4 ones x 3 = 12
14 ones – 12 ones
There are 2 ones left over.
Divide the tenths
21 ÷ 3 = 7 tenths.
So, 14.1 ÷ 3 = 4.7

Question 19.
\(\sqrt [ 6 ]{ 67.68 } \)
Answer:
Divide the ones
67 ÷ 6
11 ones x 6 = 66
67 ones – 66 ones
There are 1 ones left over.
Divide the tenths
16 ÷ 6
2 tenths x 6 = 12
16 – 12 = 4
There are 4 tenths left over.
Divide the hundredths
48 ÷ 6 = 8 hundredths.
So, 67.68 ÷ 6 = 11.28

Question 20.
\(\sqrt [ 8 ]{ 105.6 } \)
Answer:
Divide the ones
105 ÷ 8
13 ones x 8 = 104
105 ones – 104 ones
There are 1 ones left over.
Divide the tenths
16 ÷ 8 = 2 tenths.
So, 105.6 ÷ 8 = 13.2

Question 21.
Number Sense
Evaluate (84.7 + 79.8) ÷ 7.
Answer:
(84.7 + 79.8) ÷ 7 = 164.5 ÷ 7
Divide the ones
164 ÷ 7
23 ones x 7 = 161
164 ones – 161 ones
There are 3 ones left over.
Divide the tenths
35 ÷ 7
5 tenths x 7
35 – 35 = 0
There are 0 tenths left over.
So, 164.5 ÷ 7 = 23.5

7.5 Divide Decimals by Two-Digit Numbers

Find the quotient. Then check your answer.
Question 22.
\(\sqrt [ 32 ]{ 45.12 } \)
Answer:
Divide the ones
45 ÷ 32
1 ones x 32 = 32
45 ones – 32 ones
There are 13 ones left over.
Divide the tenths
131 ÷ 32
4 tenths x 32 = 128
131 – 128 = 3
There are 3 tenths left over.
Divide the hundredths
32 ÷ 32 = 1 hundredths.
So, 45.12 ÷ 32 = 1.41

Question 23.
\(\sqrt [ 15 ]{ 9.15 } \)
Answer:
Divide the tenths
91 ÷ 15
6 tenths x 15 = 90
91 – 90 = 1
There are 1 tenths left over.
Divide the hundredths
15 ÷ 15 = 1 hundredths.
So, 9.15 ÷ 15 = 0.61

Question 24.
\(\sqrt [ 73 ]{ 102.2 } \)
Answer:
Divide the ones
102 ÷ 73
1 ones x 73 = 73
102 ones – 73 ones
There are 29 ones left over.
Divide the tenths
292 ÷ 73 = 4 tenths.
So, 102.2 ÷ 73 = 1.4

Question 25.
17.4 ÷ 87 = ______
Answer:
Divide the tenths
174 ÷ 87
2 tenths x 87
174 – 174 = 0
There are 0 tenths left over.
17.4 ÷ 87 = 0.2

Question 26.
245.82 ÷ 51 = _______
Answer:
Divide the ones
245 ÷ 51
4 ones x 51 = 204
245 ones – 204 ones
There are 41 ones left over.
Divide the tenths
418 ÷ 51
8 tenths x 51
418 – 408 = 10
There are 10 tenths left over.
Divide the hundredths
102 ÷ 51 = 2 hundredths
So, 245.82 ÷ 51 = 4.82

Question 27.
5.88 ÷ 42 = ______
Answer:
Divide the tenths
58 ÷ 42
1 tenths  x 42 = 42
58 tenths – 42 tenths
There are 16 tenths left over.
Divide the hundredths
168 ÷ 42
4 hundredths x 42
168 – 168 = 0
There are 0 hundredths left over.
So, 5.88 ÷ 42 = 0.14

7.6 Use Models to Divide Decimals

Use the model to find the quotient.
Question 28.
0.9 ÷ 0.45 = ______
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals chp 28
Answer:
Shade 9 columns to represent 0.9.
Divide the model to show groups of 0.45.
There are 2 groups of 45 hundredths.
So, 0.9 ÷ 0.45 = 2

Question 29.
0.1 ÷ 0.05 = ______
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals chp 29
Answer:
Shade 1 column to represent 0.1.
Divide the model to show groups of 0.05.
There are 2 groups of 5 hundredths.
So, 0.1 ÷ 0.05 = 2

Question 30.
1.6 ÷ 0.4 = ______
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals chp 30
Answer:
Shade 16 columns to represent 1.6.
Divide the model to show groups of 0.4.
There are 4 groups of 4 tenths.
So, 1.6 ÷ 0.4 = 4

Question 31.
1.9 ÷ 0.38 = ______
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals chp 31
Answer:
Shade 19 columns to represent 1.9.
Divide the model to show groups of 0.38.
There are 5 groups of 38 hundredths.
So, 1.9 ÷ 0.38 = 5

7.7 Divide Decimals

Find the quotient. Then check your answer.
Question 32.
\(\sqrt [ 2.57 ]{ 20.56 } \)
Answer:
Multiply 2.57 by a power of 10 to make it a whole number. Then multiply 20.56 by the same power of 10.
2.57 x 100 = 257
20.56 x 100 = 2056
2056 ÷ 257 = 8
So, 20.56 ÷ 2.57 = 8.

Question 33.
\(\sqrt [ 4.7 ]{ 16.92 } \)
Answer:
Multiply 4.7 by a power of 10 to make it a whole number. Then multiply 16.92 by the same power of 10.
4.7 x 10 = 47
16.92 x 10 = 169.2
Step 2 : Divide 169.2 ÷ 47
169 ÷ 47 = 3 with remainder 28.
282 ÷ 47 = 6 with remainder 0.
So, 16.92 ÷ 4.7 = 3.6.

Question 34.
\(\sqrt [ 5.3 ]{ 63.6 } \)
Answer:
Multiply 5.3 by a power of 10 to make it a whole number. Then multiply 63.6 by the same power of 10.
5.3 x 10 = 53
63.6 x 10 = 636
636 ÷ 53 = 12
So, 63.6 ÷ 5.3 = 12.

7.8 Insert Zeros in the Dividend

Question 35.
\(\sqrt [ 4 ]{ 36.2 } \)
Answer:
36.2 ÷ 4
36 ÷ 4 = 9
Insert a zero in the dividend and continue to divide.
20 ÷ 4 = 5
So, 36.2 ÷ 4 = 9.05.

Question 36.
\(\sqrt [ 4.8 ]{ 85.2 } \)
Answer:
Multiply 4.8 by a power of 10 to make it a whole number. Then multiply 85.2 by the same power of 10.
4.8 x 10 = 48
85.2 x 10 = 852
852 ÷ 48
85 ÷ 48 = 1 with remainder 37.
372 ÷ 48 = 7 with remainder 36.
Insert a zero in the dividend and continue to divide.
360 ÷ 48 = 7 with remainder 24.
240 ÷ 48 = 5 with remainder 0.
So, 85.2 ÷ 4.8 = 17.75.

Question 37.
\(\sqrt [ 12 ]{ 52.2 } \)
Answer:
52.2 ÷ 12
52 ÷ 12 = 4 with remainder 4.
42 ÷ 12 = 3 with remainder 6.
Insert a zero in the dividend and continue to divide.
60 ÷ 12 = 5 with remainder 0.
So, 52.2 ÷ 12 = 4.35.

Question 38.
5 ÷ 0.8 = ______
Answer:
Multiply 0.8 by a power of 10 to make it a whole number. Then multiply 5 by the same power of 10.
0.8 x 10 = 8
5 x 10 = 50
50 ÷ 8
Insert a zero in the dividend and continue to divide.

8 ) 50 ( 6.25

48

——-

20

-16

——-

40

40

——–

0
So, 5 ÷ 0.8 = 6.25

Question 39.
23.7 ÷ 6 = ______
Answer:
Insert a zero in the dividend and continue to divide.

6 ) 23.7 ( 3.95

18

——-

57

– 54

——-

30

30

——–

0
23.7 ÷ 6 = 3.95

Question 40.
138.4 ÷ 16 = ______
Answer:
Insert a zero in the dividend and continue to divide.
16 ) 138.4 ( 8.65

128

——-

104

– 96

——–

80

80


7.9 Problem Solving: Decimal Operations

Question 41.
You spend $28.08 on the fabric scissors, buttons, and two craft kits. The kits each cost the same amount. How much does ASSORTED $6.13 each kit cost?
Big Ideas Math Answers 5th Grade Chapter 7 Divide Decimals chp 41
Answer:
Given that,
Total amount spent = $28.08
Fabric scissors cost = $6.13
Buttons cost = $3.97
Write and solve an equation to find the cost of each kit.
cost of each kit = (amount spend – fabric scissors cost – buttons cost) ÷ 2
= (28.08 – 6.13 – 3.97) ÷ 2
= 17.98 ÷ 2
= 8.99
So, cost of each craft kit = $8.99

Divide Decimals Cumulative Practice

Question 1.
Which statement is true?
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals cp 1
Answer:
According to BODMAS rule,
Statement c is correct.

Question 2.
You round 23 × 84 and get an underestimate. How did you estimate?
A. 20 × 80
B. 30 × 90
C. 25 × 90
D. 25 × 90
Answer:
23 × 84 round to 20 × 80 because it is closer to given equation.
84 is close to 80 and all the others options having number 90.
Difference between the numbers in remaining options is greater than the option A numbers.

Question 3.
Which expressions have a product that is shown?
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals cp 3
Answer:
Except option 1, remaining all the other options have the product(0.4) shown in the image.

Question 4.
What number is \(\frac{1}{10}\) of 800?
A. 0.8
B. 8
C. 80
D. 8,000
Answer:
\small \frac{1}{10} (800) = 80

Question 5.
Which number divided by 0.01 is 14 more than 37?
A. 0.51
B. 5.1
C. 51
D. 5,100
Answer:
14 more than 37 = 37 + 14 = 51
51 x 0.01 = 0.51
So, the answer is 0.51.

Question 6.
Which expressions have a quotient of 40?
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals cp 6
Answer:
2800 ÷ 70, 160 ÷ 4, 3600 ÷ 900 and 8000 ÷ 200 have a quotient of 40.

Question 7.
Which equation is shown by the quick sketch?
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals cp 7
Answer:

Question 8.
What is the value of k?
0.036 × k = 36
A. 10
B. 103
C. 100
D. 36
Answer:
k = 36 ÷ 0.036
k = 1000 = 103(option B).

Question 9.
What is the quotient of 11.76 and 8?
A. 1.47
B. 1.97
C. 14.7
D. 94.08
Answer:
11.76 ÷ 8
11 ÷ 8 = 1 with remainder 3.
37 ÷ 8 = 4 with remainder 5.
56 ÷ 8 = 7 with remainder 0.
So, quotient of 11.76 and 8 = 1.47(option A).

Question 10.
Newton wins a race by seven thousandths of a second. What is this number in standard form?
A. 0.007
B. 0.07
C. 0.7
D. 7,00
Answer:
0.007 is in standard form.

Question 11.
Evaluate 30 – (9 + 6) ÷ 3.
A. 5
B. 19
C. 9
D. 25
Answer:
According to BODMAS rule.
30 – (9 + 6) ÷ 3
= 30 – (15 ÷ 3)
= 30 – 5
= 25

Question 12.
A food truck owner sells 237 gyros in 1 day. Each gyro costs $7.How much money does the owner collect in 1 day?
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals cp 12
A. $659
B. $1,419
C. $1,659
D. $11,249
Answer:
Each gyro costs $7
237 gyros in 1 day cost = 237 x 7 = $1659
So, the owner collects $1659 in 1 day.

Question 13.
What is the quotient of 4,521 and 3?
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals cp 13
Answer:
4521 ÷ 3 = 1507
So, quotient of 4,521 and 3 is 1507.

Question 14.
What is the value of b?
104 = 10b × 10
A. 3
B. 4
C. 5
D. 10
Answer:
104 = 10b × 10
If b= 3,
10b × 10 = 103 × 10
= 103+1
= 104
So, b= 3.

Question 15.
Part A What is the area of the sandbox?
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals cp 15
Part B The playground committee wants to make the area of the sandbox 2 times the original area. What is the new area? Explain.
Answer:

Question 16.
Which expressions have a product of 1,200?
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals cp 16
Answer:
30 x 40, 12 x 102 and 120 x 10 have a product of 1,200.

Question 17.
A 5-day pass to a theme park costs $72.50. A 2-day pass to the same park costs $99.50. How much more does the 2-day pass cost each day than the 5-day pass each day?
A. $14.50
B. $35.25
C. $49.75
D. $64.25
Answer:
5-day pass costs each day = 72.5 ÷ 5 = $14.5
2-day pass costs each day = 99.5 ÷ 2 = $49.75
2-day pass cost each day $35.25 more than the 5-day pass each day.

Question 18.
Which expressions have a quotient with the first digit in the tens place?
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals cp 18
Answer:
4,536 ÷ 56 = 81
6,750 ÷ 45 = 150
2,403 ÷ 89 = 27
1,496 ÷ 17 = 88
Except option 2, all the other options have a quotient with the first digit in the tens place.

Divide Decimals STEAM Performance Task

You experiment with levers for your school’s science fair.
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals spt 1
Question 1.
You balance the seesaw lever by placing different weights on either side at different distances from the middle. You find the formula for balancing the seesaw lever is (left weight) × (left distance) = (right weight) × (right distance). You test the formula using various combinations of weights.
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals spt 2
a. Use the formula to complete the table for the 2nd and 3rd attempts.
b. For your 4th attempt, you have up to 25 pounds in weights to place on each side of the lever. Choose a whole pound weight for the left side and balance the lever to complete the table.
c. The total length of your seesaw lever is 40 inches. Can you balance a 50-pound weight with a 1-pound weight? Explain.
d. For your science fair display, you balance the lever by placing another gram weight on the right side. Which gram weight should you use?
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals spt 3
e. How can you apply what you learn from the science fair project to a playground?
Answer:

You help set up tables for the science fair. There are 93 science fair displays. You use the display boards to determine how many tables to use.
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals spt 4
Question 2.
Each display board opens up to form three sides of a trapezoid as shown.
a. How much room do you think each display board needs to open up? Explain.
b. You place the display boards next to each other on 12-foot long tables. How many display boards can you fit on one table?
c. You use one table for snacks and one table for award ribbons. What is the least number of tables you can use? Explain.
d. The diagram shows the room where the science fair is held. Each table for the science fair is 3 feet wide. Your teacher says the ends of the tables can touch to save space. Complete the diagram to arrange the tables so that visitors and judges can see each display board.
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals spt 5
Answer:

Question 3.
Use the Internet or some other resource to learn about other types of science fair projects. Describe one interesting science fair project you want to complete.
Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals spt 6
Answer:  One of the interesting science fair project is :-
                                                          How To Make A Bottle Rocket
-> Did you know you can make and launch a water bottle rocket using a plastic bottle, water, cork,           needle adaptor and pump ?
How do water bottle rockets work?
As you pump air into the bottle the pressure inside the bottle builds up until the force of the air pushing on the water is enough to  force the cork out of the end of the bottle. The water rushes out of the bottle in one direction whilst the bottle pushes back in the other. This results in the bottle shooting upwards.
 What you need to make a bottle rocket
 ->  An empty plastic bottle
->  Cardboard made into a cone and 4 fins
->  A cork
->  A pump with a needle adaptor
->  Water
You can buy a kit with the parts apart from the pump and the bottle-please check the contents before buying.
Instructions – How to make a bottle rocket
Push the needle adaptor of the pump through the cork, it needs to go all the way through so you might have to trim the cork a little bit.
-> Decorate the bottle with the cone and fins.
-> Fill the bottle one quarter full of water and push the cork in tightly.
-> Take the bottle outside and connect the pump to the needle adaptor. Ours wouldn’t stand up on the fins so we rested it on a box, but if you make some strong fins it should stand up by itself.
-> Pump air into the bottle, making sure all spectators stand back, the bottle will lift off with force after a few seconds.
Why does the water bottle rocket launch?
As you pump air into the bottle pressure builds up inside. If you keep pumping, the force of the air pushing on the water eventually becomes strong enough to force the cork out of the bottle allowing water to rush out in one direction while the bottle pushes back in the other direction. This forces the rocket upwards.
Space

Conclusion:

I wish the information provided in the above article regarding Big Ideas Math Book 5th Grade Answer Key Chapter 7 Divide Decimals is helpful for you. For any queries, you can post the comments in the below section.

Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths

Big Ideas Math Answers Grade 2 Chapter 11

Big Ideas Math 2nd Grade Chapter 11 Measure and Estimate Lengths Answers: Have a look at the free step-by-step explanation for all questions on Big Ideas Math Grade 2 Chapter 11 Measure and Estimate Lengths Book is provided here. The answers for the questions of grade 2 chapter 11 are in pdf format. So, download Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths PDF for free of cost and begin the preparation.

Big Ideas Math Book Grade 2 Answer Key Chapter 11 Measure And Estimate Lengths

Students who want to improve their math skills can refer to this Big Ideas Math 2nd Grade 11th Chapter Measure And Estimate Lengths Solutions and prepare well. By solving the questions, you can know how to use a ruler to measure lengths, compare the measurements of different objects. One can finish their homework easily by checking Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths. Click on the topic-wise links mentioned below to get the answers for all types of questions related to Measure And Estimate Lengths.

Vocabulary

Lesson: 1 Measure Lengths in Centimeters

Lesson: 2 Measure Objects Using Metric Length Units

Lesson: 3 Estimate Lengths in Metric Units

Lesson: 4 Measure Lengths in Inches

Lesson: 5 Measure Objects Using Customary Length Units

Lesson: 6 Estimate Lengths in Customary Units

Lesson: 7 Measure Objects Using Different Length Units

Lesson: 8 Measure and Compare Lengths

Chapter 11: Measure And Estimate Lengths 

Measure And Estimate Lengths Vocabulary

Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths v 1
Organize It
Use the review words to complete the graphic organizer.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths v 2

Answer: Tree is measured bu Height and Bird is measured by Length

Define It
Use your vocabulary cards to match.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths v 3

Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths v 4
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths v 5

Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths v 6
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths v 7

Lesson 11.1 Measure Lengths in Centimeters

Explore and Grow

Use a centimeter cube to find the length of each string.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 1
Answer:

Explain how you measured.
______________________
______________________
______________________
Answer: The centimeters were measured by Scale.

Show and Grow

Measure.
Question 1.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 2
about _______ centimeters
Answer: 1 centimeters

Question 2.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 3
about ________ centimeters
Answer: 12 centimeters

Question 3.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 4
about ______ centimeters
Answer: 20 centimeters

Apply and Grow: Practice

Measure.
Question 4.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 5
about ______ centimeters
Answer: 15 centimeters

Question 5.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 6
about ______ centimeters
Answer: 4 centimeters

Question 6.
Draw a pencil that is about 9 centimeters long.
Answer:
Big Ideas Math Grade 2 Answers Chapter 11 img_1

Question 7.
YOU BE THE TEACHER
Newton says the ribbon is about 14 centimeters long. Is he correct? Explain.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 7
_______________________
_______________________
Answer: No. It is not correctly measured on a scale. It should be measured from 0 cm to 14 cms.

Think and Grow: Modeling Real Life

Will the hammer fit inside a toolbox that is 40 centimeters long? Explain.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 8
______________________
______________________
Answer: The toolbox will be around 50 centimeters long, So the Hammer with 40 centimeters will fit in it.

Show and Grow

Question 8.
Will the sunglasses fit inside a case that is 10 centimeters long? Explain.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 9
________________________
________________________
Answer: Yes, Sunglasses will fit inside the case that is 10 centimeters as Sunglasses will be around 9 centimeters.

Measure Lengths in Centimeters Homework & Practice 11.1

Measure.
Question 1.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 10
about ______ centimeters
Answer: about 8 centimeters

Question 2.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 11
about _______ centimeters
Answer: about 15 centimeters

Question 3.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 12
about _______ centimeters
Answer: about 3 centimeters

Question 4.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 13
about _______ centimeters
Answer: about 6 centimeters

Question 5.
Precision
Which crayon is shorter than 8 centimeters?
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 14
Answer: Yellow and Green crayons are shorter than 8 centimeters.

Question 6.
Modeling Real Life
Will the pen fit inside a pouch that is 18 centimeters long? Explain.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 15
______________________
_______________________
Answer: Yes the pen will fit inside a pouch that is 18 centimeters long as the pen is around 15 centimeters.

Review & Refresh

Question 7.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 16
Answer: 55
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-11-Measure-And-Estimate-Lengths-11.1-0-Answer

Question 8.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 17
Answer: 90
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-11-Measure-And-Estimate-Lengths-11.1-01-Answer

Question 9.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.1 18
Answer: 101
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-11-Measure-And-Estimate-Lengths-11.1-02-Answer

Lesson 11.2 Measure Objects Using Metric Length Units

Explore and Grow

Which real-life objects are shorter than a centimeter ruler?
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 1
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-11-Measure-And-Estimate-Lengths-11.2-1-Answer

Show and Grow

Find and measure the object shown in your classroom.
Question 1.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 2
about _______ meter
Answer: 3 meter

Question 2.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 3
meter ______ centimeters
Answer: 3 centimeters

Question 3.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 4
about _______ meters
Answer: 2 meter

Apply and Grow: Practice

Find and measure the object shown in your classroom.
Question 4.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 5
about _______ meters
Answer: 3 meters

Question 5.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 6
about ______ centimeters
Answer: 15 centimeters

Question 6.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 7
about _______ meters
Answer: 2 meters

Question 7.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 8
about ______ centimeters
Answer: 30 centimeters

Question 8.
Choose Tools
Would you measure the length of a bus with a centimeter ruler or a meter stick? Why?
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 9
________________________
________________________
Answer: The length of a bus can be measured with a meter stick because the bus is big inside.
The centimeter-scale is small and the meter scale is big.

Think and Grow: Modeling Real Life

Your friend says a car has a length of about 4. Is the car about 4 meters long or about 4 centimeters long? Explain.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 10
The car is about 4 ________ long.
________________________
________________________
Answer: The car is about 4 meters long.

Show and Grow

Question 9.
Your friend says a shoe has a length of about 12. Is the shoe about 12 centimeters long or about 12meters long? Explain.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 11
The shoe is about 12 ____________ long.
______________________
______________________
Answer: The shoe is about 12 centimeters long.

Question 10.
DIG DEEPER!
Your friend places 2 of the same real objects end to end. Together, they have a length of about 18 centimeters. Which object did your friend use? Explain.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 12
_________________________
_________________________
Answer: 1st and 2nd object together will be 18 centimeters. As 3rd object will be larger than 18 centimeters.

Measure Objects Using Metric Length Units Homework & Practice 11.2

Find and measure the object.
Question 1.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 13
about ______ meters
Answer: 7 meters

Question 2.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 14
about ______ centimeters
Answer: about 1000 centimeters

Question 3.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 15
about ______ centimeters
Answer: 20 centimeters

Question 4.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 16
about ______ meters
Answer: 3 meters

Question 5.
Number Sense
Complete the sentences using centimeters or meters.
A window is about 2 ________ long.
Answer: A window is about 2 meters long.
A finger is about 8 ______ long.
Answer: A finger is about 8 centimeters long.
A zucchini is about 12 _______ long.
Answer: A zucchini is about 12 centimeters long.
An airplane is about 20 _______ long.
Answer: An airplane is about 20 meters long.

Question 6.
Modeling Real Life
Your friend says that the length of a soccer field is about 91. Is the soccer field about 91 centimeters long or about 91 meters long? Explain.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 17
The soccer field is about 91 _______ long.
______________________
_______________________
Answer: The soccer field is about 91 meters long.

Question 7.
DIG DEEPER!
Order the lengths from shortest to longest.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.2 18
_________, _________, _________
Answer: 3 centimeters, 1 meter, 200 centimeter.

Review & Refresh

Question 8.
3 + 7 = _____ + 3
Answer: 7+3
The commutative property of addition says that changing the order of addends does not change the sum.
So, 3 + 7 = 7 + 3

Question 9.
5 + 4 = 4 + ______
Answer: 4+5
The commutative property of addition says that changing the order of addends does not change the sum.
So, 5 + 4 = 4 + 5

Question 10.
6 + 0 = ____ + 6
Answer: 0+6
The commutative property of addition says that changing the order of addends does not change the sum.
So, 6 + 0 = 0 + 6

Question 11.
1 + 2 = 2 + ____
Answer: 2+1
The commutative property of addition says that changing the order of addends does not change the sum.
So, 1 + 2 = 2 + 1

Lesson 11.3 Estimate Lengths in Metric Units

Explore and Grow

Find an object that is shorter than the string.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 1
Without using a ruler, tell how long you think the object is.

Answer: Pencil
______ centimeters

Answer: 12 centimeters
Explain.
________________________
________________________
Answer: The Pencil is around 12 centimeters which is shorter than the 13 centimeters string.

Show and Grow

Question 1.
The chalk is about 8 centimeters long. What is the best estimate of the length of the toothpick?
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 2
Answer: 6 centimeters

Question 2.
The fishing pole is about 1 meter long. What is the best estimate of the length of the alligator?
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 3
Answer: 3 meters

Apply and Grow: Practice

Question 3.
The hover board is about 1 meter long. What is the best estimate of the length of the surfboard?
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 4
Answer: 2 meters

Question 4.
The pineapple is about 25 centimeters long. What is the best estimate of the length of the asparagus?
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 5
Answer: 20 centimeters

Question 5.
What is the best estimate of the length of a piece of notebook paper?
21 centimeters
1 meter
5 centimeters
Answer: 21 centimeters

Question 6.
What is the best estimate of the height of a traffic light?
1 meter
5 meter
30 centimeters
Answer: 5 meter

Question 7.
Precision
Match.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 6
Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-11-Measure-And-Estimate-Lengths-11.3-6-Answer

Think and Grow: Modeling Real Life

The leaf is about 8 centimeters long. Draw a tree branch that is about 16 centimeters long.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 7
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-11-Measure-And-Estimate-Lengths-11.1-Answer

Show and Grow

Question 8.
The piece of celery is about 10 centimeters long. Draw a carrot that is about 5 centimeters long.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 8
Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-11-Measure-And-Estimate-Lengths-11.3-8

Question 9.
DIG DEEPER!
Each bead is about 2 centimeters long. Draw a rectangular bead that is about 3 centimeters long.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 9
How did you use the length of the given beads to draw the rectangular bead?
________________________
__________________________
Answer:
The length of given rectangular beads were measured with scale.

Estimate Lengths in Metric Units Homework & Practice 11.3

Question 1.
The swimming pool is about 12 meters long. What is the best estimate of the length of the raft?
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 10
Answer: 2 meters
Explanation: The length of the Swimming pool is 12 meters long, the raft length will be 2 meters as it is very small.

Question 2.
What is the best estimate of the height of a tulip?
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 11
Answer: 4 meters
Explanation: The height of the tulip is big so, It can be estimated by 4 meters.

Question 3.
What is the best estimate of the height of a giraffe?
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 12
Answer: 50 meters.
Explanation: The height of the giraffe is big so it can be estimated by 50 meters.

Question 4.
Logic
Newton says the best estimate for the height of a skyscraper is 4 meters. Do you agree? Explain.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 13
_______________________
_______________________
Answer: No, The skyscraper’s estimated height is 150 meters.

Question 5.
Modeling Real Life
A granola bar is about 9 centimeters long. Draw its wrapper that is about 12 cm long.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 14
Answer:
BIM Grade 2 Answer Key Chapter 2 img_2

Review & Refresh

Is the equation true or false?
Question 6.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 15
Answer: True
Explanation: 13-5=8 and 15-7=8, they are equal.

Question 7.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 16
Answer: False
3+6=9 and 11-3=8, They are not equal.

Question 8.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 17
Answer: True
Explanation: 2+10=12 and 6+6=12

Question 9.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.3 18
Answer: False
14-9=5 and 4+9=13

Lesson 11.4 Measure Lengths in Inches

Explore and Grow

Use an inch tile to find the length of each string.
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.4 1
Explain how you measured.
______________________
______________________
Answer: It is measured with inch scale.

Show and Grow

Measure.
Question 1.
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.4 2
about _______ inches
Answer: about 3 inches

Question 2.
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.4 3
about ______ inch
Answer: about 1 inch

Question 3.
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.4 4
about _______ inches
Answer: about 6 inches.

Apply and Grow: Practice

Measure.
Question 4.
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.4 5
about ______ inches
Answer: about 6 inches

Question 5.
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.4 6
about ______ inches
Answer: about 2 inches

Question 6.
Draw a crayon that is about 4 inches long.
Answer:

Question 7.
YOU BE THE TEACHER
Your friend says the watch is about 6 inches long. Is your friend correct? Explain.
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.4 7
Answer: It is 6 inches but it should be measured from 0 inch to 6 inches.

Think and Grow: Modeling Real Life

Will the toothbrush fit inside a case that is 4 inches long? Explain.
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.4 8
_________________________
_________________________
Answer: No
Explantion: It cannot be fit in 4 inches case because the toothbrush is about 8 inches long.

Show and Grow

Question 8.
Will the colored pencil fit inside a pencil box that is 8 inches long? Explain.
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.4 9
________________________
__________________________
Answer: Yes
Explanation: The colored pencil can be fit in pencil box as colored pencil will be about 5 inches long.

Measure Lengths in Inches Homework & Practice 11.4

Measure.
Question 1.
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.4 10
about _____ inch
Answer: About 2 inch.

Question 2.
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.4 11
about _______ inches
Answer: about 3 inches.

Question 3.
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.4 12
about _____ inches
Answer: about 6 inches.

Question 4.
YOU BE THE TEACHER
Newton says the highlighter is about 5 centimeters long. Is he correct? Explain.
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.4 13
______________________
_______________________
Answer: No, The highlighter will be about 11 centimeters long,  So Newton is wrong as 5 centimeters is very small.

Question 5.
Modeling Real Life
Will the screwdriver fit inside a case that is 5 inches long? Explain.
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.4 14
____________________________
____________________________
Answer: Yes
Explanation: The screwdriver will be about 4.5 inches long so it will fit in 5 inches case.

Review & Refresh

Question 6.
Write how many tens. Circle groups of 10 tens. Write how many hundreds. Then write the number.
_____ tens ______ hundreds _____
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.4 15
Answer: 50 tens 5 hundreds 500

Lesson 11.5 Measure Objects Using Customary Length Units

Explore and Grow

Which real-life objects are longer than an inch ruler?
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.5 1
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-11-Measure-And-Estimate-Lengths-11.5-1-Answer

Show and Grow
Find the object shown in your classroom. Choose an inch ruler, a yardstick, or a measuring tape to measure the object. Then measure.
Question 1.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.5 2
Tool: _______
Length: about _________
Answer: Tool: Inch ruler
Length: about 14 inches

Question 2.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.5 3
Tool: _______
Length: about ________
Answer: Tool: Yardstick
Length: 2 meters

Question 3.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.5 4
Tool: _______
Length: about _________
Answer: Toot: Measuring tape
Length: about 15 centimeters

Apply and Grow: Practice

Find the object shown in your classroom. Choose an inch ruler, a yardstick, or a measuring tape to measure the object. Then measure.
Question 4.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.5 5
Tool: __________
Length: about ________
Answer: Tool: inch ruler
Length: about 3 inches

Question 5.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.5 6
Tool: _________
Length: about ____________
Answer: Tool: measuring tape
Length: about 200 centimeters

Question 6.
Find and measure an object using a measuring tape.
Object: _________
Length: about __________
Answer: Object: Chair
Length: about 100 centimeters

Question 7.
Find and measure an object using an inch ruler.
Object: ________
Length: about _________
Answer: Object: Phone
Length: about 6 inches

Question 8.
Choose Tools
Would you measure the length of the playground with an inch ruler or a yardstick? Explain.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.5 7
______________________
______________________
Answer: The length of the playground can be measured with a yardstick because the yardstick is long and it will be easy to measure long objects like length of playground.

Think and Grow: Modeling Real Life

Your friend says her height is about 4. Is she about 4 inches tall, about 4 feet tall, or about 4 yards tall? Explain.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.5 8
She is about 4 ______ tall.
______________________
______________________
Answer: She is about 4 feet tall
Explanation: The height of a person is measured in feet.

Show and Grow

Question 9.
Your friend says the length of a baseball bat is about 1. Is the bat about 1 inch long, about 1 foot long, or about 1 yard long? Explain.
________ long.
_________________________
_________________________
Answer: 1 foot long
Explanation: The length a baseball bat is 1 foot long.

Question 10.
Your friend says the length around an orange is about 9. Is the length about 9 inches long, about 9 feet long, or about 9 yards long? Explain.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.5 9
The length is about 9 ________ long.
________________________
_________________________
Answer: The length is about 9 inches long.
Explanation: The orange is small object so it can be measured in inches.

Measure Objects Using Customary Length Units Homework & Practice 11.5

Find the object shown. Choose an inch ruler, a yardstick, or a measuring tape to measure the object. Then measure.
Question 1.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.5 10
Tool: ______
Length: about _______
Answer:

Question 2.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.5 11
Tool: _______
Length: about ____________
Answer: Object: Basket
Tool: Measuring tape
Length: about 60 centimeters

Question 3.
Find and measure an object using an inch ruler.
Object: _________
Length: about __________
Answer: Object: Pencil
Length: about 8 inches

Question 4.
Find and measure an object using a yard stick.
Object: ____________
Length: about __________
Answer:Object: Door
Length: about 3 meter

Question 5.
YOU BE THE TEACHER
Descartes says the best tool to measure the length around a basketball is an inch ruler. Is he correct? Explain.
________________________
________________________
Answer: No
Explanation: The length of the basketball cannot be measured with inch ruler, it can be measured with measuring tape.

Question 6.
Modeling Real Life
Your friend says that the length of a toothbrush is about 8. Is the toothbrush about 8 inches, about 8 feet, or about 8 yards long? Explain.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.5 12
The toothbrush is about 8 _______ long.
________________________
________________________
Answer: The toothbrush is about 8 inches long
Explanation: The toothbrush is small object so it can be measured with inch ruler.

Question 7.
DIG DEEPER!
Order the lengths from shortest to longest.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 11.5 13
Answer: 2 feet       1 yard       39 inches
Explanation: 1 feet=12 inches, 12+12=24 inches
1 yard=36 inches

Review & Refresh

Question 8.
You read for 55 minutes. Your friend reads 28 fewer minutes. How many minutes does your friend read?
_____ minutes
Answer: 27 minutes

Explanation:
Given,
You read for 55 minutes. Your friend reads 28 fewer minutes.
28 – 55 = 27
Thus your friend read for 27 minutes

Question 9.
You score 23 points. Your two friends score 56 and 18 points. How many points do you and your friends score in all?
______ points
Answer: 97 points

Explanation:
Given,
You score 23 points. Your two friends score 56 and 18 points.
23 + 56 + 18 = 97 points
Thus you and your friend score 97 points in all/

Lesson 11.6 Estimate Lengths in Customary Units

Explore and Grow

Find an object that is shorter than the string. Draw the object.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.6 1
Without using a ruler, tell how long you think the object is.
______ inches
Explain
____________________________
____________________________
Answer: Crayon, 4 inches
Explanation: The crayon is about 4 inches and it is shorter than 5 inches string.

Show and Grow

Question 1.
The pipe cleaner is about 3 inches long. What is the best estimate of the length of the craft stick?
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.6 2
Answer: The length of craft stick is 4 inches.

Question 2.
The dog leash is about 5 feet long. What is the best estimate of the length of the dog collar?
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.6 3
Answer: The length of the dog collar is about 1 foot.

Apply and Grow: Practice

Question 3.
The poster is about 18 inches long. What is the best estimate for the length of the bed?
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.6 4
Answer: The length of bed is about 75 inches.

Question 4.
The jump rope is about 6 feet long. What is the best estimate of the length of the dog?
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.6 5
Answer: The length of the dog is about 4 feet.

Question 5.
What is the best estimate of the length of a garage?
8 inches
8 feet
8 yards
Answer: The length of a garage is about 8 yards.

Question 6.
What is the best estimate of the height of a flag pole?
20 inches
20 feet
20 yards
Answer: The height of a flag pole is about 20 yards.

Question 7.
Precision
Match
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.6 6
Answer:
Convert from feet and yards to inches.
1 feet = 12 inches
5 feet = 60 inches
1 yard = 36 inches
5 yard = 180 inches

Think and Grow: Modeling Real Life

The sticker is about 1 inch long. Draw another sticker that is about 2 inches long.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.6 7
Answer:
Big Ideas Math Grade 2 Chapter 11 Answer Key img_3

Show and Grow

Question 8.
The worm is about 4 inches long. Draw a caterpillar that is about 2 inches long.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.6 8
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-11-Measure-And-Estimate-Lengths-11.6-8

Question 9.
DIG DEEPER!
Each toy truck is about 2 inches long. Draw a building block that is about 3 inches long.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.6 9
How did you use the length of the toy trucks to draw the building block?
__________________________
____________________________
Answer: You can expand the length of the toy trucks to draw the building block.

Estimate Lengths in Customary Units Homework & Practice 11.6

Question 1.
The driveway is about 20 yards long. What is the best estimate of the length of the truck?
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.6 10
Answer: The length of the truck is about 15 yards.

Question 2.
What is the best estimate of the height of a basketball hoop?
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.6 11
Answer: The height of the basket hoop is about 3 yards.

Question 3.
What is the best estimate of the length of a hair brush?
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.6 12
Answer: The length of a hair brush is about 8 inches.

Question 4.
Logic
Descartes says the best estimate for the height of the Statue of Liberty is 5 yards. Do you agree? Explain.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.6 13
_______________________
_______________________
Answer: No, The height of the Statue of Liberty is 5 yards.
Explanation: The height of the statue of liberty is very tall, it is about 100 yards.

Question 5.
Modeling Real Life
The bug is about 4 inches long. Draw a bug that is about 2 inches long.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.6 14
Answer:
BIM Grade 2 Chapter 11 Answer Key img_4

Question 6.
DIG DEEPER!
Each paperclip is about 2 inches long. Draw a pen that is about 5 inches long.
Big Ideas Math Answers 2nd Grade Chapter 11 Measure And Estimate Lengths 11.6 15
Answer:

Review & Refresh

Question 7.
12 − 4 = ______
Answer: 8

Question 8.
15 − 6 = ________
Answer: 9

Lesson 11.7 Measure Objects Using Different Length Units

Explore and Grow

Measure the length of the string in inches then in centimeters.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.7 1
______ inches _______ centimeters
Are there more inches or centimeters? Why?
_____________________________
______________________________
Answer: 4.72 inches 12 centimeters

Show and Grow

Find and measure the object shown in your classroom two ways.
Question 1.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.7 2
about ______ centimeters
Answer: about 30 centimters
about ______ inches
about 15 inches
Did you use fewer centimeters or fewer inches to measure?
centimeters inches
Answer: inches

Question 2.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.7 3
about _______ meters
about _______ feet
Did you use fewer meters or fewer feet to measure?
meters feet
Answer: about 2 meters
about 6 feet
meters.

Apply and Grow: Practice

Find and measure the object shown in your classroom two ways.
Question 3.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.7 4
about _____ centimeters
about ______ inches
Did you use fewer centimeters or fewer inches to measure?
centimeters inches
Answer: about 2 centimeters
about 1 inch
inch

Question 4.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.7 5
about _____ meters
about ______ feet
Did you use more meters or more feet to measure?
meters feet
Answer: about 3 meters
about 9 feet
feet

Question 5.
Would you use more centimeters, inches, or feet to measure the length of a calculator?
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.7 6
Answer: Centimeters

Question 6.
Writing
What do you notice about the relationship between inches and centimeters? feet and meters?
________________________
_________________________
Answer: 1 inch is equal to 0.39 centimeters
1 foot is equal to 0.30 meters

Think and Grow: Modeling Real Life

Do you use fewer centimeters or fewer meters to measure the length of your house? Explain.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.7 7
centimeters meters
__________________________
__________________________
Answer: Meters
Explanation: 1 meter is equal to 100 centimeter, The length of the house is big So, it is easy to measure with meter.

Show and Grow

Question 7.
Do you use fewer feet or fewer yards to measure the length of a football field? Explain.
feet yards
_________________________
_________________________
Answer: Yards.
1 yard=36 inches
1 feet= 12 inches
The length of the football field is big. So, it is measured with yards.

Question 8.
Do you use more meters or more feet to measure the length of your school? Explain.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.7 9
meters feet
______________________
______________________
Answer: Feet
Explanation: 1 feet=12 inches
1 meter=39 inches
We use more feet to measure the length of the school.

Measure Objects Using Different Length Units Homework & Practice 11.7

Find and measure the object shown in two ways.
Question 1.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.7 10
about _______ centimeters
about _____ inches
Did you use more centimeters or more inches to measure the length of the umbrella?
centimeters inches
Answer: about 100 centimeters
about 40 inches
We use more centimeters to measure the length of the umbrella.

Question 2.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.7 11
about _____ meters
about _____ feet
Did you use fewer meters or fewer feet to measure the height of the cabinet?
meters feet
Answer: about 3 meters
about 10 feet
meter

Question 3.
Would you use more centimeters, inches, or feet to measure the height of a lamp?
centimeters
inches
feet
Answer: centimeters

Question 4.
Would you use fewer inches, meters, or feet to measure the length of a sink?
inches
meters
feet
Answer: Feet

Question 5.
Reasoning
Order the lengths from shortest to longest.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.7 12
_______, ________, _________
Answer: 12 centimeter, 12 inches, 12 feet

Question 6.
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.7 13
________, ________, ________
Answer: 2 centimeter, 2 feet, 2 meters

Question 7.
Precision
What is the best estimate of the height of a maraca?
Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths 11.7 14
9 inches
10 centimeters
3 centimeters
Answer: 10 centimeters

Question 8.
Modeling Real Life
Do you use fewer feet or fewer yards to measure the length of a hallway? Explain.
______________________
______________________
Answer: fewer feet

Review & Refresh

Circle the values of the underlined digit.
Question 9.
634
4
4 ones
4 hundreds
Answer: 4 ones

Question 10.
918
900
9 hundreds
100
Answer: 9 hundreds

Question 11.
257
0
5 tens
50
Answer: 5 tens

Lesson 11.8 Measure and Compare Lengths

Explore and Grow

Measure the fish. Circle the longer fish.
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.8 1
Answer: 10 centimeters

Show and Grow

Question 1.
How many centimeters longer is the marker than the paper clip?
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.8 2
Answer: 10-4=6 centimeters.

Apply and Grow: Practice

Question 2.
How many centimeters shorter is the binder clip than the stick of gum?
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.8 3
Answer: 4-1=3 inches

Question 3.
A finger is 4 centimeters longer than the finger nail. How long is the finger?
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.8 4
_______ centimeters
Answer: 1 centimeters

Question 4.
Writing
Explain how you found the length of the finger in Exercise 3.
______________________
______________________
Answer:

Think and Grow: Modeling Real Life

Whose path to school is longer? How much longer is it?
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.8 5
Addition equations:
Whose path is longer: Your path Friend’s path
Subtraction equation:
______ yards
Answer: Addition equations: your path 12+16=28 yards, your friend’s path 56+4=60 yards.
Whose path is longer: Your path Friend’s path
Subtraction equation: 60-28=32 yards

Show and Grow

Question 5.
Whose path to the pond is shorter? How much shorter is it?
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.8 6
Your path Friend’s path
______ meters
Answer: your path: 6+28=34 meters, your friend’s path: 7+15=22 meters
Your friend’s path to the pond is shorter.
It is shorter than 12 meters.

Measure and Compare Lengths Homework & Practice 11.8

Question 1.
How many inches longer is the branch than the worm?
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.8 7
Answer: 15 inches Branch
5 inches worm
15-5=10 inches

Question 2.
DIG DEEPER!
The length of a piece of string is 8 inches long. You cut off 5 inches. Draw the length of the string that is left.
Answer: _____________________________________________________________________________ – 8 inches
___________________________________________________ – 5 inches
8-5 inches=3 inches.

Question 3.
Modeling Real Life
Whose path to the playground is longer? How much longer is it?
Big Ideas Math Solutions Grade 2 Chapter 11 Measure And Estimate Lengths 11.8 8
Your path Friend’s path
_____ yards
Answer: Your path: 12+53=65 yards, Your friend’s path: 61+7=68 yards.
Your friend’s path is longer.
68-65=3 yards, It is longer by 3 yards.

Review & Refresh

Question 4.
Count by ones.
_____, _____, 71, _____, 73, _____, _____, 76
Answer: 69, 70, 71, 72, 73, 74, 75, 76
Explanation: There is difference of one number arranged in ascending order.

Question 5.
Count by fives.
85, 90, ____, _____, ______, _____, ______, ______
Answer: 85, 90, 95, 100, 105, 110, 115, 120.
Explanation: There is difference of five numbers arranged in ascending order.

Question 6.
Count by tens.
_____, 43, 53, _____, _____, ______, 93, ______
Answer: 33, 43, 53, 63, 73, 83, 93, 103.
Explanation: There is difference of ten numbers arranged in ascending order.

Measure And Estimate Lengths Performance Task

You are planting a rooftop garden. You want to build a fence around the garden. You have a piece of wood that is 16 feet long.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 1
Question 1.
a. Which designs can you make?

Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 1
b. You choose the rectangular design. Use repeated addition to find the length of each side in inches.
5 ft = _____ + ____ + ____ + _____ + _____ = in.
2 ft = ______ + ______ = in.
Answer: 5 ft =12 + 12 + 12 + 12 + 12= in
2 ft= 12 + 12 = in

Question 2.
Each seed you plant must be 6 inches apart and 6 inches away from the sides. Draw to find the number of seeds you can plant in your garden.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 3
_____ seeds
Answer: 20 seeds

Measure And Estimate Lengths Activity

Spin and Cover
To Play: Players take turns. On your turn, spin one spinner. Then cover the item you would measure using that unit. Continue playing until all objects are covered.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths 4

Measure And Estimate Lengths Chapter Practice

11.1 Measure Lengths in Centimeters

Measure.
Question 1.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths chp 1
about ______ centimeters
Answer: about 2 centimeters

Question 2.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths chp 2
about ______ centimeters
Answer: about 4 centimeters

11.2 Measure Objects Using Metric Lengths

Find and measure the object
Question 3.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths chp 3
about ______ meters
Answer: 1.5 meters

Question 4.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths chp 4
about _______ centimeters
Answer: about 15 centimeters

11.3 Estimate Lengths in Metric Units

Question 5.
The book is about 20 centimeters long. What is the best estimate of the length of the bookmark?
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths chp 5
Answer: 10 centimeters

Question 6.
What is the best estimate of the length of a paintbrush?
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths chp 6
Answer: 22 centimeters

11.4 Measure Lengths in Inches

Measure.
Question 7.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths chp 7
about ______ inches
Answer: about 30 inches

Question 8.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths chp 8
about ______ inches
Answer: about 4 inches

11.5 Measure Objects Using Customary Length Units

Find the object shown. Choose an inch ruler, a yardstick, or a measuring tape to measure the object. Then measure.
Question 9.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths chp 9
Tool: ______
Length: about _______
Answer: Object: Pencil stand
Tool: Measuring tape
Length: about 15 centimeters

Question 10.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths chp 10
Tool: _____
Length: about _______
Answer: Object: Calender
Tool: inch ruler
Length: about 10 inch

11.6 Estimate Lengths in Customary Units

Question 11.
The couch is about 8 feet long. What is best estimate of the length of the end table?
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths chp 11
Answer: The length of the end table is 2 feet.

Question 12.
What is the best estimate of the length of a pond?
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths chp 12
Answer: The length of a pond is 30 feet.

11.7 Measure Objects Using Different Length Units

Question 13.
Would you use more centimeters, meters, or inches to measure the length of a pencil?
centimeters
meters
inches
Answer: centimeters

Question 14.
Would you use fewer centimeters, meters, or feet to measure the length of the teacher’s desk?
centimeters
meters
feet
Answer: meters

Question 15.
YOU BE THE TEACHER
Newton says he uses more feet than meters to measure the length of a bicycle. Is he correct? Explain.
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths chp 15
______________________
________________________
Answer: Yes Newton uses more feet than meters to measure the length of a bicycle.

11.8 Measure and Compare Lengths

Question 16.
A guinea pig cage is 51 centimeters longer than the guinea pig. How long is the cage?
Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths chp 17
_______ centimeters
Answer: 20 centimeters

Conclusion:

I wish the information prevailed in Big Ideas Math Answer Key Grade 2 Chapter 11 Measure And Estimate Lengths is beneficial for all. Tap the links and kickstart your preparation. Share the Big Ideas Math Answers Grade 2 Chapter 11 Measure And Estimate Lengths pdf to your friends and help them to overcome their difficulties. Stay tuned to our site to get the solutions of all Big Ideas Math Answers Grade 2 Chapters.

Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes

Big Ideas Math Answers Grade 2 Chapter 15

Big Ideas Math Book Grade 2 Chapter 15 Identify and Partition Shapes Answer Key is available here. Students can download BIM Grade 2 Chapter 15 Identify and Partition Shapes Solutions PDF for free of cost. With the help of this Big Ideas Math Answers Grade 2 Ch 15, you can finish homework or assignments within time. This free BIM Book 2nd Grade 15th Chapter Identify and Partition Shapes Answer Key contains solutions for all the questions from the textbook.

Big Ideas Math Book 2nd Grade Answer Key Chapter 15 Identify and Partition Shapes

Every student must have Big Ideas Math 2nd Grade 15th Chapter Identify and Partition Shapes Answer Key to improve their math skills. By referring solution key, no one feels solving problems is difficult. Students have to practice all the topics included in Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes to get better marks in the exam.

The different lessons of Big Ideas Math Book Grade 2 Chapter 15 Identify and Partition Shapes Answer Key are Describe Two-Dimensional Shapes, Identify Angles of Polygons, Draw Polygons, Identify and Draw Cubes, Compose Rectangles, Identify Two, Three, or Four Equal Shares, Partition Shapes into Equal Shares, and Analyze Equal Shares of the Same Shape. Click on the quick link attached here to get the questions and answers for all those topics.

Vocabulary

Lesson: 1 Describe Two-Dimensional Shapes

Lesson: 2 Identify Angles of Polygons

Lesson: 3 Draw Polygons

Lesson: 4 Identify and Draw Cubes

Lesson: 5 Compose Rectangles

Lesson: 6 Identify Two, Three, or Four Equal Shares

Lesson: 7 Partition Shapes into Equal Shares

Lesson: 8 Analyze Equal Shares of the Same Shape

Chapter – 15: Identify and Partition Shapes

Identify and Partition Shapes Vocabulary

Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes v 1
Organize It
Use the review words to complete the graphic organizer.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes v 2

Define It
Use your vocabulary cards to identify the word. Find the word in the word search
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes v 3

Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes v 4
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes v 5

Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes v 6
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes v 7

Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes v 8
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes v 9

Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes v 10
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes v 11

Lesson 15.1 Describe Two-Dimensional Shapes

Explore and Grow

Create a shape with 3 sides on your geoboard. Draw your shape. Did everyone in your class make the same shape?
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 1
Circle the word that makes the sentence true.
_______ are shapes with 3 sides.
Circles Squares Triangles
Answer: Triangles

Show and Grow

Question 1.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 2
______ sides
_______ vertices
Shape : _________
Answer: 4 sides
4 vertices
Shape: Irregular Quadrilateral

Question 2.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 3
______ sides
_______ vertices
Shape : _________
Answer: 5 sides
5 vertices
Shape: Irregular Pentagon

Apply and Grow: Practice

Question 3.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 4
______ sides
_______ vertices
Shape : _________
Answer: 6 sides
6 vertices
Shape: Irregular Hexagon

Question 4.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 5
______ sides
_______ vertices
Shape : _________
Answer: 4 sides
4 vertices
Shape: Irregular Quadrilateral

Question 5.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 6
______ sides
_______ vertices
Shape : _________
Answer: 8 sides
8 vertices
Shape: Octagon

Question 6.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 7
______ sides
_______ vertices
Shape : _________
Answer: 3 sides
3 vertices
Shape: Scalene Triangle

Question 7.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 8
______ sides
_______ vertices
Shape : _________
Answer: 5 sides
5 vertices
Shape: Concave Pentagon

Question 8.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 9
______ sides
_______ vertices
Shape : _________
Answer: 4 sides
4 vertices
Shape: Concave Quadrilateral

Question 9.
Writing
How are a pentagon and an octagon different?
____________________
_____________________
Answer: Pentagon has 5 sides and Octagon has 8 sides.

Think and Grow: Modeling Real Life

Draw a pentagon to make a house. Draw 2 quadrilaterals to make windows and 1 quadrilateral to make a door. Draw an octagon to make a chimney.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 10
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.1-10-Answer

Show and Grow

Question 10.
Draw a pentagon to make a fish. Draw 4 triangles to make the fins. Draw a hexagon to make an eye.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 11
Answer:

Question 11.
You draw 5 quadrilaterals. How many sides and vertices do you draw in all?
______ sides _______ vertices
Answer: 20 sides 20 vertices

Question 12.
DIG DEEPER!
You draw an octagon and two pentagons. How many sides and vertices do you draw in all?
______ sides ______ vertices
Answer: 18 sides 18 vertices

Describe Two-Dimensional Shapes Homework & Practice 15.1

Question 1.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 12
______ sides
_______ vertices
Shape : _________
Answer: 6 sides
6 vertices
Shape: Irregular hexagon

Question 2.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 13
______ sides
_______ vertices
Shape : _________
Answer: 5 sides
5 vertices
Shape: Irregular Pentagon

Question 3.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 14
______ sides
_______ vertices
Shape : _________
Answer: 8 sides
8 vertices
Shape: Irregular Octagon

Question 4.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 15
______ sides
_______ vertices
Shape : _________
Answer: 3 sides
3 vertices
Shape: Right angle Triangle

Question 5.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 16
______ sides
_______ vertices
Shape : _________
Answer: 4 sides
4 vertices
Shape: Quadrilateral

Question 6.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 17
______ sides
_______ vertices
Shape : _________
Answer: 5 sides
5 vertices
Shape: Irregular Pentagon

Question 7.
Precision
Describe the shape in 3 ways.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 18
Answer: A 5 sided shape called Pentagon
It has 2 parallel sides
All sides are not equal.

Question 8.
Modeling Real Life
Draw a hexagon to make a dog’s body. Draw quadrilaterals for the head and tail. Draw two triangles for the ears.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.1 19
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.1-19-Answer

Question 9.
DIG DEEPER!
You draw a triangle and two hexagons. How many sides and vertices do you draw in all?
______ sides _______ vertices
Answer: 15 sides 15 vertices

Review & Refresh

Question 10.
You are building a 34-foot fence. You build 15 feet on Saturday and 13 feet on Sunday. How many feet are left to build?
______ feet
Answer: 6 feet are left to build
Explanation: Total 34 foot fence
15 feet on Saturday
13 feet on Sunday
15+13= 28 built
34-28= 6 feet left to build

Lesson 15.2 Identify Angles of Polygons

Explore and Grow

Color the triangle blue. Color the quadrilateral red. Color the pentagon green. Color the hexagon orange.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 1
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-1-Answer

Which shape is not colored? How is it different from the other shapes?
________________________
________________________
________________________
Answer: Circle is not colored. Circle has no straight lines.

Show and Grow

Question 1.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 2
_____ angles
How many right angles? ______
Shape: ______
Answer: 6 angles
2 right angles
Shape: Irregular hexagon

Question 2.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 3
______ angles
How many right angles? ______
Shape: _______
Answer: 3 angles
1 right angles
Shape: Right angle triangle

Question 3.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 4
_____ angles
How many right angles? ______
Shape: ______
Answer: 4 angles
4 right angles
Shape: Square

Question 4.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 5
______ angles
How many right angles? ______
Shape : _______
Answer: 4 angles
No right angles
Shape: Trapezium

Apply and Grow: Practice

Question 5.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 6
_____ angles
How many right angles? ______
Shape: ______
Answer: 3 angles
1 right angle
Shape: Right angle triangle

Question 6.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 7
_____ angles
How many right angles? ______
Shape: ______
Answer: 5 angles
2 right angles
Shape: irregular pentagon

Question 7.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 8
_____ angles
How many right angles? ______
Shape: ______
Answer: 8 angles
No right angle
Shape: Irregular Octagon

Question 8.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 9
_____ angles
How many right angles? ______
Shape: ______
Answer: 4 angles
2 right angles
Shape: Irregular Quadrilateral

Question 9.
Draw and name a polygon with 6 angles.
________
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.2-18-Answer

Question 10.
Draw and name a polygon with 2 right angles
_________
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.1.2-10-Answer

Question 11.
Writing
Can you draw a polygon with 4 sides and 5 angles? Explain.
__________________
____________________
Answer: No, A polygon with 4 sides and 5 angles cannot be drawn as the number of sides and angles are always equal.

Think and Grow: Modeling Real Life

You are designing a road sign. The new sign must be a pentagon with only 2 right angles. Which signs might be yours?
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 10
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-10-Answer

Show and Grow

Question 12.
You are making a sign for your lemonade stand. Your sign must be a quadrilateral with 4 right angles. Which signs might be yours?
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 11
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-11-Answer

Question 13.
You draw 3 pentagons. How many angles do you draw in all?
______ angles
Answer: 15 angles

Question 14.
DIG DEEPER!
You draw a quadrilateral and three triangles. Your friend draws an octagon and a hexagon. Who draws more angles in all? How many more?
You Friend ______ more angles
Answer: I draw 13 angles in all. My friend draws 14 angles in all. Friend draws more angles in all with 1 more angle.

Identify Angles of Polygons Homework & Practice 15.2

Question 1.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 12
______ angles
How many right angles? ______
Shape: ______
Answer: 6 angles
2 right angles
Shape: Irregular hexagon

Question 2.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 13
______ angles
How many right angles? _____
Shape: ______
Answer: 4 angles
4 right angles
Shape: Rhombus

Question 3.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 14
______ angles
How many right angles? ______
Shape: ______
Answer: 8 angles
No right angles
Shape: Irregular octagon

Question 4.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 15
_____ angles
How many right angles? ______
Shape: _______
Answer: 5 angles
1 right angle
Shape: Irregular pentagon

Question 5.
Draw and name a polygon with 4 sides and 1 right angle.
_______
Answer: Right Quadrilateral
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.2-16-Answer

Question 6.
Draw and name a polygon with 6 angles.
________
Answer: Hexagon

Question 7.

DIG DEEPER!
Draw two polygons that have 9 angles in all.
Answer: Triangle and Hexagon

Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.2-19-Answer

Question 8.
Modeling Real Life
You are designing a company logo. Your logo must be a hexagon with 2 right angles. Which logos might be yours?
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 16
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.2-20-Answer

Question 9.
DIG DEEPER!
You draw an octagon and two triangles. Your friend draws two quadrilaterals and a pentagon. Who draws more angles in all? How many more?
You Friend _______ more angles
Answer: You draw more angles. 1 angle more
You draw 14 angle in total, your friend draw 13 angle in total.

Review & Refresh

Draw to show the time.
Question 10.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 17
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-17-Answer

Question 11.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 18
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-18-Answer

Question 12.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.2 19
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-19-Answer

Lesson 15.3 Draw Polygons

Explore and Grow

Compare the shapes.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.3 1
Answer: Sqaure and right Quadrilateral

How are the shapes the same? How are they different?
_____________________
_____________________
_____________________
Answer: Both the shapes have 4 sides and 4 angles
They are different as length of the shapes are not equal.

Show and Grow

Question 1.
Draw a polygon with 6 sides. Two of the sides are the same length.
_______ angles
Polygon: ________
Answer: 6 angles
Polygon: Irregular Hexagon
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-117-Answer

Question 2.
Draw a polygon with 5 angles. One of the angles is a right angle.
______ sides
Polygon: ________
Answer: 5 sides
Polygon: Irregular Pentagon
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-118-Answer

Apply and Grow: Practice

Question 3.
Draw a polygon with 3 angles. One of the angles is a right angle.
______ sides
Polygon: _______
Answer: 3 sides
Right angle Triangle
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-119-Answer

Question 4.
Draw a polygon with 1 more side than a triangle. No sides are equal.
________ sides
Polygon: ______
Answer: 4 sides
Polygon: Irregular Quadrilateral
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.1.2-10-Answer

Question 5.
Draw a polygon with 4 fewer angles than an octagon. All sides are equal. All angles are right angles.
______ sides
Polygon: _______
Answer: 4 sides
Polygon: Square
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-chp-12

Question 6.
Draw a polygon with 4 sides. Two pairs of sides are the same length.
______ angles
Polygon: ______
Answer: 4 angles
Polygon: Rectangle
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-21-Answer

Question 7.
Precision
Which is not a polygon with only 4 angles?
square rectangle rhombus
trapezoid pentagon quadrilateral
Answer: Pentagon
Explanation: Pentagon has 5 angles

Think and Grow: Modeling Real Life

You have 9 straws. You use all the straws to create two polygons. Draw two polygons you can create. Write the names of the polygons.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.3 2
Polygon 1: ______ Polygon 2: _______
Answer: Polygon 1: Square   Polygon 2: Pentagon

Show and Grow

Question 8.
You have 7 clay balls and some toothpicks. You create two polygons using the clay balls as vertices and the toothpicks as sides. Draw two polygons you can create. Write the names of the polygons.
Polygon 1: ______ Polygon 2: _______
Answer: Polygon 1: Triangle Polygon 2: Rhombus

Question 9.
DIG DEEPER!
You draw two different polygons. One of the polygons is a pentagon. You draw 11 sides in all. Draw a possible shape for your other polygon. Write the name of the polygon.
Polygon: _______
Answer: Polygon: Hexagon

Draw Polygons Homework & Practice 15.3

Question 1.
Draw a polygon with 4 angles. There are no right angles. No sides are equal.
______ sides
Polygon: _______
Answer: 4 sides
Polygon: Trapezoid
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-120-Answer

Question 2.
Draw a polygon with 8 sides. Two of the angles are right angles.
_____ angles
Polygon: ______
Answer: 8 angles
Polygon: Irregular octagon
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-120-Answer

Question 3.
Draw a polygon with 2 more angles than a quadrilateral. Two of the angles are right angles.
______ sides
Polygon: _______
Answer: 6 sides
Polygon: Irregular hexagon
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-117-Answer

Question 4.
Draw a polygon with 3 fewer sides than an octagon.
_____ angles
Polygon: _____
Answer: 5 angles
Polygon: Pentagon
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-30b-Answer

Question 5.
Patterns
Draw 3 shapes. The first shape is a quadrilateral. The number of angles in each shape increases by two.
Name the third shape. ________
Answer: Octagon
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-29-Answer

Question 6.
Modeling Real Life
You have 9 apples and some sticks. You create two polygons using the apples for vertices and the sticks for sides. Draw two polygons you can create. Write the names of the polygons.
Polygon 1: ______ Polygon 2: ________
Answer: Polygon 1: Sqaure     Polygon 2: Pentagon

Question 7.
DIG DEEPER!
You draw two different polygons. One of the polygons is an octagon. You draw 14 sides in all. Draw a possible shape for your other polygon. Write the name of the polygon.
Polygon: ________
Answer: Polygon: Hexagon

Review & Refresh

Question 8.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.3 3
How many more students chose math than science? _____
Answer: 5 Students

Lesson 15.4 Identify and Draw Cubes

Explore and Grow

Draw an X on the shapes with curved surfaces. Circle the remaining shape with flat surfaces that are all the same.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 1
Name the shape you circled.
Answer: Cube, Cuboid
Big-Ideas-Math-Solutions-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.4-1-Answer

Show and Grow

Question 1.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 2
_____ faces
______ vertices
______ edges
Is it a cube? Yes No
Answer: 6 faces
8 vertices
12 edges
Yes, it is a cube

Question 2.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 3
____ faces
_____ vertices
_______ edges
Is it a cube? Yes No
Answer: 6 faces
8 vertices
12 edges
No, it is not a Cube

Question 3.
Use the dot paper to draw a cube.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 4
Answer:

Apply and Grow: Practice

Question 4.
Which shapes are cubes?
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 5
Answer: Big-Ideas-Math-Solutions-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.4-5-Answer

Question 5.
Use the dot paper to draw a cube.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 6
Answer: Big-Ideas-Math-Solutions-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.4-4-Answer

Question 6.
How many faces do two cubes have in all?
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 7
______ faces
Answer: 12 faces

Question 7.
Structure
Which two-dimensional shape makes up a cube? Name the shape.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 8
A cube is made up of ______.
Answer: A cube is made up of Sqaure.

Think and Grow: Modeling Real Life

You make a ballot box for a school election. Your box is in the shape of a cube. Each face of the ballot box is a different color. How many colors do you use?
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 9
_____ colors
Answer: 6 colors
Explanation: Cube has 6 faces, So 6 different colors will be used.

Show and Grow

Question 8.
You construct a cube. You use clay balls for the vertices and straws for the edges. How many clay balls do you make? How many straws do you use?
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 10
______ clay balls _____ straws
Answer: 8 clay balls 12 straws

Question 9.
The faces of the number cube are numbered, starting with 1. Draw and label all the faces of the number cube.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 11
Answer: Big-Ideas-Math-Solutions-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.4-7-Answer

Question 10.
DIG DEEPER!
You have 48 toothpicks and 32 grapes. You use all of the materials to make cubes using the toothpicks as edges and the grapes as vertices. How many cubes do you make?
_____ cubes
Answer: 4 cubes

Identify and Draw Cubes Homework & Practice 15.4

Question 1.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 12
_____ faces
______ vertices
______ edges
Is it a cube? Yes No
Answer: 6 faces
8 vertices
12 edges
No, it is not a cube.

Question 2.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 13
_____ faces
______ vertices
______ edges
Is it a cube? Yes No
Answer: 6 faces
8 vertices
12 edges
Yes, it is a cube

Question 3.
Use the dot paper to draw a cube.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 14
Answer: Big-Ideas-Math-Solutions-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.4-6-Answer

Question 4.
How many vertices do two cubes have in all?
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 15
_____ vertices
Answer: 16 vertices

Question 5.
YOU BE THE TEACHER
Newton says the cube has 3 faces. Is he correct? Explain.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 16
___________________
____________________
Answer: Cube has 6 faces

Question 6.
Modeling Real Life
You construct a cube. You use marshmallows for the vertices and pretzel rods for the edges. How many marshmallows do you use? How many pretzel rods do you use?
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 17
_______ marshmallows ________ pretzel rods
Answer: 8 marshmallows 12 pretzel rods

Question 7.
DIG DEEPER!
You have 24 cotton balls and 36 toothpicks. You use all of the materials to make cubes using the cotton balls as vertices and the toothpicks as edges. How many cubes do you make?
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.4 18
______ cubes
Answer: 3 cubes

Review & Refresh

Question 8.
43 − 5 = ____
Answer: 38
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-122-Answer

Question 9.
62 − 6 = _____
Answer: 56
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-123-Answer

Question 10.
______ = 41 − 4
Answer: 37
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-124-Answer

Question 11.
______ = 44 − 7
Answer: 37
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.2-125-Answer

Lesson 15.5 Compose Rectangles

Explore and Grow

How many square tiles do you need to cover the rectangle?
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.5 1
_____ squares
Answer: 28 squares
Write an equation to match your model.
Answer: l × b
7 × 4 = 28

Show and Grow

Question 1.
Use square tiles to cover the rectangle. Draw to show your work.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.5 2
Complete the statements.
Add by rows:
_____ + _____ + = ______
Add by columns: _____ + _____ = ______
Total square tiles: _______
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.5-2
Add by rows:
3 + 3 + 3 + 3 + 3 = 15
Add by columns:
5 + 5 + 5 = 15

Apply and Grow: Practice

Question 2.
Use square tiles to cover the rectangle. Draw to show your work.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.5 3
Complete the statements.
Add by rows: _____ + ____ + _____ = ______
Add by columns: ____ + _____ + _____ + ____ + _____ = ______
Total square tiles: ______
Answer:
5 + 5 + 5 = 15
3 + 3 + 3 + 3 + 3 = 15

Question 3.
Precision
Divide the rectangle into 6 equal parts.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.5 4
Answer: Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.5-4-Answer

Think and Grow: Modeling Real Life

You use foam mats to cover the entire floor of a square room. You fit 4 mats across one side of the room. How many rows and columns of mats will you have?
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.5 5
_____ rows _____ columns
How many foam mats do you use to cover the entire floor?
Addition equation:
______ foam mats
Answer: 4 rows 4 columns
16 foam mats

Show and Grow

Question 4.
You use square tiles to cover the floor of a square room. You fit 5 tiles across one side of the room. How many rows and columns of tiles will you have?
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.5 6
_____ rows _____ columns
DIG DEEPER!
How many tiles do you use to cover the entire floor?
_____ tiles
Answer: 5 rows 5 columns
25 tiles

Compose Rectangles Homework & Practice 15.5

Question 1.
Use square tiles to cover the rectangle. Draw to show your work.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.5 7
Complete the statements.
Add by rows: _____ = _____
Total square tiles: ______
Add by columns:
_____ + _____ + _____ + _____ + ______ + _____ = _____
Answer:

1 = 1
1 + 1 + 1 + 1 + 1 + 1 = 6

Question 2.Writing
Newton wants to cover the rectangle with square tiles. Explain what he is doing wrong.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.5 8
__________________
____________________
Answer: The Square titles are not arranged properly in the rectangle.

Question 3.
Modeling Real Life
You use square glass tiles to make a square mosaic picture. You fit 6 tiles across one side of the picture. How many rows and columns of tiles will you have?
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.5 9
______ rows _______ columns

Answer: 6 rows 6 columns

DIG DEEPER!
How many glass tiles do you use to cover the entire picture?
______ glass tiles
Answer: 36 glass tiles

Review & Refresh

Question 4.
Circle a.m. or p.m.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 15.5 10
Answer: Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.5-10-Answer

Lesson 15.6 Identify Two, Three, or Four Equal Shares

Explore and Grow

Sort the Equal Share Cards.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 1

Show and Grow

Circle the shape that shows halves.
Question 1.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 2
Answer: Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-2-Answer

Question 2.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 3
Answer: Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-3-Answer

Circle the shape that shows thirds.
Question 3.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 4
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-4-Answer

Question 4.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 5
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-5-Answer

Circle the shape that shows fourths.
Question 5.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 6
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-6-Answer

Question 6.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 7
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-6-Answer

Apply and Grow: Practice

Question 7.
Which shapes show halves?
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 8
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-8-Answer

Question 8.
Which shapes show thirds?
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 9
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-9-Answer

Question 9.
Which shapes show fourths?
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 10
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-10-Answer

Question 10.
Color a third of the shape.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 11
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-11-Answer

Question 11.
Color half of the shape.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 12
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-12-Answer

Question 12.
Color a fourth of the shape.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 13
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-13-Answer

Question 13.
YOU BE THE TEACHER
Newton says the shape shows fourths. Is he correct? Explain.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 14
________________________
_________________________
Answer: No The shape doesnot shows fourths. The square is not divided into equal parts.

Think and Grow: Modeling Real Life

You want to play 3 games in the pool. Each game needs an equal share of the pool. Show how you could divide the pool.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 15
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-15-Answer

Show and Grow

Question 14.
2 friends are making crafts. Each friend wants an equal share of the table. Show how the friends could divide the table.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 16
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-16-Answer

Question 15.
You and 3 friends want to share the piece of watermelon. Show how to cut the piece of watermelon so you and your friends each get an equal share.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 17
How did you know how many equal shares to cut?
__________________
__________________
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-17-Answer

Identify Two, Three, or Four Equal Shares Homework & Practice 15.6

Question 1.
Which shapes show halves?
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 18
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-18-Answer

Question 2.
Which shapes show thirds?
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 19
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-19-Answer

Question 3.
Which shapes show fourths?
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 20
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-20-Answer

Question 4.
Color a third of the shape.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 21
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-21-Answer

Question 5.
Color half of the shape.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 22
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-22-Answer

Question 6.
Color a fourth of the shape.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 23
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-23-Answer

Question 7.
Patterns
Draw what comes next.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 24
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-24-Answer

Question 8.
Modeling Real Life
Newton and Descartes share a bedroom. Show how they could divide their room into equal shares.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 25
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-25-Answer

Question 9.
Modeling Real Life
You and 2 friends are making a poster. Each friend wants an equal share of the poster. Show how the friends could divide the poster.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes 15.6 26
How did you know how many equal shares you need?
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-15.6-2.6-Answer

Review & Refresh

Question 10.
A pen is 16 centimeters tall. A pen holder is 11 centimeters tall. How much taller is the pen than the pen holder?
________ centimeters
Answer: 5 centimeters
Explanation: 16-11 = 5

Lesson 15.7 Partition Shapes into Equal Shares

Explore and Grow

Which pattern blocks can you use to model equal shares of the hexagon?
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.7 1
Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.7-1-Answer

Show and Grow

Draw lines to show equal shares. Complete the sentences.
Question 1.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.7 2
Each share is a _______ of the whole.
The whole is _______.
Answer:
Each share is a part of the whole.
The whole is 4.

Question 2.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.7 3
Each share is a _______ of the whole.
The whole is ______.
Answer:
Each share is a half of the whole.
The whole is 2.

Apply and Grow: Practice

Question 3.
Draw lines to show equal shares. Complete the sentences.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.7 4
Each share is a ______ of the whole.
The whole is ________.
Answer:
Each share is a one third of the whole.
The whole is 1/3.

Draw lines to show equal shares. Which word describes the parts?
Question 4.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.7 5
Answer: Fourths

Question 5.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.7 6
Answer: Thirds

Question 6.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.7 7
Answer: Halves

Question 7.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.7 8
Answer: Thirds

Question 8.
Precision
Draw lines to show thirds. Color 3 thirds.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.7 9
Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.7-9

Think and Grow: Modeling Real Life

You have 2 towels that are the same size. Half of one towel is green. A fourth of the other towel is yellow. Is the green share or the yellow share larger? Explain.
Draw to show:
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.7 10
Which share is larger? Green share Yellow share
________________________
________________________
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.1.2-127-Answer
Green share
Explanation: First towel is divided into halves and other towel is divided into fourths, So halves is larger than fourths.

Show and Grow

Question 9.
You have 2 rugs that are the same size. A fourth of one rug is red. A third of the other rug is blue. Is the red share or the blue share smaller? Explain.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.7 11
________________________
________________________
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.1.2-124-Answer
The red share is smaller as it is divided into 4 parts.

Partition Shapes into Equal Shares Homework & Practice 15.7

Draw lines to show equal shares. Complete the sentences.
Question 1.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.7 12
Each share is a ______ of the whole.
The whole is ______.
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.1.2-123-AnswerAnswer:

Question 2.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.7 13
Each share is a _______ of the whole.
The whole is _____.
Answer:  Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.1.2-122-Answer

Draw lines to show equal shares. Complete the sentences.
Question 3.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.7 14
Each share is a ______ of the whole.
The whole is _______.
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.1.2-121-Answer

Question 4.
Logic
Complete the sentences.
1 whole is ______ halves.
1 whole is ______ thirds.
1 whole is ______ fourths.
Answer: 1 whole is 2 halves.
1 whole is 3 thirds.
1 whole is 4 fourths.

Question 5.
Structure
Does the shape show thirds? Explain.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.7 15
Answer: No, The circle is not divided into 3 equal parts.

Question 6.
Modeling Real Life
You have 2 blankets that are the same size. A third of one blanket is yellow. A half of the other blanket is purple. Is the yellow share or the purple share smaller? Explain.
Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes 15.7 16
_____________________
_____________________
Answer: The Yellow Share is smaller as the blanket is divided into 3 parts whereas, the purple share is divided into 2 parts.

Review & Refresh

Question 7.
150 + 610 = ______
Answer: 760
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.1.2-125-Answer

Question 8.
553 + 250 = ______
Answer: 803
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.1.2-126-Answer

Lesson 15.8 Analyze Equal Shares of the Same Shape

Explore and Grow

Color the squares that show equal shares.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.8 1
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.1.2-111-Answer

How are the squares you colored the same? How are they different?
________________________
________________________
________________________
Answer: No, the squares colored are not same because all are differently divided.

Show and Grow

Question 1.
Draw lines to show halves in two different ways. Color one-half of each circle.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.8 2
Think: How are the halves of each circle the same? How are they different?
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.1.2-112-Answer
The Circle are divided into 2 parts. The colored part are not same because all are differently divided.

Question 2.
Draw lines to show thirds in two different ways. Color one-third of each rectangle.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.8 3
Think: How are the thirds of each rectangle the same? How are they different?
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.1.2-12-Answer
The Rectangle are divided into 3 parts. The colored part are not same because all are differently divided.

Apply and Grow: Practice

Question 3.
Draw lines to show fourths two different ways. Color one-fourth of each circle.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.8 4
Answer:

Question 4.
Draw lines to show thirds two different ways. Color one-third of each square.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.8 5
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.1.2-110-Answer

Question 5.
Draw lines to show halves two different ways. Color one-half of each rectangle.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.8 6
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.1.2-09-Answer

Question 6.
DIG DEEPER!
Explain how you know each color is a fourth of the whole square.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.8 7
________________________
________________________
_________________________
Answer:

Think and Grow: Modeling Real Life

You and your friend each cut a sandwich into fourths different ways. The sandwiches are the same size. Show how you and your friend can cut the sandwiches.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.8 8
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-12-Answer

Show and Grow

Question 7.
You, Newton, and Descartes each cut a granola bar into halves different ways. The granola bars are the same size. Show how you, Newton, and Descartes can cut the granola bars.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.8 9
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-13-Answer

Question 8.
DIG DEEPER!
There are 2 pizzas that are the same size. 6 friends each want an equal share of the pizzas. Should the pizzas be cut into halves, thirds, or fourths? Explain.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.8 10
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-10-Answer
The Pizzas should be cut into thirds as there are 2 pizzas, if one pizza is cut into 3 equal parts and other pizza as 3 equal parts then there is total 6 pieces for 6 friends.

Analyze Equal Shares of the Same Shape Homework & Practice 15.8

Question 1.
Draw lines to show fourths two different ways. Color one-fourth of each rectangle.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.8 11
Think: How are the fourths of each rectangle the same? How are they different?
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-9-Answer

Question 2.
Draw lines to show thirds two different ways. Color one-third of each circle.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.8 12
Answer:
Big-Ideas-Math-Solutions-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.8-12

Question 3.
Reasoning
Descartes says there are only two ways to divide a rectangle into 3 equal shares. Is he correct? Explain.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.8 13
Answer:Yes. Descartes is correct. the rectangle can be divided equally horizontally and vertically.

Question 4.
Modeling Real Life
You and your friend each cut a loaf of bread into thirds different ways. The loaves of bread are the same size. Show how you and your friend can cut the loaves of bread.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.8 14
Answer:
Big-Ideas-Math-Solutions-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.8-14

Question 5.
DIG DEEPER!
There are 2 quesadillas that are the same size. 8 friends each want an equal share of the quesadillas. Should the quesadillas be cut into halves, thirds, or fourths? Explain.
Big Ideas Math Solutions Grade 2 Chapter 15 Identify and Partition Shapes 15.8 15
Answer: Fourths
Explanation: There are 2 quesadillas. It can be cut into fourths So, it will be 8 parts in total and given to 8 friends equally.

Review & Refresh

Question 6.
841 − 603 = _____
Answer: 238

Question 7.
439 − 210 = _______
Answer: 229

Identify and Partition Shapes Performance Task

You paint a square suncatcher in art class.
Question 1.
You paint each shape a different color. Color to show how you paint the sun catcher.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 1
a. Each triangle is red.
b. Each octagon is orange.
c. Each pentagon with more than 1 right angle is yellow.
d. The rest of the pentagons are green.
e. Each shape with 6 angles is blue.
f. Each quadrilateral with all right angles is purple.
g. The rest of the quadrilaterals are pink.
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-1-Answer

Question 2.
The length of one side of the suncatcher is 12 inches. What are the lengths of the other sides?
______ inches
Answer: 12 inches

Question 3.
Your friend paints a rectangular suncatcher.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 2
a. What share of your friend’s design is blue? _______
b. What share of your friend’s design is orange or yellow? ________
Answer: a. second
b. third or fourth

Identify and Partition Shapes Activity

Three In a Row: Equal Shares
To Play: Players take turns. On your turn, spin the spinner. Cover a square that matches your spin. Continue playing until a player gets three in a row.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes 3

Identify and Partition Shapes Chapter Practice

15.1 Describe Two-Dimensional Shapes

Question 1.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes chp 1
______ sides
_____ vertices
Shape: ______
Answer: 6 sides
6 vertices
Shape: Irregular hexagon

Question 2.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes chp 2
______ sides
_____ vertices
Shape: ______
Answer: 5 sides
5 vertices
Shape: Irregular pentagon

Question 3.
Modeling Real Life
You draw three quadrilaterals and an octagon. How many sides and vertices do you draw in all?
______ sides ______ vertices
Answer: 20 sides 20 vertices

15.2 Identify Angles of Polygons

Question 4.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes chp 4
______ angles
How many right angles? ______
Shape: ______
Answer: 5 angles
2 right angles
Shape: Irregular pentagon

Question 5.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes chp 5
______ angles
How many right angles? ______
Shape: ______
Answer: 6 angles
2 right angles
Shape: Irregular hexagon

Question 6.
Draw and name a shape with 2 right angles.
________
Answer: Pentagon
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-11-Answer

15.3 Draw Polygons

Question 7.
Draw a polygon with 4 angles. All sides are equal length.
______ sides
Polygon: _______
Answer: 4 sides
Polygon: Square
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-chp-12

Question 8.
Draw a polygon with 5 sides. Two of the angles are right angles.
______ angles
Polygon: ________
Answer: 5 angles
Polygon: Pentagon
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-11-Answer

15.4 Identify and Draw Cubes

Question 9.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes chp 9
______ faces
______ vertices
______ edges
Is it a cube? Yes No
Answer: 6 faces
8 vertices
12 edges
Yes it is cube.

Question 10.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes chp 10
______ faces
______ vertices
______ edges
Is it a cube? Yes No
Answer: 6 faces
8 vertices
12 edges
No it is not cube.

Question 11.
Use the dot paper to draw a cube.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes chp 11
Answer:
Big-Ideas-Math-Solutions-Grade-2-Chapter-15-Identify-and-Partition-Shapes-15.4-6-Answer

15.5 Compose Rectangles

Question 12.
Use square tiles to cover the rectangle. Draw to show your work.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes chp 12
Complete the statements.
Add by rows:
_____ + _____ = ______
Add by columns:
_____ + _____ = _______
Total square tiles: _______
Answer:
Add by rows:
2 + 2 = 4
Add by columns:
2 + 2 = 4
Total square tiles: 4

15.6 Identify Two, Three, or Four Equal Shares

Question 13.
Which shapes show halves?
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes chp 13
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-chp-13-Answer

Question 14.
Which shapes show thirds?
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes chp 14
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-chp-14-Answer

Question 15.
Which shapes show fourths?
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes chp 15
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-chp-15-Answer

15.7 Partition Shapes into Equal Shares

Draw lines to show equal parts. Complete the sentences.
Question 16.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes chp 16
Each share is a ______ of the whole.
The whole is ______.
Answer:
Each share is a fraction or part of the whole.
The whole is 3.

Question 17.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes chp 17
Each share is a ______ of the whole.
The whole is _____.
Answer:
Each share is a part of the whole.
The whole is 2.

Question 18.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes chp 18
Each share is a ______ of the whole.
The whole is _____.

Answer:
Each share is a part of the whole.
The whole is 4.

15.8 Analyze Equal Shares of the Same Shape

Question 19.
Modeling Real Life
There are 3 bagels that are the same size. 6 friends each want an equal share of the bagels. Should the bagels be cut into halves, thirds, or fourths? Explain.
Big Ideas Math Answer Key Grade 2 Chapter 15 Identify and Partition Shapes chp 19
__________________
___________________
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-6-Answer
Explanation: 3 bagels cut into Halves will be 6 bagels.

Identify and Partition Shapes Cumulative Practice

Question 1.
Your bed is 39 inches long. Your comforter is 66 inches long. How much longer is the comforter than the bed?
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes cp 1
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-8-Answer

Question 2.
Find each difference.
700 – 465 = _____
910 – 186 = _______
302 – 176 = ______
Answer: 700 – 465 = 235
910 – 186 = 724
302 – 176 = 126

Question 3.
A dog park is 48 yards long. Your dog enters the park and runs 29 yards. You run 13 yards. How far is your dog from the other end of the park?
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes cp 3
Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-15-Identify-and-Partition-Shapes-7-Answer
Explanation: 29+13=42
48-42=6 yards

Question 4.
Which shapes show thirds?
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes cp 4
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-cp-4-Answer

Question 5.
The girls’ soccer team raises $237. The boys’ soccer team raises $113 more. How much money do both teams raise in all?
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes cp 5
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-cp-5-Answer
Explanation: 237+113=350

Question 6.
Complete the bar graph.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes cp 6
What mascot got the most votes? _______
How many more votes did Warrior get than Tiger? ______
Answer: Knight
3 more votes Warrior get than Tiger.

Question 7.
Count on to find the total value.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes cp 7
Answer: Total value: 91

Question 8.
Which expressions have a difference of 34?
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes cp 8
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-cp-8-Answer

Question 9.
Complete the line plot. Then choose all of the statements that are true.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes cp 9
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-cp-9-Answer

Question 10.
Which clock shows 10:40?
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes cp 10
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-cp-10-Answer

Question 11.
The phone is about 12 centimeters long. What is the best estimate for the length of the tablet?
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes cp 11
Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-15-Identify-and-Partition-Shapes-cp-11-Answer

Question 12.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes cp 12
______ sides
_______ vertices
Shape: _____
Answer: 6 sides
6 vertices
Shape: Irregular hexagon

Question 13.
Big Ideas Math Answers 2nd Grade Chapter 15 Identify and Partition Shapes cp 13
______ sides
_______ vertices
Shape: _______
Answer: 5 sides
5 vertices
Shape: pentagon

Conclusion:

I hope the details given here regarding Big Ideas Math Grade 2 Chapter 15 Identify and Partition Shapes Answer Key PDF is useful for you to prepare well for the exams. Stay in touch with our site to get the answer key of Big Ideas Math all grades and remaining chapters of grade 2.

Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies

Big Ideas Math Answers Grade 2 Chapter 5

Big Ideas Math Book Grade 2 Chapter 5 Subtraction to 100 Strategies Answer Key is helpful for the students who are willing to be perfect in Math skills. At this Big Ideas Math 2nd Grade 5th Chapter Subtraction to 100 Strategies, you can find the solutions for all the questions in a simple manner. Practice various topics covered in this chapter and prepare well for the exam. Download Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies PDF for free of cost.

Big Ideas Math Book 2nd Grade Answer Key Chapter 5 Subtraction to 100 Strategies

Students who are facing difficulties in solving Big Ideas Math Book Grade 2 Chapter 5 Subtraction to 100 Strategies problems have reached the correct place. This BIM Book 2nd Grade 5th Chapter Subtraction to 100 Strategies Answer Key gives the most accurate answers to all the problems you have related to this chapter. It has different methods of solving every question in a simple way to perform in their exams.

This Subtraction to 100 Strategies consists of Subtract Tens Using a Number Line, Subtract Tens and Ones Using a Number Line, Use Addition to Subtract, Decompose to Subtract, Decompose to Subtract Tens and Ones, Use Compensation to Subtract, Practice Subtraction Strategies and Problem Solving: Subtraction. It is also helpful for the students to have a real-life calculation go very smoothly and neat defining their quick responses to daily life tasks.

Lesson: 1 Subtract Tens Using a Number Line

Lesson: 2 Subtract Tens and Ones Using a Number Line

Lesson: 3 Use Addition to Subtract

Lesson: 4 Decompose to Subtract

Lesson: 5 Decompose to Subtract Tens and Ones

Lesson: 6 Use Compensation to Subtract

Lesson: 7 Practice Subtraction Strategies

Lesson: 8 Problem Solving: Subtraction

Chapter: 5 – Subtraction to 100 Strategies

Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 0.1

Organize It

Use the review words to complete the graphic organizer.
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 0.2

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-0.2

Define It
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 0.3

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-0.3

Lesson 5.1 Subtract Tens Using a Number Line

Color to show how you can use the hundred chart to solve.

Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 1

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-1

Show and Grow

Question 1.
70 – 50 = __

Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 3

Answer : 20

Explanation: 70-50=20 first you subtract since difference is often a synonym for subtraction.

Question 2.
33 – 20 = ___
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 3

Answer : 13

Explanation : 33-20=13 first you subtract since difference is often a synonym for subtraction.

Apply and Grow: Practice

Question 3.
60 – 40 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 4

Answer : 20

Explanation : 60 – 40 = 20 first you subtract since difference is often a synonym for subtraction.

Question 4.
71 – 20 = ___
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 5

Answer : 51

Explanation : 71 –  20 = 51 first you substract since difference is often a synonym for substraction.

Question 5.
46 – 30 = ___
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 6

Answer :  16

Explanation : 46 – 30 = 16 first you subtract since difference is often a synonym for substraction.

Question 6.
YOU BE THE TEACHER
Your friend shows 79 − 40 on a number line. Is your friend correct? Explain.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 7

Answer : True

Think and Grow: Modeling Real Life

You have a 74-piece set of magnetic tiles. You use 60 of them to make buildings. How many pieces are left?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 8
Subtraction equation:
Model:
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 9

Answer : 74 – 60 = 14

Explanation : 14 pieces are left.

Show and Grow

Question 7.
A clown has 62 balloons. She uses 40 of them to make balloon animals. How many balloons are left?

Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 10

Answer : 62 – 40 = 12

Explanation:
Given,
A clown has 62 balloons.
She uses 40 of them to make balloon animals.
Subtract 40 from 62 you get 12.
12 balloons are left.

Question 8.
DIG DEEPER!
There are 35 people at a park. 20 of them leave. Then 10 more arrive at the park. How many people are at the park now?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 11

Answer: 25 people

Explanation:
Given,
There are 35 people at a park. 20 of them leave.
35 – 20 = 15
Then 10 more arrive at the park.
15 + 10 = 25 people
Therefore 25 people are at the park now.

Subtract Tens Using a Number Line Homework & Practice 5.1

Question 1.
90 – 50 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 12

Answer: 40

Explanation:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-12

Question 2.
84 – 60 = ___
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 13

Answer: 24
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-13

Question 3.
22 – 10 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 14

Answer: 12
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-13

Question 4.
54 – 50 = ___
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 15

Answer: 4
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-13

Question 5.
Number Sense
Write the equation shown by the number line.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 16

Answer: 100 – 60 = 40
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-16

Question 6.
Modeling Real Life
There are 52 cards in a deck. You pass out 20 of them. How many cards are left in the deck?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 17

Answer:
Given,
There are 52 cards in a deck. You pass out 20 of them.
52 – 20 = 32
32 cards are left in the deck.

Review & Refresh

Question 7.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 18

Answer: 51

Question 8.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 19

Answer: 93

Question 9.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 20

Answer: 54

Lesson 5.2 Subtract Tens and Ones Using a Number Line

Explore and Grow

Color to sh

ow how you can use the hundred chart to solve.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 21

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-21

Show and Grow

Question 1.
80 – 34 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 22

Answer: 46
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-22

Question 2.
56 – 23 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 23

Answer: 33
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-23

Apply and Grow: Practice

Question 3.
74 – 51 = ___
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 24

Answer: 23

Question 4.
86 – 44 = ___

Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 25

Answer: 42

Question 5.
97 – 61 = ___
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 26

Answer: 36

Question 6.
46 – 15 = ___
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 27

Answer: 31

Question 7.
69 – 35 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 28

Answer: 34

Question 8.
38 – 22 = ___
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 29

Answer: 16

Question 9.
Reasoning
Complete the number line and the equation.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 30

Answer: 47 – 30 = 17
17 – 2 = 15

Think and Grow: Modeling Real Life

You have 85 baseball cards and 54 football cards. How many more baseball cards do you have?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 31
Subtraction equation:
Model:
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 32

Answer:
Given,
You have 85 baseball cards and 54 football cards.
85 – 54 = 31
Thus there are 31 more baseball cards.

Show and Grow

Question 10.
A carnival has 17 rides and 48 games. How many more games are there?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 33

Answer:
Given,
A carnival has 17 rides and 48 games.
48 – 17 = 31 games
Therefore there are 31 more games.

Question 11.
DIG DEEPER!
There are 63 people in a theater, 21 people in the lobby, and 10 people in the parking lot. How many more people are in the theater than in both the lobby and the parking lot?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 34

Answer:
Given,
There are 63 people in a theater, 21 people in the lobby, and 10 people in the parking lot.
21 + 10 = 31
63 – 31 = 32
Thus there are 32 people in the theater than in both the lobby and the parking lot.

Subtract Tens and Ones Using a Number Line Homework & Practice 5.2

Question 1.
95 – 40 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 35

Answer: 55

Question 2.
29 – 12 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 36

Answer: 17

Question 3.
58 – 14 = ___
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 37

Answer: 44

Question 4.
77 – 31 = ___
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 38

Answer: 46

Question 5.
86 – 26 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 39

Answer: 60

Question 6.
70 – 18 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 40

Answer: 52

Question 7.
Structure
Use the number lines to show 84 −62 in two ways.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 41

Answer: 22

Question 8.
Modeling Real Life
Your classroom has 26 desks and 38 chairs. How many more chairs are there?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 42

Answer:
Given,
Your classroom has 26 desks and 38 chairs.
38 – 26 = 12 chairs
Thus there are 12 more chairs.

Question 9.
Modeling Real Life
A grocery store orders 54 pineapples and 22 watermelons. How many more pineapples are there?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 43

Answer:
Given,
A grocery store orders 54 pineapples and 22 watermelons.
54 – 22 = 32 pineapples
Thus there are 32 more pineapples.

Review & Refresh

Is the number even or odd?

Question 10.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 44

Answer: Even
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-44
8 is divisible by 2 so 8 is an even number.

Question 11.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 45

Answer: Odd
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-45

Lesson 5.3 Use Addition to Subtract

Explore and Grow

Show how you can use a number line to solve.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 46
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 47

Answer:
29 + x = 52
x = 52 – 29
x = 23
52 – 29 = 23

Show and Grow

Add to find the difference

Question 1.
43 – 15 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 48

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-48
43 – 15 = 28

Question 2.
76 – 59 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 49

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-49
76 – 59 = 17

Apply and Grow: Practice

Add to find the difference.

Question 3.
56 – 27 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 50

Answer: 29
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-50

Question 4.
21 – 13 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 51

Answer: 8
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-51

Question 5.
72 – 57 = ___
Big Ideas Math Answers 2nd Grade Chapter 5 Subtraction to 100 Strategies 52

Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-5-Subtraction-to-100-Strategies-52

Question 6.
33 – 15 = ___
Big Ideas Math Answers 2nd Grade Chapter 5 Subtraction to 100 Strategies 53

Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-5-Subtraction-to-100-Strategies-53

Question 7.
45 – 36 = ___
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 54

Answer: 9
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-54

Question 8.
61 – 46 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 55

Answer: 15
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-55

Question 9.
Structure
Use addition and the number lines to show 64 − 35 in two ways.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 56

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-55

Think and Grow: Modeling Real Life

A ship has a crew of 52 pirates. Some of them leave. There are 27 left. How many pirates got off the ship?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 57
Model:
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 58

Answer:
A ship has a crew of 52 pirates. Some of them leave. There are 27 left.
52 – 27 = 25
Thus 25 pirates got off the ship.

Show and Grow

Question 10.
A pumpkin patch has 85 pumpkins. Some of them are picked. There are 48 left. How many pumpkins were picked?
Big Ideas Math Answers 2nd Grade Chapter 5 Subtraction to 100 Strategies 59

Answer:
Given,
A pumpkin patch has 85 pumpkins. Some of them are picked. There are 48 left.
85 – 48 = 37 pumpkins
Thus 37 pumpkins were picked.

Question 11.
DIG DEEPER!
There are 96 treats in a bowl. Newton takes 15 treats. Descartes takes some treats. There are 68 treats left. How many treats did Descartes take?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 60

Answer:
Given,
There are 96 treats in a bowl. Newton takes 15 treats. Descartes takes some treats. There are 68 treats left.
96 – 15 = 81 treats
81 – 68 = 13 treats
Thus Descartes take 13 treats.

Use Addition to Subtract Homework & Practice 5.3

Add to find the difference.

Question 1.
92 – 67 = __
Big Ideas Math Answers 2nd Grade Chapter 5 Subtraction to 100 Strategies 61

Answer: 25
Big-Ideas-Math-Answers-2nd-Grade-Chapter-5-Subtraction-to-100-Strategies-61

Question 2.
43 – 24 = __
Big Ideas Math Answers 2nd Grade Chapter 5 Subtraction to 100 Strategies 62

Answer: 19
Big-Ideas-Math-Answers-2nd-Grade-Chapter-5-Subtraction-to-100-Strategies-62

Question 3.
71 – 42 = ___
Big Ideas Math Answers 2nd Grade Chapter 5 Subtraction to 100 Strategies 63

Answer:
Big-Ideas-Math-Answers-2nd-Grade-Chapter-5-Subtraction-to-100-Strategies-63

Question 4.
63 – 58 = __
Big Ideas Math Answers 2nd Grade Chapter 5 Subtraction to 100 Strategies 64

Answer: 5
Big-Ideas-Math-Answers-2nd-Grade-Chapter-5-Subtraction-to-100-Strategies-64

Question 5.
55 – 19 = __
Big Ideas Math Answers 2nd Grade Chapter 5 Subtraction to 100 Strategies 65

Answer: 36
Big-Ideas-Math-Answers-2nd-Grade-Chapter-5-Subtraction-to-100-Strategies-65

Question 6.
86 – 29 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 66

Answer: 57
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-66

Question 7.
YOU BE THE TEACHER
Descartes adds to find 35 − 12. Is he correct? Explain.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 67

Answer: Yes he is correct

Question 8.
Modeling Real Life
A farmer has 96 cornstalks. Some of them are sold. There are 38 left. How many cornstalks were sold?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 68

Answer:
Given,
A farmer has 96 cornstalks. Some of them are sold. There are 38 left.
96 – 38 = 58
58 cornstalks were sold

Question 9.
DIG DEEPER!
There are 56 bouncy balls in a pack. Your friend takes some. You take 23. There are 23 bouncy balls left. How many did your friend take?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 69

Answer:
Given,
There are 56 bouncy balls in a pack. Your friend takes some.
You take 23. There are 23 bouncy balls left.
56 – 23 = 33
33 – 23 = 10
Your friend take 10 bouncy balls.

Review & Refresh

Draw to show the time

Question 10.
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 70

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-70

Question 11.
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 71

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-71

Lesson 5.4 Decompose to Subtract

Explore and Grow

Color to show how you can get to a decade number by subtracting.

Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 72How can the equation above help you find 36 − 9?
______________________________
______________________________
______________________________

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-72

Show and Grow

Break apart the number being subtracted. Then find the difference. Use the number line to help.
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 73

Question 1.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 74

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-74

Question 2.
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 75

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-75

Question 3.
75 – 7 = __

Answer: 68

Question 4.
82 – 6 = __

Answer: 76

Apply and Grow: Practice

Break apart the number being subtracted. Then find the difference.

Question 5.
47 – 8 = __

Answer: 39

Question 6.
56 – 9 = __

Answer: 47

Question 7.
43 – 5 = __

Answer: 38

Question 8.
62 – 6 = __

Answer: 56

Question 9.
__ = 41 – 4

Answer: 37

Question 10.
__ = 44 – 7

Answer: 37

Question 11.
Reasoning
Which equation is shown by the number line?
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 76

Answer:
50 + 5 = 55
Mark 50 on the line and add 5 from 5 we get 55
55 – 8 = 47
First mark 55 on the line and count 8 before 55 we get 47
47 + 3 = 50
First, mark on 47 and add 3 from 47 we get 50 as an answer.

Think and Grow: Modeling Real Life

Your friend has 45 comic books. You have 8 fewer. How many comic books do you have?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 77
Subtraction equation:
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 78

Answer:
Given,
Your friend has 45 comic books. You have 8 fewer.
45 – 8 = 37 comic books

Show and Grow

Question 12.
Your friend can do 33 tricks on a yo-yo. You can do 9 fewer. How many tricks can you do?
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 79

Answer:
Given,
Your friend can do 33 tricks on a yo-yo. You can do 9 fewer.
33 – 9 = 24

Question 13.
Descartes’s walk was 8 minutes longer than Newton’s. Descartes’s walk was 56 minutes. How long was Newton’s walk?
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 80

Answer:
Given,
Descartes’s walk was 8 minutes longer than Newton’s.
Descartes’s walk was 56 minutes.
56 – 8 = 48 minutes
Thus Newton’s walk was 48 minutes.

Decompose to Subtract Homework & Practice 5.4

Break apart the number being subtracted. Then find the difference. Use the number line to help
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 81

Question 1.
95 – 6 = __
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 82

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-82

Question 2.
86 – 8 = __
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 83

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-83

Question 3.
89 – 9 = __

Answer: 80

Question 4.
82 – 7 = __

Answer: 75

Question 5.
__ = 83 – 5

Answer: 78

Question 6.
__ = 98 – 9

Answer: 89

Question 7.
Number Sense
Which way would you break apart 9 to find 25 – 9 ? Explain. Then find the difference.
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 84

Answer: 16

Question 8.
Modeling Real Life
You build a train track with 32 pieces. You remove 6 pieces. How many pieces does the train track have now?
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 85

Answer:
Given,
You build a train track with 32 pieces. You remove 6 pieces.
32 – 6 = 26 pieces

Question 9.
Modeling Real Life
You read 42 pages on Friday. You read 8 fewer pages on Saturday. How many pages do you read on Saturday?
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 86

Answer:
Given,
You read 42 pages on Friday.
You read 8 fewer pages on Saturday.
42 – 8 = 34 pages

Review & Refresh

Question 10.
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 87

Answer: 3 rows of 5
5 + 5 + 5 = 15

Lesson 5.5 Decompose to Subtract Tens and Ones

Explore and Grow

Color to show how you can break apart 16 to find the difference.
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 88

Explain your strategy
______________________________
______________________________
______________________________

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-88

Show and Grow

Break apart the number being subtracted. Then find the difference.

Question 1.
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 89

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-89

Question 2.
63 – 26 = __
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 90

Answer: 37
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-90

Apply and Grow: Practice

Break apart the number being subtracted. Then find the difference.

Question 3.
32 – 13 = __
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 91

Answer: 19
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-91

Question 4.
46 – 17 = __
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 92

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-92

Question 5.
93 – 45 = __

Answer: 48
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-92.1

Question 6.
71 – 24 = __

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-92.2

Question 7.
Structure
Can you use the equations to find 87 − 29?
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 93

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-93

Think and Grow: Modeling Real Life

How many more pizzas do you sell than Newton?
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 94
How many fewer pizzas does Newton sell than Descartes?
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 95

Answer:
Number of pizzas Descartes sold = 57
Number of pizzas Newton sold = 38
57 – 38 = 19 fewer pizzas

Show and Grow

Question 8.
How many more tickets does Newton sell than Descartes?
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 96

Answer:
85 – 47 = 38 more tickets
Thus Newton sell 38 more tickets than Descartes.

Question 9.
DIG DEEPER!
Your friend picks 49 apples. 11 apples are green and 14 apples are red. The rest are yellow. How many apples are yellow?
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 97

Answer:
Given,
Your friend picks 49 apples. 11 apples are green and 14 apples are red. The rest are yellow.
11 + 14 = 25
49 – 25 = 24 yellow apples

Decompose to Subtract Tens and Ones Homework & Practice 5.5

Break apart the number being subtracted. Then find the difference.

Question 1.
45 – 16 = __
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 98

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-98

Question 2.
52 – 27 = __
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 99

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-99

Question 3.
84 – 55 = __

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-100

Question 4.
76 – 29 = __

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-101

Question 5.
__ = 23 – 14

Answer: 9

Question 6.
__ = 68 – 49

Answer: 19

Question 7.
Reasoning
Complete the number line and the equation.
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 100

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-100 (2)

Question 8.
Modeling Real Life
How many more cups does Descartes sell than Newton?

Question 9.
DIG DEEPER!
In Exercise 8, 100 cups are sold for the day. Newton sold the rest. How many cups did Newton sell?
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 101

Review & Refresh

Question 10.
47 + 32 = ___

Answer: 79

Question 11.
74 + 15 = __

Answer: 89

Lesson 5.6 Use Compensation to Subtract

Explore and Grow

Use mental math to find each difference.
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 102

How did you use mental math and 41 − 20 to find each difference?
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 103

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-102

Show and Grow

Use compensation to subtract.

Question 1.
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 104

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-104

Question 2.
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 105

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-105

Question 3.
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 106

Answer:
Big-Ideas-Math-Solutions-Grade-2-Chapter-5-Subtraction-to-100-Strategies-106

Question 4.
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 107

Answer:
Big-Ideas-Math-Solutions-Grade-2-Chapter-5-Subtraction-to-100-Strategies-107

Apply and Grow: Practice

Question 5.
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 108

Answer:
Big-Ideas-Math-Solutions-Grade-2-Chapter-5-Subtraction-to-100-Strategies-108

Question 6.
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 109

Answer:
Big-Ideas-Math-Solutions-Grade-2-Chapter-5-Subtraction-to-100-Strategies-109

Question 7.
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 110

Answer:
Big-Ideas-Math-Solutions-Grade-2-Chapter-5-Subtraction-to-100-Strategies-110

Question 8.
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 111

Answer:
Big-Ideas-Math-Solutions-Grade-2-Chapter-5-Subtraction-to-100-Strategies-111

Question 9.
35 – 7 = __

Answer: 28

Question 10.
53 – 37 = __

Answer: 16

Question 11.
Reasoning
Match the expressions that have the same difference.
Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies 112

Answer:
Big-Ideas-Math-Answers-Grade-2-Chapter-5-Subtraction-to-100-Strategies-112

Think and Grow: Modeling Real Life

You blow up 57 balloons for a carnival game. Some of them pop. There are 29 left. How many balloons popped?
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 113
Subtraction equation:
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 114

Answer:
Given,
You blow up 57 balloons for a carnival game. Some of them pop.
There are 29 left.
57 – 29 = 28
28 balloons are popped.

Show and Grow

Question 12.
There are 66 cars in a parking lot. Some of them leave. There are 31 left. How many cars leave the parking lot?
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 115

Answer:
Given,
There are 66 cars in a parking lot. Some of them leave. There are 31 left.
66 – 31 = 35
35 cars leave the parking lot.

Question 13.
You have 78 pictures on your tablet. You take 4 more pictures. Then you delete 17. How many pictures are on your tablet now?
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 116

Answer:
Given,
You have 78 pictures on your tablet. You take 4 more pictures. Then you delete 17.
78 + 4 = 82
84 – 17 = 67
67 pictures are on your tablet now.

Question 14.
You pick 59 strawberries. You eat 5 of them. Then you give 22 to your friend. How many strawberries do you have left?
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 117

Answer:
Given,
You pick 59 strawberries. You eat 5 of them. Then you give 22 to your friend.
59 – 5 = 54
54 – 22 = 32
Thus 32 strawberries are left.

Use Compensation to Subtract Homework & Practice 5.6

Use compensation to subtract.

Question 1.
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 118

Answer:
Big-Ideas-Math-Solutions-Grade-2-Chapter-5-Subtraction-to-100-Strategies-118

Question 2.
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 119

Answer:
Big-Ideas-Math-Solutions-Grade-2-Chapter-5-Subtraction-to-100-Strategies-119

Question 3.
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 120

Answer:
Big-Ideas-Math-Solutions-Grade-2-Chapter-5-Subtraction-to-100-Strategies-120

Question 4.
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 121

Answer:
Big-Ideas-Math-Solutions-Grade-2-Chapter-5-Subtraction-to-100-Strategies-121

Question 5.
27 – 6 = __

Answer: 21

Question 6.
67 – 14 = __

Answer: 53

Use compensation to subtract.

Question 7.
77 – 52 = __

Answer: 25

Question 8.
69 – 44 = ___

Answer: 25

Question 9.
Reasoning
Use the numbers to complete the problem.
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 122

Answer:
Big-Ideas-Math-Solutions-Grade-2-Chapter-5-Subtraction-to-100-Strategies-122

Question 10.
Modeling Real Life
There are 36 boats on a lake. Some of them leave. There are 21 boats left. How many boats leave the lake?
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 123

Answer:
Given,
There are 36 boats on a lake. Some of them leave. There are 21 boats left.
36 – 21 = 15
15 boats leave the lake.

Review & Refresh

Question 11.
Circle groups of 3. Write a repeated addition equation to match.
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 124

Answer: 4 groups of 3
3 + 3 + 3 + 3 =12

Lesson 5.7 Practice Subtraction Strategies

Explore and Grow

Use any strategy to find the difference.
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 125

Compare your strategy to your partner’s strategy. How are your strategies alike? How are they different?
_______________________________
_______________________________
_______________________________

Answer: 42
Use mental math strategy to find the difference of the two numbers 76 and 34
76 – 34 = 42

Show and Grow

Question 1.
81 – 50 = ___

Answer: 31

Question 2.
94 – 8 = __

Answer: 86

Question 3.
58 – 49 = __

Answer: 9

Question 4.
77 – 35 = ___

Answer: 42

Apply and Grow: Practice

Question 5.
97 – 71 = __

Answer: 26

Question 6.
68 – 9 = __

Answer: 59

Question 7.
52 – 28 = ___

Answer: 24

Question 8.
83 – 60 = ___

Answer: 23

Question 9.
__ = 75 – 11

Answer: 64

Question 10.
___ = 46 – 35

Answer: 11

Question 11.
YOU BE THE TEACHER
Your friend uses compensation to subtract. Is your friend correct? Explain.
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 126

Answer:
35 – 30 = 5
Yes, your friend is correct.

Question 12.
A store has 38 hats. 17 of them are sold. How many hats are left?
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 127

Answer:
Given,
A store has 38 hats. 17 of them are sold.
38 – 17 = 21
21 hats are left.

Think and Grow: Modeling Real Life

You have 41 toys. You put some away. There are 22 toys left. How many toys did you put away?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 128
Subtraction equation:
Big Ideas Math Solutions Grade 2 Chapter 5 Subtraction to 100 Strategies 129

Answer:
Given,
You have 41 toys. You put some away.
There are 22 toys left.
41 – 22 = 19 toys
Thus you put away 19 toys.

Show and Grow

Question 13.
A teacher has 62 prizes. He gives some away. There are 26 left. How many prizes did the teacher give away?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 130

Answer:
Given,
A teacher has 62 prizes. He gives some away. There are 26 left.
62 – 26 = 36
Thus the teacher gives away 36 prizes.

Question 14.
A roller-skating rink rents 28 pairs of skates. There are 52 pairs left. How many pairs of skates were there to start?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 131

Answer:
Given,
A roller-skating rink rents 28 pairs of skates. There are 52 pairs left.
52 + 28 = 80
80 pairs of skates were there to start.

Question 15.
A baker has 16 loaves of french bread and 31 loaves of wheat bread. She sells 18 loaves. How many loaves does the baker have left?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 132

Answer:
Given,
A baker has 16 loaves of french bread and 31 loaves of wheat bread. She sells 18 loaves.
16 + 31 = 47 loaves
47 – 18 = 29 loaves
The baker has left 29 loaves.

Practice Subtraction Strategies Homework & Practice 5.7

Question 1.
50 – 20 = __

Answer:
By using the mental math we can subtract the two numbers 50 and 20
50 – 20 = 30

Question 2.
62 – 30 = ___

Answer:
By using the mental math we can subtract the two numbers 62 and 30
62 – 30 = 32

Question 3.
88 – 64 = ___

Answer:
By using the mental math we can subtract the two numbers 88 and 64
88 – 64 = 24

Question 4.
42 – 17 = __

Answer:
By using the mental math we can subtract the two numbers 42 and 17
42 – 17 = 25

Question 5.
__ = 97 – 56

Answer:
By using the mental math we can subtract the two numbers 97 and 56
97 – 56 = 41

Question 6.
___ = 71 – 18

Answer:
By using the mental math we can subtract the two numbers 71 and 18
71 – 18 = 53

Question 7.
___ = 63 – 25

Answer:
By using the mental math we can subtract the two numbers 63 and 25
63 – 25 = 38

Question 8.
__ = 21 – 6

Answer:
By using the mental math we can subtract the two numbers 21 and 6
21 – 6 = 15

Question 9.
Number Sense
Which expressions have a difference of 24?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 133

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-133

Question 10.
Modeling Real Life
27 dogs were adopted from a shelter. There are 14 left. How many dogs were there to start?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 134

Answer:
Given,
27 dogs were adopted from a shelter. There are 14 left.
27 – 14 = 13

Question 11.
Modeling Real Life
86 hot dogs were sold at a baseball game. There are 14 left. How many hot dogs were there to start?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 135

Answer:
Given,
86 hot dogs were sold at a baseball game. There are 14 left.
86 – 14 = 72 hot dogs

Review and Refresh

Question 12.
Circle the shapes that show halves.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 136

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-136
The above two shapes are divided into two equal parts.
Thus the second figure and fourth figure are halves.

Lesson 5.8 Problem Solving: Subtraction

Explore and Grow

Model the story.

Newton collects 58 flowers. He gives 27 away. How many flowers does Newton have left?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 137

Answer:
Given,
Newton collects 58 flowers. He gives 27 away.
58 – 27 = 31
Thus 31 flowers are left.

Newton gives 11 more flowers away. How many flowers does Newton have now?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 138

Answer:
Given,
31 – 11 = 20
Newton has 20 flowers now.

Show and Grow

Question 1.
There are 60 kids at a summer camp. 26 are swimming. 15 are playing soccer. The rest are hiking. How many kids are hiking?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 139

Answer:
Total kids =  60
Swimming = 26
Playing soccer  = 15
Hiking = 60 – 26 – 15  = 19 .

Apply and Grow: Practice

Question 2.
Your class recycles 72 cans. You collected 18 of them. Your friend collected 9. The other students collected the rest. How many cans did the other students collect?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 140

Answer:
Given,
Your class recycles 72 cans. You collected 18 of them.
72 – 18 = 54
Your friend collected 9. The other students collected the rest
54 – 9 = 45
Therefore the other students collect 45 cans.

Question 3.
98 people visit the library in a week. 34 visit on Monday. 14 visit on Tuesday. How many people visit the library the rest of the week?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 141

Answer:
Given,
98 people visit the library in a week. 34 visit on Monday. 14 visit on Tuesday.
34 + 14 = 48
98 – 48 = 50
50 people visit the library the rest of the week.

Question 4.
You have 61 stickers. You give 24 stickers to your friend. Then you get 6 more stickers. How many stickers do you have now?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 142

Answer:
Given,
You have 61 stickers. You give 24 stickers to your friend.
61 – 24 = 37 stickers
Then you get 6 more stickers.
37 + 6 = 43 stickers
Thus you have 43 stickers now.

Think and Grow: Modeling Real Life

You collect 47 pine cones. Your friend collects 21 fewer than you. How many pine cones do you and your friend collect in all?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 143
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 144

Answer:
Given,
You collect 47 pine cones. Your friend collects 21 fewer than you.
47 – 21 = 26
Now we have to find how many pine cones do you and your friend collect in all.
47 + 26 = 73 pine cones

Show and Grow

Question 5.
A garbage truck collects trash from 68 trash cans. Another truck collects trash from 39 fewer cans. How many cans of trash do the trucks collect from in all?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 145

Explain the steps you used to solve the problem.
_________________________________
_________________________________
_________________________________

Answer:
Given,
A garbage truck collects trash from 68 trash cans. Another truck collects trash from 39 fewer cans
68 – 39 = 29 trash cans are collected by another cans.
68 + 29 = 97 trash cans

Problem Solving: Subtraction Homework & Practice 5.8

Question 1.
There are 39 people in a pool. 8 are floating on rafts. 11 are playing a game. The rest are swimming laps. How many people are swimming laps?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 146

Answer:
Given,
There are 39 people in a pool. 8 are floating on rafts. 11 are playing a game. The rest are swimming laps.
39 – 19 = 20
Thus 20 people are swimming laps.

Question 2.
Newton collects 24 rocks. He gives 13 to Descartes. Then Newton collects 8 more rocks. How many rocks does Newton have now?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 147

Answer:
Given,
Newton collects 24 rocks. He gives 13 to Descartes.
24 – 13 = 11
Then Newton collects 8 more rocks
11 + 8 = 19
Newton has 19 rocks now.

Question 3.
Modeling Real Life
You use 76 craft sticks. Your friend uses 62 fewer than you. How many craft sticks do you and your friend use in all?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 148

Answer:
Given,
You use 76 craft sticks. Your friend uses 62 fewer than you.
76 – 62 = 14 craft sticks
your friend uses 14 craft sticks
76 + 14 = 90 craft sticks

Question 4.
Modeling Real Life
You put 52 photos in an album. Your friend puts in 17 fewer than you. How many photos do you and your friend put in the album in all?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 149

Answer:
Given,
You put 52 photos in an album. Your friend puts in 17 fewer than you.
52 – 17 = 35 photos
52 + 35 = 87 photos
Thus 87 photos you and your friend put in the album in all.

Review & Refresh

Question 5.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 150

Answer: A hexagon is a polygon that contains 6 straight sides and 6 vertices.

Question 6.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 151

Answer: A triangle is a polygon that consists of 3 straight sides and 3 vertices.

Subtraction to 100 Strategies Performance Task

A science class uses an incubator to hatch chicken eggs.

Question 1.
The temperature of the incubator must be 99°F. The current temperature is 25°F less than the correct temperature. What is the current temperature?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 152

Answer:
Given,
The temperature of the incubator must be 99°F. The current temperature is 25°F less than the correct temperature.
99°F – 25°F = 74°F
The current temperature is 74°F.

Question 2.
a. The school has 4 incubators. Each one has 8 eggs. Each egg must be rotated 3 times every day. How many total rotations must be made to all of the eggs in all 4 incubators?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 153

Answer:
Given,
The school has 4 incubators.
Each one has 8 eggs. Each egg must be rotated 3 times every day.
8 × 4 = 32 eggs in all 4 incubators.
32 × 4 = 128 rotations

b. Two of your friends each complete 25 rotations. How many rotations are left?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 154

Answer:
Two of your friends each complete 25 rotations.
128 – 25 = 103 rotations are left

Question 3.
a. The first egg hatches at 11:00. The second egg hatches a half hour late. What time does the second egg hatch?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 155

Answer:
Given,
The first egg hatches at 11:00. The second egg hatches a half hour late.
11:00 + 00:30 = 11:30

b. The third egg hatches an hour after the second egg. What time does the third egg hatch?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 155.1

Answer:
Given,
The third egg hatches an hour after the second egg.
11:30 + 1:00 = 12:30

Subtraction to 100 Strategies Activity

Three in a Row: Subtraction

To Play: Players take turns. On your turn, spin both spinners. Subtract the numbers, and cover the difference on the game board. Continue until someone gets three in a row.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 156

Subtraction to 100 Strategies Chapter Practice 5

5.1 Subtract Tens and Ones Using a Number Line

Question 1.
90 – 40 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 157

Answer: 50
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-157

Question 2.
66 – 20 = ___
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 158

Answer: 46
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-157

5.2 Subtract Tens and Ones Using a Number Line

Question 3.
78 – 32 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 159

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-159

Question 4.
49 – 16 = ___
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 160

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-159

Question 5.
Modeling Real Life
You have 54 stickers and 21 key chains. How many more stickers do you have than key chains?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 161

Answer:
Given,
You have 54 stickers and 21 key chains.
54 – 21 = 33 stickers
Thus you have 33 stickers than key chains.

5.3 Use Addition to Subtract

Add to find the difference.

Question 6.
44 – 28 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 162

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-161

Question 7.
84 – 56 = __
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 163

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-162

5.4 Decompose to Subtract

Break apart the number being subtracted. Then find the difference.

Question 8.
44 − 5 = __

Answer: 39
Big Ideas Math Book 2nd Grade Answer Key Chapter 5 Subtraction to 100 Strategies img_164
Break the number into two parts and find the difference of two numbers.

Question 10.
67 − 9 = __

Answer: 58
Big Ideas Math Book 2nd Grade Answer Key Chapter 5 Subtraction to 100 Strategies img_165
Break the number into two parts and find the difference of two numbers.

Question 11.
32 − 4 = ___

Answer: 28
Big Ideas Math Book 2nd Grade Answer Key Chapter 5 Subtraction to 100 Strategies img_166
Break the number into two parts and find the difference of two numbers.

Question 12.
Number Sense
Which way would you break apart 8 to find 56 − 8? Explain.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 164

Answer: Both are correct to use break apart strategy to find the difference between 56 and 8.

5.5 Decompose to Subtract Tens and Ones

Break apart the number being subtracted. Then find the difference.

Question 13.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 165

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-165

Question 14.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 166

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-166

5.6 Use Compensation to Subtract

Use compensation to Subtract

Question 15.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 167

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-167

Question 16.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 168

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-168

Question 17.
Reasoning
Match the expressions that have the same difference.
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 169

Answer:
Big-Ideas-Math-Answer-Key-Grade-2-Chapter-5-Subtraction-to-100-Strategies-169

5.7 Practice Subtraction Strategies

Question 18.
58 − 36 = ___

Answer: 22

Question 19.
67 − 52 = ___

Answer: 15

5.8 Problem Solving: Subtraction

Question 20.
There are 31 papers to pass out. You pass out 12 papers. Then you pass out 8 more. How many papers do you have left?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 170

Answer:
Given,
There are 31 papers to pass out. You pass out 12 papers.
31 – 12 = 19 papers
Then you pass out 8 more.
19 + 8 = 27 papers are left.

Question 21.
47 students are on the playground. 23 fewer students are playing soccer than on the playground. How many students are on the playground and playing soccer in all?
Big Ideas Math Answer Key Grade 2 Chapter 5 Subtraction to 100 Strategies 171

Answer:
Given,
47 students are on the playground.
23 fewer students are playing soccer than on the playground.
47 – 23 = 24 students
47 + 24 = 71 students

Final Words:

I hope the data mentioned here about Big Ideas Math Answers Grade 2 Chapter 5 Subtraction to 100 Strategies are useful to score better marks in the exam. Students are advised to prepare well by referring Big Ideas Math Book Grade 2 Chapter 5 Subtraction to 100 Strategies Answer Key. Bookmark our site https://bigideasmathanswers.com/ to get the updates on other solution keys of Big Ideas Math Grade 2 Chapters.

Big Ideas Math Answers Grade 5 Chapter 14 Classify Two-Dimensional Shapes

Big Ideas Math Answers Grade 5 Chapter 14 Classify Two-Dimensional Shapes

The various topics included in the Big Ideas Math Answers Grade 5 Chapter 14 Classify Two-Dimensional Shapes. Check your math skills by taking the practice sections provided on this page. If you are looking for the Big Ideas Math Book 5th Grade Answer Key Chapter 14 Classify Two-Dimensional Shapes, then get it here. Begin your practice immediately using BIM 5th Grade Answer Key Chapter 14 Classify Two-Dimensional Shapes. Freely access all of our math answers to learn them perfectly. Download Big Ideas Math Answers Grade 5 Chapter 14 Classify Two-Dimensional Shapes PDF for free.

Big Ideas Math Book 5th Grade Chapter 14 Classify Two-Dimensional Shapes Answer Key

We have given all the topics for the sake of students to help them while preparing for the exam. Practice all given problems and know the various problems those impose in the exam. Every problem has its own answer and explanation that makes the student’s preparation easier. Go through the list given below to know the topics covered in Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes. The main topics covered in this chapter are Classify Triangles, Relate Quadrilaterals, and Quadrilaterals are explained here.

Lesson: 1 Classify Triangles

Lesson: 2 Classify Quadrilaterals

Lesson: 3 Relate Quadrilaterals

Classify Two-Dimensional Shapes

Lesson 14.1 Classify Triangles

Explore and Grow

Draw and label a triangle for each description. If a triangle cannot be drawn, explain why.
Big Ideas Math Answers Grade 5 Chapter 14 Classify Two-Dimensional Shapes 1

Precision
Draw a triangle that meets two of the descriptions above.

Answer:
Big-Ideas-Math-Answers-Grade-5-Chapter-14-Classify-Two-Dimensional-Shapes-1

Think and Grow: Classify Triangles

Key Idea
Triangles can be classified by their sides.

Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 2
An equilateral triangle has three sides with the same length.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 3
An isosceles triangle has two sides with the same length.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 4
A scalene triangle has no sides with the same length.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 5

Key Idea
Triangles can be classified by their angles.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 6
An acute triangle has three acute angles.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 7
An obtuse triangle has one obtuse angle.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 8
A right triangle has one right angle.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 9
An equiangular triangle has three angles with the same measure.
Example
Classify the triangle by its angles and its sides.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 10
The triangle has one ___ angle
and ___ sides with the same length.
So, it is a ___ triangle.

Answer:
The triangle has one right angle
and no sides with the same length.
So, it is a right triangle.

Show and Grow

Classify the triangle by its angles and its sides

Question 1.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 11

Answer:  Equilateral triangle.

Explanation: An equilateral triangle has three sides of the same length.

Question 2.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 12

Answer: Isosceles triangle

Explanation: An Isosceles triangle has two sides of the same size. Two of its angle also measure equal.

Question 3.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 13

Answer:  Scalene triangle.

Explanation: A Scalene triangle has no sides are congruent (same size)

Apply and Grow: Practice

Classify the triangle by its angles and its sides.

Question 4.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 14

Answer:  Right triangle.

Explanation: In a triangle one of the angle is a right angle (90 Deg ) called as Right triangle.

Question 5.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 15

Answer: Isosceles triangle.

Explanation: An Isosceles triangle has two sides of the same size. Two of its angle also measure equal.

Question 6.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 16

Answer: Equiangular triangle

Explanation: In an equilateral triangle, all the lengths of the sides are equal. In such a case, each of the interior angles will have a measure of 60 degrees. Since the angles of an equilateral triangle are the same, it is also known as an equiangular triangle. The figure given below illustrates an equilateral triangle.

Question 7.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 17

Answer:  Isosceles triangle.

Explanation: An Isosceles triangle has two sides of the same length. Two of its angle also measure equal.

Question 8.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 18

Answer:  Scalene triangle.

Explanation: A Scalene triangle has no sides are congruent (Same size) and angles also all different.

Question 9.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 19

Answer:  Right triangle.

Explanation: In a triangle one of the angle is a right angle (90 deg ) called a Right triangle.

Question 10.
A triangular sign has a 40° angle, a 55° angle, and an 85° angle. None of its sides have the same length. Classify the triangle by its angles and its sides.

Answer:  Scalene triangle.

Explanation: A Scalene triangle has no sides that are congruent (Same size) and angles also all different.

Question 11.
YOU BE THE TEACHER
Your friend says the triangle is an acute triangle because it has two acute angles. Is your friend correct? Explain.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 20

Answer:  Above is no acute triangle and it is called a scalene triangle.

Explanation: A Scalene triangle has only no sides that are congruent (Same size) and angles also all different. So it is called a scalene triangle.

Question 12.
DIG DEEPER!
Draw one triangle for each category. Which is the appropriate category for an equiangular triangle? Explain your reasoning.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 21

Answer:
Big-Ideas-Math-Answer-Key-Grade-5-Chapter-14-Classify-Two-Dimensional-Shapes-21
From the figure, we can say that acute triangles have the same length. So, the first triangle is the equiangular triangle.

Think and Grow: Modeling Real Life

Example
A bridge contains several identical triangles. Classify each triangle by its angles and its sides. What is the length of the bridge?
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 22
Each triangle has ___ angles with the same measure and ___ sides with the same length.
So, each triangle is ___ and ___.
The side lengths of 6 identical triangles meet to form the length of the bridge. So, multiply the side length by 6 to find the length of the bridge.
27 × 6 = ___
So, the bridge is ___ long.

Answer:
Each triangle has 3 angles with the same measure and 3 sides with the same length.
The side lengths of 6 identical triangles meet to form the length of the bridge. So, multiply the side length by 6 to find the length of the bridge.
27 × 6 = 162
So, the bridge is 162 ft long.

Show and Grow

Question 13.
The window is made using identical triangular panes of glass. Classify each triangle by its angles and its sides. What is the height of the window?
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 23

Answer:
Big-Ideas-Math-Answer-Key-Grade-5-Chapter-14-Classify-Two-Dimensional-Shapes-23
The length of the two sides of the triangle is the same.
18 in + 18 in = 36 inches
Thus the height of the window is 36 inches

Question 14.
DIG DEEPER!
You connect four triangular pieces of fabric to make the kite. Classify the triangles by their angles and their sides. Use a ruler and a protractor to verify your answer.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 24

Answer:
The name of the blue triangle is isosceles right angle triangle.
The two sides of the triangle are the same.
The name of the red triangle is isosceles right-angle triangle.
The two sides of the triangle are the same.
The name of the green triangle is isosceles right angle triangle.
The two sides of the triangle are the same.
The name of the yellow triangle is isosceles right angle triangle.
The two sides of the triangle are the same.

Classify Triangles Homework & Practice 14.1

Classify the triangle by its angles and its sides.

Question 1.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 25

Answer:  Scalene triangle.

Explanation: A Scalene triangle has only no sides that are congruent (Same size) and angles also all different. So it is called a scalene triangle

Question 2.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 26

Answer: Isosceles triangle.

Explanation: An Isosceles triangle has two sides of the same size. Two of its angle also measure equal.

Question 3.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 27

Answer: Scalene triangle.

Explanation: A Scalene triangle has no sides that are congruent (Same size) and angles also all different.

Question 4.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 28

Answer: Isosceles triangle.

Explanation: An Isosceles triangle has two sides of the same length. Two of its angle also measure equal.

Question 5.

Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 29

Answer:  Scalene triangle.

Explanation: A Scalene triangle has no sides that are congruent (Same size) and angles also all different.

Question 6.

Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 30

Answer:  Equiangular triangle.

Explanation:
In an equilateral triangle, all the lengths of the sides are equal. In such a case, each of the interior angles will have a measure of 60 degrees. Since the angles of an equilateral triangle are the same, it is also known as an equiangular triangle. The figure given below illustrates an equilateral triangle.

Question 7.
A triangular race flag has two 65° angles and a 50° angle. Two of its sides have the same length. Classify the triangle by its angles and its sides.

Answer: Isosceles triangle.

Explanation:  An Isosceles triangle has two sides of the same size. Two of its angle also measure equal.

Question 8.
A triangular measuring tool has a 90° angle and no sides of the same length. Classify the triangle by its angles and its sides.

Answer: Right triangle.

Explanation: In a triangle one of the angle is a right angle (90 Deg ) called a Right triangle.

Question 9.

Structure

Draw a triangle with vertices A(2, 2), B(2, 6), and C(6, 2) in the coordinate plane. Classify the triangle by its angles and its sides. Explain your reasoning.

Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 31

Answer:
Big-Ideas-Math-Answer-Key-Grade-5-Chapter-14-Classify-Two-Dimensional-Shapes-31

Question 10.

YOU BE THE TEACHER

Your friend says that both Newton and Descartes are correct. Is your friend correct? Explain.

Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 32

Answer: Yes

Explanation:  An acute triangle is a triangle in which each angle is an acute angle. Any triangle which is not acute is either a right triangle or an obtuse triangle. All acute triangle angles are less than 90 degrees. For example, an equilateral triangle is always acute, since all angles (which are 60) are all less than 90.

Question 11.
DIG DEEPER!
The sum of all the angle measures in a triangle is 180°. A triangle has a 34° angle and a 26° angle. Is the triangle acute, right, or obtuse? Explain.

Answer: Scalene triangle.

Explanation: A Scalene triangle has no sides that are congruent (Same size) and angles also all different.

Question 12.
Modeling Real Life
A designer creates the logo using identical triangles. Classify each triangle by its angles and its sides. What is the perimeter of the logo?

Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 33

Answer: Equiangular triangle

Explanation: In an equilateral triangle, all the lengths of the sides are equal. In such a case, each of the interior angles will have a measure of 60 degrees. Since the angles of an equilateral triangle are the same, it is also known as an equiangular triangle. The figure given below illustrates an equilateral triangle.

Question 13.
DIG DEEPER!
The window is made using identical triangular panes of glass. Classify each triangle by its angles and its sides. What are the perimeter and the area of the window? Explain your reasoning.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 34

Answer: Right triangle.

Explanation: A right triangle is a triangle in which one of the angles is 90 degrees. In a right triangle, the side opposite to the right angle (90-degree angle) will be the longest side and is called the hypotenuse. You may come across triangle types with combined names like right isosceles triangle and such, but this only implies that the triangle has two equal sides with one of the interior angles being 90 degrees. The figure given below illustrates a right triangle

Review & Refresh

Question 14.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 35

Answer : \(\frac{1}{4}\) =0.25

Explanation: 2 divides by 8  with 1/4 times, So the answer is 1/4.

Question 15.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 36

Answer : \(\frac{15}{4}\) = 3.75

Explanation: 15 divides by 4 with \(\frac{15}{4}\) times, So the answer is \(\frac{15}{4}\) or 3.75.

Question 16.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 37

Answer : \(\frac{15}{12}\) = \(\frac{1}{4}\) = 1.25

Explanation: 15 divides by 12 with \(\frac{1}{4}\) times, So the answer is \(\frac{1}{4}\).

Lesson 14.2 Classify Quadrilaterals

Explore and Grow

Draw and label a quadrilateral for each description. If a quadrilateral cannot be drawn, explain why

Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 38

Precision
Draw a quadrilateral that meets three of the descriptions above.

Answer:
Big-Ideas-Math-Answer-Key-Grade-5-Chapter-14-Classify-Two-Dimensional-Shapes-38

Think and Grow: Classify Quadrilaterals

Key Idea
Quadrilaterals can be classified by their angles and their sides.
A trapezoid is a quadrilateral that has exactly one pair of parallel sides.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 39
A parallelogram is a quadrilateral that has two pairs of parallel sides. Opposite sides have the same length.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 40
A rectangle is a parallelogram that has four right angles.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 41
A rhombus is a parallelogram that has four sides with the same length.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 42
A square is a parallelogram that has four right angles and four sides with the same length.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 43

Example
Classify the quadrilateral in as many ways as possible.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 44

Answer:
Big-Ideas-Math-Answer-Key-Grade-5-Chapter-14-Classify-Two-Dimensional-Shapes-44

Show and Grow

Classify the quadrilateral in as many ways as possible.

Question 1.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 45

Answer:  Square

Explanation: A square is a parallelogram that has four right angles and four sides with the same length.

Question 2.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 46

Answer: Trapezoid 

Explanation: A trapezoid is a quadrilateral that has exactly one pair of parallel sides

Apply and Grow: Practice

Classify the quadrilateral in as many ways as possible.

Question 3.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 47

Answer: Parallelogram

Explanation: A parallelogram is a quadrilateral that has two pairs of parallel sides. The opposite sides have the same length.

Question 4.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 48

Answer:  Square

Explanation: A square is a parallelogram that has four right angles and four sides with the same length.

Question 5.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 49

Answer: Rectangle

Explanation: A rectangle is a parallelogram that has four right angles and diagonals are congruent.

Question 6.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 50

Answer: Rhombus

Explanation: A rhombus is a parallelogram with four congruent sides and A rhombus has all the properties of a parallelogram. The diagonals intersect at right angles.

Question 7.
A sign has the shape of a quadrilateral that has two pairs of parallel sides, four sides with the same length, and no right angles

Answer: Parallelogram

Explanation:
Assume that a quadrilateral has parallel sides or equal sides unless that is stated. A parallelogram has two parallel pairs of opposite sides. A rectangle has two pairs of opposite sides parallel, and four right angles.

Question 8.
A tabletop has the shape of a quadrilateral with exactly one pair of parallel sides.

Answer: A trapezoid is a quadrilateral that has exactly one pair of parallel sides. A parallelogram is a quadrilateral that has two pairs of parallel sides.

Question 9.
YOU BE THE TEACHER
Your friend says that a quadrilateral with at least two right angles must be a parallelogram. Is your friend correct? Explain.

Explanation: A trapezoid is only required to have two parallel sides. However, a trapezoid could have one of the sides connecting the two parallel sides perpendicular to the parallel sides which would yield two right angles.

enter image source here

Question 10.
Which One Doesn’t Belong? Which cannot set of lengths be the side lengths of a parallelogram?
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 51

Answer: 9 yd, 5 yd, 5 yd, 3 yd

Explanation: A parallelogram is a quadrilateral that has two pairs of parallel sides. Opposite sides have the same length, So the above one is not a parallelogram.

Think and Grow: Modeling Real Life

Example
The dashed line shows how you cut the bottom of a rectangular door so it opens more easily. Classify the new shape of the door.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 52
Draw the new shape of the door.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 53

Answer:
The original shape of the door was a rectangle, so it had one pairs of parallel sides. The new shape of the door has exactly one pair of parallel sides. So, the new shape of the door is a trapezoid.

Show and Grow

Question 11.
DIG DEEPER!
The dashed line shows how you cut the corner of the trapezoidal piece of fabric. The line you cut is parallel to the opposite side. Classify the new shape of the four-sided piece of fabric.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 54

Answer: Parallelogram

Explanation: A parallelogram is a quadrilateral that has two pairs of parallel sides. The opposite sides have the same length.

Question 12.
A farmer encloses a section of land using the four pieces of fencing. Name all of the four-sided shapes that the farmer can enclose with the fencing.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 55

Answer: Parallelogram

Explanation: A parallelogram is a quadrilateral that has two pairs of parallel sides. Opposite sides have the same length, So four-sided shapes of fencing look like Parallelogram.

Classify Quadrilaterals Homework & Practice 14.2

Classify the quadrilateral in as many ways as possible.

Question 1.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 56

Answer: Trapezoid 

Explanation: A trapezoid is a quadrilateral that has exactly one pair of parallel sides

Question 2.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 57

Answer: Trapezoid

Explanation: A Trapezoid is a quadrilateral with exactly one pair of parallel sides. (There may be some confusion about this word depending on which country you’re in. In India and Britain, they say trapezium; in America, trapezium usually means a quadrilateral with no parallel sides.)

Question 3.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 58

Answer: Rectangle

Explanation: A rectangle is a parallelogram that has four right angles and diagonals are congruent.

Question 4.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 59

Answer: Square

Explanation: The diagonals of a square bisect each other and meet at 90°. The diagonals of a square bisect its angles. The opposite sides of a square are both parallel and equal in length. All four angles of a square are equal (each being 360°/4 = 90°, a right angle).

Question 5.
A name tag has the shape of a quadrilateral that has two pairs of parallel sides and four right angles. Opposite sides are the same length, but not all four sides are the same length.

Answer: Rectangle

Explanation: A rectangle is a parallelogram that has four right angles and diagonals are congruent.

Question 6.
A napkin has the shape of a quadrilateral that has two pairs of parallel sides, four sides with the same length, and four right angles.

Answer: Square

Explanation: A square is a parallelogram that has four right angles and four sides of the same length.

Question 7.
Reasoning
Can you draw a quadrilateral that is not a square, but has four right angles? Explain.

Answer: A rectangle is a parallelogram that has four right angles

Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 58

Question 8.
Structure
Plot two more points in the coordinate plane to form a square. What two points can you plot to form a parallelogram? What two points can you plot to form a trapezoid? Do not use the same pair of points twice.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 60

Answer:
Big-Ideas-Math-Answer-Key-Grade-5-Chapter-14-Classify-Two-Dimensional-Shapes-60

Question 9.
DIG DEEPER!
Which quadrilateral can be classified as a parallelogram, and rectangle, square, rhombus? Explain.

Answer: Square

Explanation: A square can be defined as a rhombus which is also a rectangle – in other words, a parallelogram with four congruent sides and four right angles. A trapezoid is a quadrilateral with exactly one pair of parallel sides.

Question 10.
Modeling Real Life
The dashed line shows how you fold the flap of the envelope so it closes. Classify the new shape of the envelope.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 61

Answer: Rectangle

Explanation: A rectangle is a parallelogram that has four right angles and diagonals are congruent.

Question 11.
DIG DEEPER!
A construction worker tapes off a section of land using the four pieces of caution tape. Name all of the possible shapes that the worker can enclose with the tape.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 62

Answer: Trapezoid

Explanation: A trapezoid is a quadrilateral that has exactly one pair of parallel sides.

Question 12.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 62.1

Answer: \(\frac{1}{2}\)

Explanation: \(\frac{2}{3}\) –\(\frac{1}{6}\) equal to \(\frac{1}{2}\).

Question 13.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 62.2

Answer: 0.112

Explanation: \(\frac{1}{2}\) is equal to 0.5 and 7/18 is equal to 0.3888.So subtraction from 0.5 to 0.3888 is 0.112.

Question 14.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 62.3

Answer: 0.289

Explanation: \(\frac{2}{5}\) is equal to 0.4 and 1/9 is equal to 0.111,So subtraction from 0.4 to 0.111is 0.289.

Lesson 14.3 Relate Quadrilaterals

Explore and Grow

Label the Venn diagram to show the relationships among quadrilaterals. The first one has been done for you.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 63

Reasoning
Explain how you decided where to place each quadrilateral.

Think and Grow: Relate Quadrilaterals

Key Idea
The Venn diagram shows the relationships among quadrilaterals.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 64

Example
Tell whether the statement is true or false.
All rhombuses are rectangles.
Rhombuses do not always have four right angles.
So, the statement is ___.

Answer: So, the statement is true.

Example
Tell whether the statement is true or false.
All rectangles are parallelograms.
All rectangles have two pairs of parallel sides.
So, the statement is ___.

Show and Grow

Tell whether the statement is true or false. Explain.

Question 1.
Some rhombuses are squares.

Answer: true

Explanation: A rhombus is a quadrilateral (plane figure, closed shape, four sides) with four equal-length sides and opposite sides parallel to each other. All squares are rhombuses, but not all rhombuses are squares. The opposite interior angles of rhombuses are congruent.

Question 2.
All parallelograms are rectangles.

Answer: False

Explanation: A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. On the other hand, not all quadrilaterals and parallelograms are rectangles. A rectangle has all the properties of a parallelogram

Apply and Grow: Practice

Tell whether the statement is true or false. Explain.

Question 3.
All rectangles are squares.

Answer: False

Explanation: All squares are rectangles, but not all rectangles are squares.

Question 4.
Some parallelograms are trapezoids.

Answer: True

Explanation: A trapezoid has one pair of parallel sides and a parallelogram has two pairs of parallel sides. So a parallelogram is also a trapezoid.

Question 5.
Some rhombuses are rectangles.

Answer: False

Explanation: A rhombus is defined as a parallelogram with four equal sides. Is a rhombus always a rectangle? No, because a rhombus does not have to have 4 right angles. Kites have two pairs of adjacent sides that are equal.

Question 6.
All trapezoids are quadrilaterals.

Answer: True

Explanation: Trapezoids have only one pair of parallel sides; parallelograms have two pairs of parallel sides. The correct answer is that all trapezoids are quadrilaterals. Trapezoids are four-sided polygons, so they are all quadrilaterals

Question 7.
All squares are rhombuses.

Answer: True

Explanation: All squares are rhombuses, but not all rhombuses are squares. The opposite interior angles of rhombuses are congruent

Question 8.
Some trapezoids are squares.

Answer: True

Explanation: A trapezoid is a quadrilateral with at least one pair of parallel sides. In a square, there are always two pairs of parallel sides, so every square is also a trapezoid. Conversely, only some trapezoids are squares

Question 9.
Reasoning
Use the word cards to complete the graphic organizer.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 65

Answer: The first box to be filled with Square, 3d box to be filled with Rectangle,4th box to be filled with trapezoid and final box to be filled with Quadrilateral.

Explanation: A Square can be defined as a rhombus which is also a rectangle, in other words, a parallelogram with four congruent sides and four right angles. A trapezoid is a quadrilateral with exactly one pair of parallel sides.

Question 10.
Reasoning
All rectangles are parallelograms. Are all parallelograms rectangles? Explain.

Answer: True

Explanation: A rectangle is considered a special case of a parallelogram because, A parallelogram is a quadrilateral with 2 pairs of opposite, equal and parallel sides. A rectangle is a quadrilateral with 2 pairs of opposite, equal and parallel sides but also forms right angles between adjacent sides.

Question 11.
Precision
Newton says the figure is a square. Descartes says the figure is a parallelogram. Your friend says the figure is a rhombus. Are all three correct? Explain.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 66

Answer: No

Explanation:  A square has two pairs of parallel sides, four right angles, and all four sides are equal. It is also a rectangle and a parallelogram. A rhombus is defined as a parallelogram with four equal sides. No, because a rhombus does not have to have 4 right angles.

Think and Grow: Modeling Real Life

Example
You use toothpicks to create several parallelograms. You notice that opposite angles of parallelograms have the same measure. For what other quadrilaterals is this also true?
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 66.1
Parallelograms have the property that opposite angles have the same measure. Subcategories of parallelograms must also have this property.
___, ___, and ___ are subcategories of parallelograms.
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 67
So, ___, ____, and ____ also have opposite angles with the same measure.

Answer: Rectangle, Rhombus and Square are subcategories of parallelograms.

Show and Grow

Question 12.
You use pencils to create several rhombuses. You notice that diagonals of rhombuses are perpendicular and divide each other into two equal parts. For what other quadrilateral is this also true? Explain your reasoning.
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 68

Answer: Square, Parallelogram, Rhombus are perpendicular and divided into the equal parts.

Question 13.
DIG DEEPER!
You place two identical parallelograms side by side. What can you conclude about the measures of adjacent angles in a parallelogram? For what other quadrilaterals is this also true? Explain your reasoning.
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 69

Answer:
The adjacent angles of the parallelogram is supplementary.
Opposite angles of the parallelogram are equal.

Relate Quadrilaterals Homework & Practice 14.3

Tell whether the statement is true or false. Explain.

Question 1.
All trapezoids are parallelograms.

Answer: False

Explanation: The pair of opposite sides of a parallelogram are equal and parallel but in the case of trapezium, this is not true in that only one pair of opposite sides are equal. Therefore every parallelogram is not a trapezium.
Question 2.

All rectangles are parallelograms.

Answer: True

Explanation: Each pair of co-interior angles are supplementary, because two right angles add to a straight angle, so the opposite sides of a rectangle are parallel. This means that a rectangle is a parallelogram, so, Its opposite sides are equal and parallel. Its diagonals bisect each other.

Question 3.
All squares are quadrilaterals.

Answer: True

Explanation: A closed figure with four sides. For example, kites, parallelograms, rectangles, rhombuses, squares, and trapezoids are all quadrilaterals. Kite: A quadrilateral with two pairs of adjacent sides that are equal in length; a kite is a rhombus if all side lengths are equal.
Question 4.

Some quadrilaterals are trapezoids.

Answer: True

Explanation: Trapezoids have only one pair of parallel sides, parallelograms have two pairs of parallel sides. A trapezoid can never be a parallelogram. The correct answer is that all trapezoids are quadrilaterals.

Question 5.
Some parallelograms are rectangles.

Answer: True

Explanation: Not all parallelograms are rectangles. A parallelogram is a rectangle if it has four right angles and two pairs of parallel and congruent sides.

Question 6.
All squares are rectangles and rhombuses.

Answer: False

Explanation: No, because all four sides of a rectangle don’t have to be equal. However, the sets of rectangles and rhombuses do intersect, and their intersection is the set of squares, all squares are both a rectangle and a rhombus.

Question 7.
YOU BE THE TEACHER
Newton says he can draw a quadrilateral that is not a trapezoid and not a parallelogram. Is Newton correct? Explain.

Answer: False

Explanation: Trapezoids have only one pair of parallel sides; parallelograms have two pairs of parallel sides. A trapezoid can never be a parallelogram. The correct answer is that all trapezoids are quadrilaterals.

Question 8.
Writing
Explain why a parallelogram is not a trapezoid.

Explanation: a square is a quadrilateral, a parallelogram, a rectangle, and a rhombus Is a trapezoid a parallelogram? No, because a trapezoid has only one pair of parallel sides.

Reasoning
Write always, sometimes, or never to make the statement true? Explain.

Question 9.
A rhombus is ___ a square.

Answer: A rhombus is  some times a square

Explanation: A rhombus is a square. This is sometimes true. Â It is true when a rhombus has 4 right angles. It is not true when a rhombus does not have any right angles.

Question 10.
A trapezoid is __ a rectangle.

Answer: A trapezoid is sometimes a rectangle.

Explanation: A rectangle has one pair of parallel sides.

Question 11.
A parallelogram is ___ a quadrilateral.

Answer: A parallelogram is always a quadrilateral.

Explanation: A parallelogram must have 4 sides, so they must always be quadrilaterals.

Question 12.
DIG DEEPER!
A quadrilateral has exactly three sides that have the same length. Why can the figure not be a rectangle?

Explanation: A rectangle is a parallelogram that has four right angles. opposite sides are in the same length, so the above one is not a rectangle.

Question 13.

Modeling Real Life
You fold the rectangular piece of paper. You notice that the line segments connecting the halfway points of opposite sides are perpendicular. For what other quadrilateral is this also true?
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 70

Explanation: A rectangle is a parallelogram that has four right angles. opposite sides are in the same length, so the above one is not a rectangle.

Question 14.
DIG DEEPER!
You tear off the four corners of the square and arrange them to form a circle. You notice that the sum of the angle measures of a square is equal to 360°. For what other quadrilaterals is this also true?
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 71

Answer: The sum of the angles in a parallelogram are 360°

Review & Refresh

Question 15.
5 pt = ___ c

Answer : 5 pt = 10 c

Explanation:
Convert from pints to cups.
1 pint = 2 cups
5 pints = 5 × 2 cups
5 pints = 10 cups

Question 16.
32 fl oz = ___ c
Answer: 32 fl oz =  4 c
Explanation:
Convert from fl oz to cups.
1 fl oz = 0.125 cups
32 fl oz are equal to 4 c.

Question 17.
20 qt = ___ c

Answer : 20 qt = 80 c

Explanation:
Convert from quarts to cups.
1 quart = 4 cups
20 qt = 20 × 4 cups = 80 cups

Classify Two-Dimensional Shapes Performance Task 14

A homeowner wants to install solar panels on her roof to generate electricity for her house. A solar panel is 65 inches long and 39 inches wide.

Question 1.
a. The shape of the panel has 4 right angles. Sketch and classify the shape of the solar panel.

Answer : Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 41

Explanation: A rectangle is a parallelogram that has four right angles. So the shape of the solar panel is a rectangle.

b. There are 60 identical solar cells in a solar panel, arranged in an array. Ten cells meet to form the length of the panel, and six cells meet to form the width. Classify the shape of each solar cell. Explain your reasoning.
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 72

Answer: A rectangle is a parallelogram that has four right angles. So the shape of the solar panel is a rectangle.

Question 2.
The home owner measures three sections of her roof.
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 73
a. Classify the shape of each section in as many ways as possible.

Answer:  Right triangle.

Explanation: In a triangle one of the angle is a right angle (90 Deg ) called as Right triangle

Answer: Rectangle

Explanation: Rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. On the other hand, not all quadrilaterals and parallelograms are rectangles.

Answer: Isosceles trapezoid

Explanation: An isosceles trapezoid is a trapezoid whose non-parallel sides are congruent.

b. About how many solar panels can fit on the measured sections of the roof? Explain your reasoning.

Question 3.
One solar panel can produce about 30 kilowatt-hours of electricity each month. The homeowner uses her electric bills to determine that she uses about 1,200 kilowatt-hours of electricity each month.

a. How many solar panels should the homeowner install on her roof?

Answer: 40 Solar panels

Explanation: 40 Solar panels X 30 kilowatt-hours of electricity each month per one solar panel equal to 1,200 kilowatt-hours of electricity per month, So the answer is 40 solar panels.

b. Will all of the solar panels fit on the measured sections of the roof? Explain.

Classify Two-Dimensional Shapes Activity

Quadrilateral Lineup

Directions:

  1. Players take turns spinning the spinner.
  2. On your turn, cover a quadrilateral that matches your spin.
  3. If you land on, Lose a turn, then do not cover a quadrilateral.
  4. The first player to get four in a row twice, horizontally, vertically, Recor diagonally, wins!

Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 74
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 75

Classify Two-Dimensional Shapes Chapter Practice 14

14.1 Classify Triangles

Classify the triangle by its angles and its sides.

Question 1.
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 76

Answer: Scalene triangle.
Explanation: A Scalene triangle has no sides that are congruent (Same size) and angles also all different.

Question 2.
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 77

Answer: Right triangle.
Explanation: In a triangle one of the angle is a right angle (90 deg ) called as Right triangle.

Question 3.
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 78

Answer: Isosceles triangle.

Explanation: An Isosceles triangle has two sides of the same length. Two of its angle also measure equal.

Question 4.
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 79

Answer: Equiangular triangle

Explanation: In an equilateral triangle, all the lengths of the sides are equal. In such a case, each of the interior angles

Question 5.
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 80

Answer: Right triangle.

Explanation: In a triangle one of the angle is a right angle (90° ) called as Right triangle.

Question 6.
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 81

Answer: Scalene triangle.

Explanation: A Scalene triangle has no sides that are congruent (Same size) and angles also all different.

14.2 Classify Quadrilaterals

Classify the quadrilateral in as many ways as possible.

Question 7.
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 82

Answer: Square

Explanation: A square is a parallelogram that has four right angles and four sides of the same length.

Question 8.
Big Ideas Math Answers 5th Grade Chapter 14 Classify Two-Dimensional Shapes 83

Answer: Rectangle

Explanation: A rectangle is a parallelogram that has four right angle, Opposite sides are the same length

Question 9.
Big Ideas Math Solutions Grade 5 Chapter 14 Classify Two-Dimensional Shapes 84

Answer: Square

Explanation: The diagonals of a square bisect each other and meet at 90°. The diagonals of a square bisect its angles. The opposite sides of a square are both parallel and equal in length. All four angles of a square are equal (each being 360°/4 = 90°, a right angle).

Question 10.
Big Ideas Math Solutions Grade 5 Chapter 14 Classify Two-Dimensional Shapes 85

Answer: Isosceles trapezoid

Explanation: An isosceles trapezoid is a trapezoid whose non-parallel sides are congruent.

Question 11.
Big Ideas Math Solutions Grade 5 Chapter 14 Classify Two-Dimensional Shapes 86

Answer: Rectangle

Explanation: A rectangle is a parallelogram that has four right angle, Opposite sides are the same length

Question 12.
Big Ideas Math Solutions Grade 5 Chapter 14 Classify Two-Dimensional Shapes 87

Answer: Trapezoid

Explanation: A trapezoid is a quadrilateral that has exactly one pair of parallel sides.

Question 13.
Structure
Plot two more points in the coordinate plane to form a quadrilateral that has exactly two a rectangle. What two points can you plot to form a trapezoid? What two points can you plot to form a rhombus? Do not use the same pair of points twice.
Big Ideas Math Solutions Grade 5 Chapter 14 Classify Two-Dimensional Shapes 88

Answer:
Big-Ideas-Math-Solutions-Grade-5-Chapter-14-Classify-Two-Dimensional-Shapes-88

Question 14.
Reasoning
Can you draw a quadrilateral that has exactly two right angles? Explain.

Explanation: A quadrilateral with only 2 right angles and it is called a trapezoid .

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Question 15.
Modeling Real Life
The dashed line shows how you break apart the graham cracker. Classify the new shape of each piece of the graham cracker.
Big Ideas Math Solutions Grade 5 Chapter 14 Classify Two-Dimensional Shapes 89

Answer: Square

Explanation: The diagonals of a square bisect each other and meet at 90°.

14.3 Relate Quadrilaterals

Tell whether the statement is true or false.

Question 16.
All rectangles are quadrilaterals.

Answer: True

Explanation: A closed figure with four sides. For example, kites, parallelograms, rectangles, rhombuses, squares, and trapezoids are all quadrilaterals

Question 17.
Some parallelograms are squares.

Answer: True

Explanation: Squares fulfill all criteria of being a rectangle because all angles are right angle and opposite sides are equal. Similarly, they fulfill all criteria of a rhombus, as all sides are equal and their diagonals bisect each other.

Question 18.

All trapezoids are rectangles.

Answer: False

Explanation: Rectangles are defined as a four-sided polygon with two pairs of parallel sides. On the other hand, a trapezoid is defined as a quadrilateral with only one pair of parallel sides.

Question 19.
Some rectangles are rhombuses.

Answer: True

Explanation: A rectangle is a parallelogram with all its interior angles being 90 degrees. A rhombus is a parallelogram with all its sides equal. This means that for a rectangle to be a rhombus, its sides must be equal. A rectangle can be a rhombus only if has extra properties which would make it a square

Question 20.
Some squares are trapezoids.

Answer: True

Explanation: The definition of a trapezoid is that it is a quadrilateral that has at least one pair of parallel sides. A square, therefore, would be considered a trapezoid.

Question 21.
All quadrilaterals are squares.

Answer: False

Explanation : Quadrilateral: A closed figure with four sides. For example, kites, parallelograms, rectangles, Square: A rectangle with four sides of equal length. Trapezoid: A quadrilateral with at least one pair of parallel sides So, All quadrilaterals are not squares.

Classify Two-Dimensional Shapes Cumulative Practice 1-14

Question 1.
Which model shows 0.4 × 0.2?
Big Ideas Math Solutions Grade 5 Chapter 14 Classify Two-Dimensional Shapes 90

Answer:

Question 2.
A triangle has angle measures of 82°, 53°, and 45°. Classify the triangle by its angles.
Big Ideas Math Solutions Grade 5 Chapter 14 Classify Two-Dimensional Shapes 91

Answer: C

Explanation: An obtuse triangle has one angle measuring more than 90º but less than 180º (an obtuse angle). It is not possible to draw a triangle with more than one obtuse angle

Question 3.
Which expressions have an estimated difference of \(\frac{1}{2}\) ?
Big Ideas Math Solutions Grade 5 Chapter 14 Classify Two-Dimensional Shapes 92

Answer:

Question 4.
A rectangular prism has a volume of 288 cubic centimeters. The height of the prism is 8 centimeters. The base is a square. What is a side length of the base?
Big Ideas Math Solutions Grade 5 Chapter 14 Classify Two-Dimensional Shapes 93

Answer: A

Explanation: volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units. So,6 X 6 X 8 is equal to 288 cubic centimeters, Therefore the side length of the base is 6 cm.

Question 5.
A sandwich at a food stand costs $3.00. Each additional topping costs the same extra amount. The coordinate plan shows the costs, in dollars, of sandwiches with different numbers of additional toppings. What is the cost of a sandwich with 3 additional toppings?
Big Ideas Math Solutions Grade 5 Chapter 14 Classify Two-Dimensional Shapes 94

Answer:

Question 6.
Which statements are true?
Big Ideas Math Solutions Grade 5 Chapter 14 Classify Two-Dimensional Shapes 95

Answer:  The following statements are true
Option 2,option 3 and option 4 .

Explanation :
Option 2 :
All squares are rectangles are parallelograms is true, why because squares fulfill all criteria of being a rectangle because all angles are right angle and opposite sides are equal. Similarly, they fulfill all criteria of a rhombus, as all sides are equal and their diagonals bisect each other.
Option 3: All squares are rhombuses is true, why because All squares are rhombuses, but not all rhombuses are squares. The opposite interior angles of rhombuses are congruent.
Option 4:  Every trapezoid is a quadrilateral is true, why because Trapezoids have only one pair of parallel sides; parallelograms have two pairs of parallel sides.

Question 7.
Your friend makes a volcano for a science project. She uses 10 cups of vinegar. How many pints of vinegar does he use?
Big Ideas Math Solutions Grade 5 Chapter 14 Classify Two-Dimensional Shapes 96

Answer: Option B

Explanation: 1 cup is equal to  0.5 pints, therefore 10 cups are equal to 5 pints.

Question 8.
The volume of the rectangular prism is 432 cubic centimeters. What is the length of the prism?
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 97

Answer: Option A

Explanation: volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.
So, 6 cm X 9 cm X 8 cm is equal to 432 cubic centimeters.
Therefore the length of prim is 9 cm.

Question 9.
Descartes draws a pentagon by plotting another point in the coordinate plane and connecting the points. Which coordinates could he use?
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 98

Answer:

Question 10.
Newton rides to the dog park in a taxi. He owes the driver $12. He calculates the driver’s tip by multiplying $12 by 0.15. How much does he pay the driver, including the tip?
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 99

Answer: Option  C

Explanation: Driver cost $12 + ($12 X 0.15 )= 12+1.8 =13.8
Therefore answer is $13.8.

Question 11.
A quadrilateral has four sides with the same length, two pairs of parallel sides, and four 90° angles. Classify the quadrilateral in as many ways as possible.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 100

Answer: Square, Parallelogram

Explanation: A quadrilateral has four sides with the same length, two pairs of parallel sides and four 90° angles is called as square. All squares are parallelograms.

Question 12.
Which ordered pair represents the location of a point shown in the coordinate plane?
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 101

Answer:

Question 13.
What is the product of 5,602 and 17?
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 102

Answer: 95234

Explanation: 5602 X 17 is equal to 95234.

Question 14.
Which pair of points do not lie on a line that is perpendicular to the x-axis?
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 103

Answer:

Question 15.
Newton has a gift in the shape of a rectangular prism that has a volume of 10,500 cubic inches. The box he uses to ship the gift is shown.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 104
Part A What is the volume of the box?
Part B What is the volume, in cubic inches, of the space inside the box that is not taken up by gift? Explain.?

Answer:

Question 16.
Which expressions have a product greater than \(\frac{5}{6}=\)?
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 105

Answer:
Big-Ideas-Math-Answer-Key-Grade-5-Chapter-14-Classify-Two-Dimensional-Shapes-105

Question 17.
Newton is thinking of a shape that has 4 sides, only one pair of parallel sides, and angle measures of 90°, 40°, 140°, and 90°. Which is Newton’s shape?
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 106

Answer: D

Explanation: Trapezoid Only one pair of opposite sides is parallel.

Question 18.
Which rectangular prisms have a volume of 150 cubic feet?
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 107

Answer: Option 1

Explanation: volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic feet.
So,2 ft X 25 ft X 3 ft is equal to 150 cubic ft, Therefore the right answer is option 1.

Classify Two-Dimensional Shapes Steam Performance Task 1-14

Each student in your grade makes a constellation display by making holes for the stars of a constellation on each side of the display. Each display is a rectangular prism with a square base.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 108

Question 1.
Your science teacher orders a display for each student. The diagram shows the number of packages that can fit in a shipping box.
a. How many displays come in one box?
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 109
b. There are 108 students in your grade. How many boxes of displays does your teacher order? Explain.
c. The volume of the shipping box is 48,000 cubic inches. What is the volume of each display?
d. The height of each display is 15 inches. What are the dimensions of the square base?
e. Estimate the dimensions of the shipping box.
f. You paint every side of the display except the bottom. What is the total area you will paint?
g. You need a lantern to light up your display. Does the lantern fit inside of your display? Explain.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 111

Question 2.
On one side of your display, you create an image of the constellation Libra. Each square on the grid is 1 square inch.
a. Classify the triangle formed by the points of the constellation.
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 112

Answer: Equiangular triangle
Explanation: In an equilateral triangle, all the lengths of the sides are equal. In such a case, each of the interior angles

b. What are the coordinates of the points of the constellation?
c. What is the height of the constellation on your display?

Question 3.
You use the coordinate plane to create the image of the Big Dipper.
a. Plot the points A(6, 2), B(8, 2), C(7, 6), D(5, 5), E(7, 9), F(6, 12), and G(4, 14).
b. Draw lines connecting the points of quadrilateral ABCD. Draw \(\overline{C E}\), \(\overline{E F}\) and \(\overline{F G}\).
Big Ideas Math Answer Key Grade 5 Chapter 14 Classify Two-Dimensional Shapes 113

Answer:
Big-Ideas-Math-Answer-Key-Grade-5-Chapter-14-Classify-Two-Dimensional-Shapes-113
c. Is quadrilateral ABCD a trapezoid? How do you know?

Answer: Yes ABCD is a trapezoid because all sides are not equal and only one pair has parallel sides.

Question 4.
Use the Internet or some other resource to learn more about constellations. Write one interesting thing you learn.

Answer: A constellation is a group of stars that appears to form a pattern or picture like Orion the Great Hunter, Leo the Lion, or Taurus the Bull. Constellations are easily recognizable patterns that help people orient themselves using the night sky. There are 88 “official” constellations.

Conclusion:

Sharpen your math skills by practicing the problems from Big Ideas Math Book 5th Grade Answer Key Chapter 14 Classify Two-Dimensional Shapes. All the solutions of Grade 5 Chapter 14 Classify Two-Dimensional Shapes are prepared by the math professionals. Thus you can prepare effectively and score good marks in the exams.

Bar Graphs – Types, Properties, Uses, Advantages | How to Draw a Bar Graph? | Bar Graph Questions and Answers

Construction of Bar Graphs

Let us see how to remember easily the marks of every student in all subjects using bar graphs. Suppose your teacher wants to show the comparison of the marks of students in all subjects, then it will take more time for comparing all subjects, to avoid this problem we can use bar graphs concept. In this platform, we can easily learn the bar graph definition, construction of a bar graph, advantages of bar graph, and examples.

We learned that a bar chart is beneficial for comparing facts. The bars provide a visible display for comparing quantities in several categories. Bar graphs can have horizontal or vertical bars. In this lesson, we’ll show you the steps for constructing a bar chart.

Also, Read:

Bar Graph – Definition

Bar graphs are defined as the pictorial representation of data, it’s within the sort of vertical rectangular bars or horizontal rectangular bars, where the length of bars are proportional to the measure of data. Bar graphs are also called as Bar charts, it is one for data handling in statistics.

Types of Bar Graphs

There are two types of bar graphs, those are namely

  1. Horizontal Bar Graphs
  2. Vertical Bar Graphs

Uses of Bar Graphs

  • Bar graphs are match things between different groups or trace changes over time. when trying to estimate change over time, bar graphs are best suitable when the changes are bigger.
  •  Bar charts possess a discrete domain of divisions and are normally scaled so that all the information can fit on the graph. When there’s no regular order of the divisions being matched, bars on the chart could also be organized in any order.
  • Bar charts organized from the high to the low number are called Pareto charts.

Properties of Bar Graphs

Bar graphs are used for pictorial representation of the data. Some of the properties of Bar Graphs are listed below,

  • In Bar graphs, each column or bar in a bar graph is of equal width.
  • All bar graphs bars have a common base.
  • The height of the bar corresponds to the worth of the information.
  • The distance between each bar is the same.

Advantages of Bar Graphs

The important advantages of the bar graphs are given below and they are along the lines,

  1. Bar graphs are easily understood because of widespread use in business and therefore the media.
  2. Bar graphs show each data category during a frequency distribution.
  3. It summarizes an outsized data set in visual form.
  4. A bar chart is often used with numerical or categorical data.
  5. Bar graph permits a visual check of accuracy.

How to Construct Bar Graph? | Steps to Make a Bar Graph

To represent the information using the bar graph, you need to follow the steps given below.

Step 1: First, keep the title of the bar graph or bar chart.

Step 2: Next, Draw the vertical axis and horizontal axis.

Step 3: Now, we can label the horizontal axis.

Step 4: Write the horizontal axis names.

Step 5: Now, label the vertical axis.

Step 6: Finalise the size range for the given data.

Step 7: Finally, draw the bar graph that ought to represent each category of the information with their respective numbers.

Bar Graph Construction Examples

Let us consider an example, we have four different years of population, such as 1991, 1992, 1993,1994 and the corresponding percentages are 82, 85, 90, and 92 respectively.

To visually representing the given information using the bar graph, we need to follow the steps given below.

Step 1: First, fix the title of the bar chart or bar graph.

Step 2: Draw the horizontal axis and vertical axis. (write, population years)

Step 3: Now, label the horizontal axis.

Step 4: Write the names on the horizontal axis, such as 1991, 1992, 1993, 1994

Step 5: Now, label the vertical axis. (write percentage)

Step 6: Finalise the size range for the given data.

Step 7: Finally, draw the bar graph that should represent each year’s population with their respective percentages.

Example 1:

Study the subsequent graph carefully and answer the questions that follow. The results of students in a school graph are as shown

1. What is the difference in the number of students who passed to those who failed is minimum in which year?

2. How many times the number of students are failed as same?

3. What percentage will increase within the total number of students maximum as compared to the previous year?

4. What is the approximate percentage of students who failed during 5 years?

Solution:

Given the results of student in a school in the form of a bar graph

Now we can find the given questions,

(i) In these, first find the difference in all the years

The difference between the number of students passed to those who failed in the year 1991 – 1992 is,

=150 – 100 = 50

The difference between the number of students passed to those who failed in the year 1992 – 1993 is,

=200 – 100 = 100

The difference between the number of students passed to those who failed in the year 1993 – 1994 is,

=300 – 50 = 250

The difference between the number of students passed to those who failed in the year 1994 – 1995 is,

=250 – 100 = 150.

Therefore, considering all the difference the minimum number of students passed to those who failed is, in the year 1991 – 1992 = 50.

(ii) In this, we find the number of times students failed as same,

Based on the observation number of failed students are the same in the years 1991- 1992, 1992- 1993, 1994- 1995, and 1995- 1996.

Therefore, the number of failed students is the same as are Four times.

(iii) In this we are finding how much percentage will be increased compared to the previous year.

Firstly we can find the percentage of every year,

In the year 1992- 1993, percentage(%) increase is

= 100 x (300 – 250) / 250 = 100 x (50)/ 250 = 20%

In the year 1993- 1994, percentage(%) increase is

= 100 x (350 – 300) / 300 = (50 / 3)% = 16.6%

In the year 1994- 1995, percentage (%) increase is,
= 100 x (350 – 350) / 350 = 0%

In the year 1995-1996, percentage(%) increase is

= 100 x (400 – 350) / 350 = 100 x (50)/350 = 14.2%.

Therefore, considering all the percentage 20% is higher than the previous year.

(iv) In this we are finding the total number of failed students,

The total number of failed students is,

= 50+100+100+100+100 = 450

Therefore, the Required average of students is = 450/5 = 90.

FAQs on Construction of Bar Graph

1. What are the various types of Bar graphs?

Bar graphs are of two types, namely:

  1. Horizontal Bar Graph
  2. Vertical Bar Graph

Based on these two types, again bar graphs are two types

  1. Grouped Bar Graph
  2. Stacked Bar Graph

2. List the advantages of a Bar Graph?

  •  Bar graphs are easily understood due to widespread use in business and therefore the media.
  • It summarizes an outsized data set in visual form.
  • A bar chart is often used with numerical or categorical data.
  • Bar graph permits a visual check of accuracy.

3. How do you calculate a bar graph?

Draw two perpendicular lines intersecting each other at a point O. The vertical line is that the y-axis and therefore the horizontal is that the x-axis. Choose an appropriate scale to work out the peak (height) of every bar. On the horizontal line, draw the bars at equal distances with corresponding heights.

Comparison of Three Digit Numbers – Definition, Rules, Examples | How to Compare 3-Digit Numbers?

Comparison of Three Digit Numbers

If you find any difficulty in understanding three-digit numbers, here you can have good knowledge of three-digit numbers like its definition, comparison of three-digit numbers. Learn How to arrange 3 digit numbers in ascending order and descending order. For a better understanding of this concept check the examples on comparison of three-digit numbers.

Also, Read:

What are Three-Digit Numbers?

Three-digit numbers have only three digits. In three-digit numbers, the numbers are placed at one’s, ten’s, and hundred’s place. In the right of the number the last digit is one’s place, then the second digit is ten’s place and to the left of it, there is a hundred’s place. The digits have their face value in a given number. Three-digit numbers are from 100 to 999.

For example, in 635 the place value of 6 is 600, 3 is 30, and 5 is 5. In other words, we can write this as six hundred thirty-five.

How to Compare Three-Digit Numbers?

Know the procedure on how to compare 3 digit numbers by going through the below-listed steps. They are along the lines

(i) The numbers which have less than three digits are always smaller than the numbers having three digits as:

128 > 73 , 120 > 7 or 7 < 120 , 58 < 158

175 > 65 , 529 > 59 , 703 > 8 , etc.

(ii) If both the numbers have the same number (three) of digits, then the digits of the hundred-place and tens place are compared.

a) If the third digit from the right (Hundred-place digit) of a number is greater than the third digit from the right (Hundred-place digit) of the other number then the number having the greater is the greater one.

855>713, 984>981, 100>9,100>99.

b) If the numbers have the same third digit from the right, then the digits at ten’s place are compared and follow the rules of comparison of two-digit numbers.

967 > 929 , 586 > 567 , 462 > 449

c) If the digits at Hundred-place and ten’s place are equal, then follow the rules of comparison of single-digit numbers.

958 > 953 , 876 > 872 , 634 > 631

Comparing 3 Digit Numbers Examples

Example1:

Compare three digit numbers 534, 345

Solution:

In 534 ,5 is in hundreds place.

3 is in the tens place.

4 is in one’s place.

In 345,3 is in the hundreds place.

4 is in the tens place.

5 is in one’s place.

since two numbers have three digits compare the hundreds place of two numbers.

5 is greater than 3.

so 534 greater than(>) 345.

Example 2.

Compare three-digit numbers 583, 526

Solution:

In 583,5 is in the hundreds place.

8 is in the tens place.

3 is in one’s place.

In 526, 5 is in the hundreds place.

2 is in the tens place.

6 is in one’s place.

since the hundreds place of both the numbers are same compare tens place.

8>2

So 583>526.

Numbers can be arranged in two ways.1) Ascending order 2) Descending Order.

Ascending Order

Ascending order means the numbers are arranged from smallest to largest. the smallest number comes first and then the largest numbers.

How to arrange 3-Digit Numbers in Ascending Order?

1. Arrange the numbers 100,150,567,120,852,480 in ascending order.

The numbers in ascending order are 100,120,150,480,567,852.

2. Arrange the numbers 354,764,120,967,534,423 in ascending order.

The numbers in ascending order are 120, 354, 423, 534, 764, 967.

3. Arrange the numbers 220,560,420,678,168,934 in ascending order.

The numbers in ascending order are 168, 220,420,560,678,934.

Descending Order

Descending order means the numbers are arranged from largest to smallest. the largest number comes first and then the smallest numbers.

How to arrange 3-Digit Numbers in Descending Order?

1. Arrange the numbers 345,567,987,213,621,789 in descending order.

The numbers in descending order are 987,789,621,567,345,213.

2. Arrange the numbers 150,533,189,256,876,323 in descending order.

The numbers in descending order are 876,533,323,256,189,150.

3. Arrange the numbers 100,623,345,750,923,420 in descending order.

The numbers in descending order are 923, 750, 623, 420, 345, 100.

FAQ’s on Three Digits Numbers Comparison

1. What is the greatest three-digit number?

The greatest three-digit number is 999.

2. What is the smallest three-digit number?

The smallest three-digit number is 100.

3. Is a three-digit number greater than any single-digit number?

Yes, any Three-digit number is greater than any single-digit number.

4. Is a three-digit number greater than any two-digit number?

Yes, a three-digit number is greater than any two-digit number.

Comparison of Two Digit Numbers – Definition, Examples | How to Compare 2 Digit Numbers?

Comparison of Two Digit Numbers

If you are looking for the concept of two-digit numbers, you have landed on the correct page. This page gives you clear information about two-digit numbers,two-digit number definition, comparison of two-digit numbers, arranging 2 digit numbers in ascending order, descending order. Also, find examples of comparison of two-digit numbers so that you can solve related problems on your own.

Also, Read:

Two-Digit Numbers – Definition

Two-digit numbers have two digits. The last digit from the right-hand side represents one’s place and the other digit represents tens place. Two-digit numbers start from 10 and end with 99. Example of two-digit numbers are 10,14, 17, 19, 25, 50, 100 etc.

How do you Compare Two-Digit Numbers?

When comparing two-digit numbers we use greater than symbol(>) for greater values and less than a symbol for lesser values. When both the numbers are equal then we use equal to (=). The two other symbols used for comparison are ≥ (greater than or equal to) and ≤ (less than or equal to).

When comparing two digits we must consider the following rules.
  • The number which has greater valued digit at ten’s place is greater as compared to other:85 > 24, 98 > 53 , 65 > 29 ,72>33,49>14 etc.
  •  If the digits at ten’s place of both the numbers are equal, then the digits at one’s place of both the numbers are compared. The number which has the greater digit at one’s place is greater than the other.43>42, 65>61, 15>11,29>25,38>36 etc.consider other examples on comparison of two-digit numbers.

Comparing 2 Digit Numbers Examples

Example 1.

Compare Two-digit numbers 72, 47.

Solution:

In 72 7 is in the tens place and 2 is in one’s place.

In 47 4 is in the tens place and 7 is in one’s place.

When we compare tens place of both the numbers 7>4.So 72>47.

Example 2.

Compare two digit numbers 95, 68.

Solution:

In 95 9 is in the tens place and 5 is in one’s place.

In 68 6 is in the tens place and 8 is in one’s place.

when we compare tens place of both the numbers 9>6.So 95>68.

Example 3.

Compare two digits 65, 84.

Solution:

In 65 6 is in the tens place and 5 is in one’s place.

In 84 8 is in the tens place and 4 is in one’s place.

when we compare tens place of both the numbers 8>6.So 84>65

Example 4.

Compare two digits 69, 63.

Solution:

In 69 6 is in the tens place and 9 is in one’s place.

In 63 6 is in the tens place and 3 is in one’s place.

When we compare, tens place of both the numbers are same i.e.  6. so compare one’s digit of both the numbers. one’s digit of 69 is 9 and one’s digit of 63 is 3.

9>3.

So 69 is greater than 63.

Example 5.

Compare two digit numbers 81, 85.

Solution:

In 81 8 is in the tens place and 1 is in one’s place.

In 85 8 is in the tens place and 5 is in one’s place.

when we compare, the tens place of both the numbers is the same. Compare one’s place of both the numbers5>1. So 85 is greater than 81.

Example 6.

Compare two digit numbers 71, 78?

Solution:

In 71 7 is in the tens place and 1 is in one’s place.

In 78 7 is in the tens place and 8 is in one’s place.

when we compare, the tens place of both the numbers is the same. compare one’s place of both the numbers8>1. So 78 is greater than 71.

Two-Digit numbers are always greater than the one-digit number. Consider the following examples

15>9, 25>5, 33>6, 68>8, 18>9, 12>4 etc.

Numbers can be arranged in two ways. One is in Ascending Order and the other one is Descending Order.

Arranging 2 Digit Numbers in Ascending Order

Ascending order means to arrange numbers from smallest to largest. i.e. smaller digit numbers come first and then larger numbers.

For example Arrange the numbers 15,92,27,87,62,23,48,63,76 in ascending order.

Ascending order are 15, 23,27, 48,62, 63, 76,

Arrange the numbers 12,22,66,43,56,85,14,10,38 in ascending order.

Ascending order are 10, 12, 14, 22, 38, 43, 56, 66, 85.

Arrange the numbers 52,22,66,14,56,85,64,70,38 in ascending order.

Ascending order are 14, 22, 38, 52, 56, 64, 66, 70, 85.

Arrange the numbers 85,12,76,41,96,58,44,20,68 in ascending order.

Ascending order are 12, 20, 41, 44, 58, 68, 76, 85, 96.

Arranging 2 Digits Numbers in Descending Order

Descending order means arranging numbers from largest to smallest. i.e. larger digit numbers come first and then smaller numbers.

Consider the following examples

Arrange the numbers 75,32,66,11,96,58,34,20,48 in Descending order.

Descending order are 96, 75, 66, 58, 48, 34, 32, 20, 11.

Arrange the numbers 15,72,66,11,69,28,54,20,98 in Descending order.

Descending order are 98, 72, 69, 66, 54, 28, 20, 15, 11.

Arrange the numbers 13,32,46,10,29,78,42,60,88 in Descending order.

Descending order are 88, 78, 60, 46, 42, 32, 29, 13, 10.

Arrange the numbers 18,62,36,48,29,78,42,20,80in Descending order.

Descending order are 80, 78, 62, 48, 42, 36, 29, 20, 18.

FAQ’S on 2 Digits Comparison

1. What is a two-digit number?

A two-digit number has two digits.

2. What is the smallest two-digit number?

The smallest two-digit number is 10.

3. What is the largest two-digit number?

The largest two-digit number is 99.

4. How many two-digit numbers are there?

There are 90 two-digit numbers.

Class Limits in Exclusive and Inclusive Form – Definitions, Examples | How to find Class Limits in Exclusive and Inclusive Form?

Class Limits in Exclusive and Inclusive Form

The class limit corresponds to a class interval and the class limits are defined as the minimum value and the maximum value of the class interval may be contained. The maximum value in the class is known as the Upper-class limit whereas the minimum value in the class is known as the Lower class limit. The Lower Class Limit is represented as LCL  and the Upper-Class Limit is represented as UCL. Class limits have two series (or) form one is exclusive series (or) form and another one is inclusive series (or) form.

The Upper-Class Limit of a class is the largest data value that will go into the class and the lower class limit of a class is the smallest data value that can go into the class. Class limits have an equivalent accuracy of knowledge values, an equivalent number of decimal places because of the data values.

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Exclusive Form – Definition

The exclusive form is defined as the series in which the upper limit is not included in the class and is included in an upcoming class. The exclusive series of a class type is a continuous series. Consider the example of the exclusive form is  0- 10, 10- 20, 20- 30, 30- 40, 40- 50 we can also see that the upper limit of the class is included in the next class interval. In exclusive form, the lower class limit and upper-class limit are known as true lower class limit and true upper-class limit of the interval.

Inclusive Form of Class Limit – Definition

The inclusive form of class limit is defined as when the lower class limit and the upper-class limit are included, then it is an inclusive class interval. Consider the example of the inclusive form is 0- 10, 11- 20, 21- 20, 31- 40, etc are the inclusive type of class intervals. Usually, in the case of discrete variables, the inclusive form of class intervals is used.

The inclusive class limit series are obtained by subtracting 0.5 from the lower class limit and adding 0.5 to the upper-class limit. Therefore, class limits of 10- 20 class intervals in the inclusive form are 9.5 is the lower class limit and 20.5 is the upper-class limit.

Related Terms to Class Limits

Below we have provided related terms of class limits along with their definitions in detail. They are explained as such

Class Mark

The classmark is also called the Class midpoint. The classmark is a specific point in the center of the categories in a frequency distribution table. Classmark is also the center of a bar in a histogram. It is defined as the average of the upper class and lower class limit.

Therefore, Class Mark = ½ (upper-class limit + lower class limit)

Class Size

The difference between the true lower class limit and the true upper-class limit is called Class size. The class size will always remain the same in all the class intervals.

Range

The difference between the maximum value of observation and the minimum value of observation is called Range.

Difference between Exclusive and Inclusive Class Limits

                         Exclusive Class Limit              Inclusive Class Limit
1. When the upper limit of the class is excluded from the class and is included in the next class or upcoming class, it is called the exclusive class limit. 1. In the inclusive class limit, the upper-class limit of a class interval is included in the class itself.
2. Exclusive class limit is suitable for continuous variables. 2. Inclusive class limit is suitable for discrete variables
3. In the exclusive class limit, the class intervals are 10- 20, 20- 30, 30- 40. 3. In the inclusive class limit, the class intervals are 10- 20, 21- 30, 31- 40.

Inclusive and Exclusive Class Interval Examples

Problem 1:

Find the upper-class limit in inclusive form for the class interval of 20- 25.

Solution:

Given, the class interval of 20- 25,

Now, we can find the upper-class limit of an inclusive

We know that in an inclusive class limit subtracting 0.5 on the lower class limit and adding 0.5 on the upper-class limit.

Here we find the upper-class limit. So, we can add 0.5 to the upper-class limit.

Therefore, the upper-class limit of an inclusive form is 25+ 0.5 = 25.5.

Problem 2:

Find the actual upper-class limit value, lower-class limit, and mid-value of the class interval 10- 15, 16- 20, 21- 25, 26- 30, 31- 35?

Solution:

Given the class interval 10- 15, 16- 20, 21- 25, 26- 30, 31- 35

Now we can find the values of upper-class limit, lower-class limit, and mid-value (or) class mark.

The  Actual lower class limit value is 10.

The  Actual upper-class limit value is 35.

Now, we can find the mid-value or class mark,

We know the formula of class mark i.e,

Class Mark = ½ (upper-class limit + lower class limit)

Substitute the upper-class value and lower class value in the above formula, we get

Class Mark = ½ (35 + 10)  = ½ (45)

Class Mark = 22.5

Therefore, the mid value is 22.5

FAQ’S on Class Limits in Exclusive and Inclusive Form

1. What is a class limit?

Class limit is defined as the minimum value and the maximum value of the class interval may be contained.  The maximum value in the class is known as the Upper-class limit whereas the minimum value in the class is known as the Lower class limit.

2. Define Range?

The difference between the maximum value of observation and the minimum value of observation is called Range.

3. Define Class Mark?

The classmark is defined as the average of upper-class limit and lower class limit, the formula of classmark is,

Class Mark = ½ (upper-class limit + lower class limit)

4. What are the full forms of LCL and UCL?

LCL means Lower Class Limit and UCL means Upper-Class Limit.

5. What is meant by the Inclusive Form of Class Limit?

The inclusive form is defined as when the lower class limit and the upper-class limit are included, then it is an inclusive class interval. These are obtained by subtracting 0.5 from the lower class limit and adding 0.5 to the upper-class limit.

Comparison of One Digit Numbers – Definition, Examples | How to Compare 1 Digit Numbers?

Comparison of One Digit Numbers

Here you can have knowledge about one-digit numbers, examples of one-digit numbers, comparison of one-digit numbers. How to arrange numbers in ascending order and descending order. Check the solved examples on comparison of one-digit numbers. You can have a better understanding of this concept by going through this entire article.

Also, Check:

One-Digit Number – Definition

One-Digit Number has only One Digit. Of all the One-Digit Numbers 1 is the smaller one-digit number and 9 is the greatest one-digit number. There are 10 One-Digit Numbers in Decimal System including 0.

For Example 1,2,3,4,5,6,7,8,9 are one-digit numbers.

How to Compare One-Digit Numbers?

We can compare numbers depending on their values. value of a number is found by adding place values of the digits. we can find the value of the One-Digit Number by its place or face value. The place value or face value of a one-digit number is the same.

The number which has a greater face or place value is greater than the number which has a smaller face value. Greater than symbol is > and less than symbol is <.

Comparison of One-Digit Numbers Examples

8>6

8 is greater than 6

7>2

7 is greater than 2

9>5

9 is greater than 5

6>5

6 is greater than 5

7<9

7 is less than 9

We also know 3<9 or 9>3

The value of 9 is greater than 3

The value of 3 is less than 9

similarly 5<8 or 8>5

The value of 8 is greater than 5

The value of 5 is less than 8

One-Digit Number is always smaller than Two-digit, Three-digit, Four-digit Number, etc. For Example

3<10 or 10>3

One-Digit Number is 3.

Two-Digit Number is 10.

One-Digit Number 3 is less than Two-Digit Number 10.

5<100 or 100>5

One-Digit Number is 5.

Three-Digit Number is 100.

One-Digit Number 5 is less than Three-Digit Number 100.

Numbers can be arranged in two ways. i.e. 1.Ascending Order 2.Descending order.

Arranging 1 Digit Numbers in Ascending Order

In ascending Order, numbers are arranged from smaller to larger. i.e. smaller numbers come first and then larger numbers.

For Example Arrange the digits 1, 7, 3, 5, 9, 6 in Ascending Order

The numbers arranged in ascending order are 1, 3, 5, 6, 7, 9.

Arrange the digits 2,5,7,3,8,9 in Ascending Order

The numbers arranged in ascending order are 2, 3, 5, 7, 8, 9.

Arranging 1 Digit Numbers in Descending Order

In Descending Order, numbers are arranged from larger to smaller. i.e. larger numbers come first and then smaller numbers.

For Example Arrange the digits 1, 7, 3, 5, 9, 6 in Descending Order

The numbers arranged in descending order are 9, 7, 6, 5, 3, 1.

Arrange the digits 2,5,7,3,8,9 in Descending Order

The numbers arranged in descending order are 9, 8, 7, 5, 3, 2.

FAQ’s on Comparing 1 Digit Numbers

1. Is the Face value or place value of one-digit numbers the same?

The face value or place value of one-digit numbers are the same.

2. What is the face value of 7?

The face value of 7 is 7.

3. How one-digit numbers are compared?

One-digit numbers are compared by using face values. The number which has a greater face value or place value is greater than the number which has a lesser face or place value.

4. How many ways one-digit numbers can be arranged?

One-digit numbers can be arranged in two ways i.e. Ascending Order and Descending order.

5. What is the symbol of greater than?

The symbol of greater than is >.

6. What is the symbol of less than?

The symbol of less than is <.

Four Digit Numbers in Numerals and Words | How to Read and Write Four Digit Numbers?

Four Digit Numbers in Numerals and Words

On this page, we will discuss all about Four-Digit Numbers such as writing them in numerals and words. Check out how 4 digit numbers can be written both in short form and expanded form in the later sections. Refer to the solved examples on writing four-digit numbers in both numerals and words. Go through the complete article to have a complete idea of the entire concept of four-digit numbers.

Also, Read: Reading and Writing Large Numbers

Four Digit Numbers – Definition

Four Digit Numbers have four digits. Digits are positioned from right to left at one’s place, ten’s place, hundred’s place, and thousand’s place. The first four-digit number is 1000. The next 9000 numbers are all four-digit numbers, for example, 2465,6789, etc.

How Four-Digit Numbers are Formed?

When we multiply a unit digit with 1000 four-digit numbers are formed. For every Four-Digit Number, the fourth digit from the left represents thousands places, the third digit represents hundreds, the second digit represents tens, and the first represents ones. we can have a four-digit number by adding one to the largest three-digit number. For example: 9834, 2753, 5900.

For example: In the four-digit number 8673

3 is at the unit/one’s place having its value 3 × 1 = 3
7 is at ten’s place having its value 7 × 10 = 70
6 is at hundred’s place having its value 6× 100 = 600
8 is at the thousand’s place having its value 8 × 1000 = 8000
So, 8673 = 8000 + 600 + 70 + 3
8673 is the short form whereas 8000 + 600 + 70 + 3 is the expanded form.

It is read as ‘Eight  Thousand Six Hundred Seventy-Three’.

A comma is marked in Four-digit numbers in numerals before writing the three digits from the right. The digit of thousands is at the left. Since Four-Digit Numbers are longer, the comma helps us to make the number more readable.

As in 7682, a comma is marked before 682, the only digit left is 7, whose value is 7000. The number will be written in numerals as 7682 and written in words as seven thousand six hundred eighty-two.

We can write Four-digit numbers in three ways i.e., numbers in numerals, numbers in words, and numbers in expanded form.

Consider an example 5678 and see how we can write numbers in numerals, numbers in words, and numbers in expanded form.

Number in numerals: 5,678

Number in words: Five thousand six hundred seventy-eight

Numbers in Expanded Form: 5000 + 600 + 70 + 8

4-Digit Numbers in Numerals and Words Examples

Some examples of  four-digit numbers in numerals and words and in expanded form are given below

(i) 5,847

5847 in words – Five thousand eight hundred forty seven

5847 in Expanded Form – 5000 + 800 + 40 + 7

(ii) 6,234

6234 in words: Six thousand two hundred thirty four

6234 in expanded form: 6000 + 200 + 30 + 4

(iii) 9,163

9163 in words: Nine thousand one hundred sixty three

9163 in expanded form: 9000 + 100 + 60 + 3

(iv) 2,645

2645 in words: Two thousand six hundred forty five

2645 in expanded form: 2000 + 600 + 40 + 5

(v) 9,999

9999 in words: Nine thousand nine hundred ninety nine

9999 in expanded form: 9000 + 900 + 90 + 9

(vi) 8,003

8003 in words: Eight thousand and three

8003 in expanded form: 8000 + 000 + 00 + 3

(vii) 6,302

6302 in words: Six thousand three hundred two

6302 in expanded form: 6000 + 300 + 00 + 2

(viii) 2,541

2541 in words: Two thousand five hundred forty one

2541 in expanded form: 2000 + 500 + 40 + 1

(ix) 7,301

7301 in words: Seven thousand three hundred one

7301 in expanded form: 7000 + 300 + 00 + 1

(x) 1,738

1738 in words: one thousand seven hundred thirty eight

1738 in expanded form: 1000 + 700 + 30 + 8

(xi) 3,001

3001 in words: Three thousand and one

3001 in expanded form: 3000 + 000 + 00 + 1

(xii) 5,005

5005 in words: Five thousand and Five

5005 in expanded form: 5000 + 000 + 00 + 5

(xiii) 1,405

1405 in words: One thousand four hundred five

1405 in expanded form: 1000 + 400 + 5

(xiv) 3,333

3333 in words: Three thousand three hundred thirty three

3333 in expanded form: 3000 + 300 + 30 + 3

(xv) 6,724

6724 in words: Six thousand seven hundred twenty four

6724 in expanded form: 6000 + 700 + 20 + 4

(xvi) 8,888

8888 in words: Eight thousand eight hundred eighty eight

8888 in expanded form: 8000 + 800 + 80 + 8

These are the examples of four digits written and explained on how to identify the place value in a four-digit number in numerals, words and in expanded form.

FAQ’s on Four Digit Numbers

1. What is the expanded form of 6789?

The expanded form of 6789 is 6000+700+80+9.

2. How four-digit numbers are formed?

Four-digit numbers are formed by multiplying 1000 with units digit.

3. What is the place value or face value of 7 in 9786?

Face value or place value of 7 in 9786 is hundred.

4. What is the greatest four-digit number?

The greatest four-digit number is 9999.

5. What is the smallest four-digit number?

The smallest four-digit number is 1000.

Conversion of Roman Numerals to Numbers – Rules, Examples | How to Convert Roman Numerals to Numbers?

Conversion of Roman Numerals to Numbers

Find a way for converting Roman Numerals to Numbers. You can learn about the basic details such as Roman Number Definition, Procedure for Converting Roman Numerals to Numbers. You can also check the solved Examples on how to change Roman Numerals to Numbers by going through this article completely.

Do Check:

Roman Numerals – Definition

Romans used some roman alphabets to specify numbers. These are called Roman Numerals. Roman Numerals are nothing but English alphabets except j, u, and w. There are seven Roman numerals. Roman Numerals are I, V, X, C, L, D, and M. Bar on the Roman letters means its value is multiplied by 1000 times. The values of Roman Numerals are as follows

Commonly Used Roman Numeral Symbols and their Equivalent Numbers
I=1 V=5
X=10 C=100
L=50 D=500
M=1000

Roman Numeral Chart for 1 to 1000 Numbers

Roman Numerals for 1-1000 Numbers

How to Convert Roman Numerals to Numerals?

For a given roman numeral r

  • Find the largest roman numeral(n) with the large decimal value(v) taken from the  roman numeral r:
Roman Numeral(n) Decimal Value(v)
I 1
v 5
IX 9
X 10
XL 40
L 50
XC 90
C 100
CD 400
D 500
M 1000
  • If the largest numeral appears first then count how many times it appears. It appears a Maximum of three times. Multiply its value by the number of times it appeared. The value V of the roman number is added to the decimal number x.
  • If the largest numeral appears second then subtract the value of the numeral before it from its value. The value v of the Roman Numeral is added to the decimal number X.

X=X + V

  • Repeat steps 1 to 3 until you find Roman Numerals of r.

Roman Numerals to Numbers Conversion Examples

1. Convert the roman numeral XXXVII to Number?

Solution:

In this example, Highest Roman Numeral is X. Roman Numeral X appeared three times. The value of X multiplied by three times. So the decimal number (X) has 30. The Second highest decimal number is V and its value is 5 and it is added to the decimal number. I is appearing two times and its value is 1 and it is added to a decimal number(X). Therefore, the given roman number XXXVII converted to numbers is 37.

Iteration Highest Roman Numeral(n) Highest Decimal value(v) Decimal Number(X)
I X 10 10
2 X 10 20
3 X 10 30
4 V 5 35
5 I 1 36
6 I 1 37

2. Convert Roman Numeral MMXXI to Number?

Solution:

In this example, Highest Roman Numeral is M. Roman Numeral M appeared two times. The value of M multiplied by two times.so the decimal number X has 2000. Second, the highest decimal number is X and its value is 10 and it appeared two times. Its value is added to the decimal number. Now decimal number(X) has 2020. I appear one-time. Its value is 1 and it is added to the decimal number. Thus given number MMXXI converted to Numbers is 2021.

Iteration Highest Roman Numeral(n) Highest Decimal Value(v) Decimal Number(X)
I M 1000 1000
2 M 1000 2000
3 X 10 2010
4 X 10 2020
5 I 1 2021

3. Convert Roman Numeral CDLII to Number?

Solution:

In this example, Highest Roman Numeral is D. It appeared second of the Roman Numeral, so subtract the value of the Roman Numeral before its value.  so the decimal number( X) has 400. Roman Numeral L has the decimal value 50 and it is added to a decimal number(X). The value of I is 1 and it is added to a decimal number. The given number is 451.

Iteration Highest Roman Numeral(n) Highest Decimal value(v) Decimal Number(X)
I D 500 500
2 c 100 400
3 L 50 450
4 I 1 451
5 I 1 452

4. Convert Roman Numeral CCCL to Number?

Solution:

In this example, Highest Roman Numeral is c. Roman Numeral C appeared three times. The value of X multiplied by three times. So the decimal number X has 300.second highest decimal number is L. Its value is 50 and it is added to a decimal number(X). The given number CCCL is 350.

Iteration Highest Roman Numeral(n) Highest Decimal value(v) Decimal Number(X)
I C 100 100
2 C 100 200
3 C 100 300
4 L 50 350

FAQ’s on Conversion of Roman Numerals to Numbers

1. What is the value of XLVI?

Here the largest value of the Roman Numeral is L. since it is placed second the value of the L numeral is subtracted from first. So the total is 40. The values of V and I are added to the total. The value of XLVI is 46.

2. What is the value of L in Roman Numerals?

The value of L in Roman Numerals is 50.

3. Why bar is placed on the Roman Numeral?

when a bar is placed on the roman numeral its value is increased by 1000 times.

4. What is the value of M?

The value of M is 1000.