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Big Ideas 4th Grade Math Book Chapter 8 Add and Subtract Fractions Answer Key

Big Ideas Math Chapter 8 Add and Subtract Fractions Questions are provided as per the updated syllabus guidelines. Also, the answers and explanations are given by highly subject expertise people. Furthermore, the Big Ideas Grade 4 Chapter 8 Math Answer key covers assignment tests, questions from exercises, practice tests, etc. Prepare the topics you wish to prepare and you feel the lag. The below quick links will help you to find each and every concept along with questions.

Lesson 1: Use Models to Add Fractions

• Lesson 8.1 Use Models to Add Fractions
• Use Models to Add Fractions Homework & Practice 8.1

Lesson 2: Decompose Fractions

• Lesson 8.2 Decompose Fractions
• Decompose Fractions Homework & Practice 8.2

Lesson 3: Add Fractions with Like Denominators

• Lesson 8.3 Add Fractions with Like Denominators
• Add Fractions with Like Denominators Homework & Practice 8.3

Lesson 4: Use Models to subtract Fractions

• Lesson 8.4 Use Models to subtract Fractions
• Use Models to subtract Fractions Homework & Practice 8.4

Lesson 5: Subtract Fractions with Like Denominators

• Lesson 8.5 Subtract Fractions with Like Denominators
• Subtract Fractions with Like Denominators Homework & Practice 8.5

Lesson 6: Model Fractions and Mixed Numbers

• Lesson 8.6 Model Fractions and Mixed Numbers
• Model Fractions and Mixed Numbers Homework & Practice 8.6

Lesson 7: Add Mixed Numbers

• Lesson 8.7 Add Mixed Numbers
• Add Mixed Numbers Homework & Practice 8.7

Lesson 8: Subtract Mixed Numbers

• Lesson 8.8 Subtract Mixed Numbers
• Subtract Mixed Numbers Homework & Practice 8.8

Lesson 9: Problem Solving: Fractions

• Lesson 8.9 Problem Solving: Fractions
• Problem Solving: Fractions Homework & Practice 8.9

Performance Task

• Add and Subtract Fractions Performance Task 8
• Add and Subtract Fractions Activity
• Add and Subtract Fractions Chapter Practice 8

Lesson 8.1 Use Models to Add Fractions

Explore and Grow

Draw models to show \(\frac{2}{8}\) and \(\frac{5}{8}\).

Answer:
You can add fractions by joining parts that refer to the same whole.

Use your models to find \(\frac{2}{8}\) + \(\frac{5}{8}\). Explain your method.

Answer:
Combine the like terms
\(\frac{2}{8}\) + \(\frac{5}{8}\) = (2 + 5)/8 = 7/8

Repeated Reasoning
Write two fractions that have a sum of \(\frac{6}{8}\). Explain your reasoning.

Think and Grow: Use Models to Add Fractions

You can add fractions by joining parts that refer to the same whole.

Answer:
The denominators of the fraction are the same so you have to add numerators.
\(\frac{1}{5}\) + \(\frac{3}{5}\) = \(\frac{4}{5}\)

Example
Use a number line to find \(\frac{5}{4}\) + \(\frac{2}{4}\).

Answer:
The denominators of the fraction are the same so you have to add numerators.
\(\frac{5}{4}\) + \(\frac{2}{4}\) = \(\frac{7}{4}\)

Show and Grow

Find the sum. Explain how you used the model to add.

Question 1.

Answer:
The denominators of the fraction are the same so you have to add numerators.

(3+4)/10 = 7/10

Question 2.

Answer:
The denominators of the fraction are the same so you have to add numerators.

Apply and Grow: Practice

Find the sum. Use a model or a number line to help.

Question 3.

Answer:
The denominators of the fraction are the same so you have to add numerators.

Question 4.

Answer:
The denominators of the fraction are the same so you have to add numerators.

\(\frac{5}{12}\) + \(\frac{4}{12}\) = \(\frac{9}{12}\)

Question 5.

Answer:
The denominators of the fraction are the same so you have to add numerators.

Question 6.

Answer:
The denominators of the fraction are the same so you have to add numerators.

Question 7.

Answer:
The denominators of the fraction are the same so you have to add numerators.

Question 8.

Answer:
Add a fraction to the whole number.

5 + \(\frac{6}{8}\) = \(\frac{46}{8}\)

Question 9.

Answer:
The denominators of the fraction are the same so you have to add numerators.

Question 10.

Answer:
The denominators of the fraction are the same so you have to add numerators.

Question 11.

Answer:
The denominators of the fraction are the same so you have to add numerators.

Question 12.
Structure
Write the addition equation represented by the models.

Answer:
By seeing the above model we can find the addition equation.
\(\frac{4}{8}\) + \(\frac{3}{8}\) = \(\frac{7}{8}\)

Question 13.
Open-Ended
Write three fractions with different numerators that have a sum of 1.

Answer:
\(\frac{2}{8}\) + \(\frac{5}{8}\) + \(\frac{1}{8}\) = \(\frac{8}{8}\) = 1

Question 14.
Writing
Explain why \(\frac{1}{8}\) + \(\frac{4}{8}\) does not equal \(\frac{5}{16}\).

Answer:
In the above expressions, the denominators are the same but the numerators are different.
So, you have to add the numerators not denominators.
\(\frac{1}{8}\) + \(\frac{4}{8}\) = \(\frac{5}{8}\)

Think and Grow: Modeling Real Life

Example
You need \(\frac{2}{3}\) cup of hot water and \(\frac{4}{3}\) cups of cold water for a science experiment. How many cups of water do you need in all?

Because each fraction represents a part of the same whole you can join the parts.
Use a model to find \(\frac{2}{3}\) + \(\frac{4}{3}\).

Answer:
Given that,
You need \(\frac{2}{3}\) cup of hot water and \(\frac{4}{3}\) cups of cold water for a science experiment.

Thus you need 2 cups of water in all.

Show and Grow

Question 15.
You cut a foam noodle for a craft. You use \(\frac{2}{4}\) of the noodle for one part of the craft and \(\frac{1}{4}\) of the noodle for another part. What fraction of the foam noodle do you use altogether?

Answer:
Given that,
You cut a foam noodle for a craft. You use \(\frac{2}{4}\) of the noodle for one part of the craft and \(\frac{1}{4}\) of the noodle for another part.
\(\frac{2}{4}\) + \(\frac{1}{4}\) = \(\frac{3}{4}\)
Thus \(\frac{3}{4}\) of the foam noodle is used.

Question 16.
You make a fruit drink using \(\frac{4}{8}\) gallon of orange juice, \(\frac{2}{8}\) gallon of mango juice, and \(\frac{4}{8}\) gallon of pineapple juice. How much juice do you use in all?

Answer:
Given that,
You make a fruit drink using \(\frac{4}{8}\) gallon of orange juice, \(\frac{2}{8}\) gallon of mango juice, and \(\frac{4}{8}\) gallon of pineapple juice.
\(\frac{4}{8}\) + \(\frac{2}{8}\) = \(\frac{6}{8}\)
\(\frac{6}{8}\) + \(\frac{4}{8}\) = \(\frac{10}{8}\)
Thus you used \(\frac{10}{8}\) fraction of juice.

Question 17.
DIG DEEPER!
A community plants cucumbers in \(\frac{5}{12}\) of a garden, broccoli in \(\frac{3}{12}\) of the garden, and carrots in \(\frac{4}{12}\) of the garden. What fraction of the garden is planted with green vegetables?

Answer:
Given that,
A community plants cucumbers in \(\frac{5}{12}\) of a garden, broccoli in \(\frac{3}{12}\) of the garden, and carrots in \(\frac{4}{12}\) of the garden.
\(\frac{5}{12}\) + \(\frac{3}{12}\) + \(\frac{4}{12}\) = \(\frac{12}{12}\) = 1
\(\frac{12}{12}\) fraction of the garden is planted with green vegetables.

Use Models to Add Fractions Homework & Practice 8.1

Find the sum. Explain how you used the model to add.

Question 1.

Answer: \(\frac{9}{6}\)

Question 2.

Answer: 1

Find the sum. Use a model or a number line to help.

Question 3.

Answer: \(\frac{7}{8}\)
You can add fractions by joining parts that refer to the same whole.

Question 4.

Answer: 2

Question 5.

Answer: 3 \(\frac{1}{4}\)

Explanation:
Add fraction to the whole number.
\(\frac{1}{4}\) + 3
\(\frac{1}{4}\) + 3 × \(\frac{4}{4}\)
\(\frac{1}{4}\) + \(\frac{13}{4}\) = \(\frac{13}{4}\)

Question 6.

Answer: \(\frac{9}{12}\)

Question 7.

Answer: 2

\(\frac{12}{10}\) = \(\frac{10}{10}\) + \(\frac{2}{10}\)
\(\frac{10}{10}\) + \(\frac{2}{10}\) + \(\frac{8}{10}\) = \(\frac{20}{10}\) = 2

Question 8.

Answer:
4/8 = 1/2
6 + 1/2 = (12 + 1)/2 = 13/2

Find the sum. Use a model or a number line to help.

Question 9.

Answer:
Add all the three unit fractions.

Question 10.

Answer:

Question 11.

Answer:
The denominators of all the fractions are the same. So you have to add the numerators of the fraction.
\(\frac{50}{100}\) + \(\frac{25}{100}\) + \(\frac{5}{100}\) = \(\frac{80}{100}\)

Question 12.
YOU BE THE TEACHER
Newton says \(\frac{3}{5}\) + \(\frac{1}{5}\) = \(\frac{4}{10}\). Descartes says the sum is \(\frac{4}{5}\). Who is correct? Explain.

Answer:
Newton says \(\frac{3}{5}\) + \(\frac{1}{5}\) = \(\frac{4}{10}\). Descartes says the sum is \(\frac{4}{5}\).
Descartes is correct.
\(\frac{3}{5}\) + \(\frac{1}{5}\) = \(\frac{4}{5}\)
You have to add numerators, not denominators.
So, Newton’s equation is not correct.

Question 13.
Make each statement true by writing two fractions whose denominators are the same and whose numerators are 3 and 2.
The sum of ___ and __ is greater than 1.
___________________________
The sum of ___ and ___ is less than 1.
___________________________
The sum of ___ and ___ is equal to 1.

Answer:
The sum of 3/2 and 2/2 is greater than 1.
3/2 + 2/2 = 5/2
5/2 > 1
The sum of 3/6 and 2/6 is less than 1.
3/6 + 2/6 = 5/6
5/6 < 1
The sum of 3/5 and 2/5 is equal to 1.
3/5 + 2/5 = 5/5 = 1

Question 14.
Modeling Real Life
Your teacher assigns 5 pages to read. You read \(\frac{3}{5}\) of the pages in class and \(\frac{1}{5}\) of the pages at home. What fraction of the reading assignment is complete?

Answer:
Given that,
Your teacher assigns 5 pages to read. You read \(\frac{3}{5}\) of the pages in class and \(\frac{1}{5}\) of the pages at home.
The denominators of all the fractions are the same. So you have to add the numerators of the fraction.
\(\frac{3}{5}\) + \(\frac{1}{5}\) = \(\frac{4}{5}\)

Question 15.
Modeling Real Life
In the Sahara Desert, it rains \(\frac{2}{10}\) inch in September, \(\frac{3}{10}\) inch in October, and \(\frac{5}{10}\) inch in November. How much does it rain in the 3 months?

Answer:
Given that,
In the Sahara Desert, it rains \(\frac{2}{10}\) inch in September, \(\frac{3}{10}\) inch in October, and \(\frac{5}{10}\) inch in November.
\(\frac{2}{10}\) + \(\frac{3}{10}\) + \(\frac{5}{10}\)
The denominators of all the fractions are the same. So you have to add the numerators of the fraction.
\(\frac{2}{10}\) + \(\frac{3}{10}\) + \(\frac{5}{10}\) = (2 + 3 + 5)/10 = 10/10 = 1
It rains 10/10 in the 3 months.

Review & Refresh

Tell whether the number is prime or composite. Explain.

Question 16.
37

Answer: 37 is a prime number.
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number.

Question 17.
21

Answer: 21 is a composite number.
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself.

Question 18.
99

Answer: 99 is a composite number.
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself.

Lesson 8.2 Decompose Fractions

Explore and Grow

Use a model to find .

How can you write \(\frac{7}{10}\) as a sum of unit fractions? Explain your reasoning.

Answer: The sum of unit fraction of \(\frac{7}{10}\) is \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\)

Structure
Explain how you can write \(\frac{7}{10}\) as a sum of two fractions. Draw a model to support your answer.

Answer: You can write sum of \(\frac{7}{10}\) as \(\frac{2}{10}\) + \(\frac{5}{10}\)

Think and Grow: Decompose Fractions

A unit fraction represents one equal part of a whole. You can write a fraction as a sum of unit fractions.

Answer:

Answer:

Show and Grow

Question 1.
Write \(\frac{4}{5}\) as a sum of unit fractions.

Answer: The unit fraction of \(\frac{4}{5}\) is \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\)
A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.

Question 2.
Write \(\frac{5}{6}\) as a sum of fractions in two different ways.

Answer: The unit fraction of \(\frac{5}{6}\) is \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\)
A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.
You can also write \(\frac{5}{6}\) as \(\frac{2}{6}\) + \(\frac{3}{6}\)
That means \(\frac{5}{6}\) can be written as 2 parts of \(\frac{1}{6}\) and 3 parts of \(\frac{1}{6}\)

Apply and Grow: Practice

Question 3.
\(\frac{4}{7}\)

Answer: The unit fraction of \(\frac{4}{7}\) is \(\frac{1}{7}\) + \(\frac{1}{7}\) + \(\frac{1}{7}\) + \(\frac{1}{7}\)
A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.

Question 4.
\(\frac{7}{8}\)

Answer: The unit fraction of \(\frac{7}{8}\) is \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\)
A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.

Question 5.
\(\frac{3}{10}\)

Answer: The unit fraction of \(\frac{3}{10}\) is  \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\)
A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.

Question 6.
\(\frac{10}{100}\)

Answer: The unit fraction of \(\frac{10}{100}\) is \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\)
A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.

Question 7.
\(\frac{6}{2}\)

Answer: 3
The unit fraction of \(\frac{6}{2}\) is \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\)
A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.

Question 8.
\(\frac{9}{4}\)

Answer:
Break apart 9 parts of \(\frac{1}{4}\) into 5 parts of \(\frac{1}{4}\) and 4 parts of \(\frac{1}{4}\).

Question 9.
\(\frac{8}{12}\)

Answer: Break apart 8 parts of \(\frac{1}{12}\) into 5 parts of \(\frac{1}{12}\) and 3 parts of \(\frac{1}{12}\).

Question 10.
\(\frac{5}{3}\)

Answer: The unit fraction of \(\frac{5}{3}\) is \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\)
A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.

Question 11.
Writing
You write \(\frac{4}{6}\) as a sum of unit fractions. Explain how the numerator of \(\frac{4}{6}\) is related to the number of addends.

Answer: The unit fraction of \(\frac{4}{6}\) is \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\)
A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.
Also, you can write \(\frac{4}{6}\) as 4 parts of \(\frac{1}{6}\), 2 equal parts of \(\frac{1}{6}\) and 2 equal parts of \(\frac{1}{6}\).

Question 12.
DIG DEEPER!
Why is it important to be able to write a fraction as a sum of fractions in different ways?

Answer:
Asking students to write a fraction as a sum of unit fractions, or as a sum of other fractions, encourages students to make sense of quantities and their relationships. Students further develop their understandings about fractions and decomposing numbers through this process.

Question 13.
Precision
Match each fraction with an equivalent expression.

Answer:

Think and Grow: Modeling Real Life

Example
A chef has \(\frac{8}{10}\) liter of soup. How can the chef pour all of the soup into 2 bowls?

Break apart \(\frac{8}{10}\) into any two fractions that have a sum of \(\frac{8}{10}\).

Answer:

Show and Grow

Question 14.
You have \(\frac{7}{3}\) pounds of almonds. What are two different ways you can put all of the almonds into 2 bags?

Answer:
Given that,
You have \(\frac{7}{3}\) pounds of almonds.
Break apart 7 parts of \(\frac{1}{3}\) into 5 parts of \(\frac{1}{3}\) and 2 parts of \(\frac{1}{3}\)
Thus you can put 5 parts of \(\frac{1}{3}\) and 2 parts of \(\frac{1}{3}\) of the almonds into 2 bags.

Question 15.
A 3-person painting crew has \(\frac{10}{12}\) of a fence left to paint. What is one way the crew can finish painting the fence when each person paints a fraction of the fence?

Answer:
Given that,
A 3-person painting crew has \(\frac{10}{12}\) of a fence left to paint.
\(\frac{10}{12}\) can be written as \(\frac{3}{12}\) + \(\frac{3}{12}\) + \(\frac{4}{12}\)
Thus each person paints \(\frac{3}{12}\) + \(\frac{3}{12}\) + \(\frac{4}{12}\) fraction of the fence.

Question 16.
DIG DEEPER!
Three teammates have to run a total of miles for a relay race. Can each team member run the same fraction of a mile, in fourths, to complete the race? Explain.

Answer:
Three teammates have to run a total of miles for a relay race.
No three members cannot run the same fraction of a mile, in fourths, to complete the race
\(\frac{10}{12}\) can be written as \(\frac{3}{12}\) + \(\frac{3}{12}\) + \(\frac{4}{12}\)

Decompose Fractions Homework & Practice 8.2

write the fraction as a sum of unit fractions.

Question 1.
\(\frac{2}{2}\)

Answer: 1
The sum of unit fractions of \(\frac{2}{2}\) is \(\frac{1}{2}\) + \(\frac{1}{2}\)

Question 2.
\(\frac{3}{5}\)

Answer: The sum of unit fractions of \(\frac{3}{5}\) is \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\)

Question 3.
\(\frac{4}{3}\)

Answer: The sum of unit fractions of \(\frac{4}{3}\) is \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\)

Question 4.
\(\frac{6}{4}\)

Answer: The sum of unit fractions of \(\frac{6}{4}\) is \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\)

write the fraction as a sum of fractions in two different ways.

Question 5.
\(\frac{8}{12}\)

Answer: The sum of unit fractions of \(\frac{8}{12}\) is \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\)

Another Way:
Break apart \(\frac{8}{12}\) as 4 parts of \(\frac{1}{12}\) and 4 parts of \(\frac{1}{12}\)

Question 6.
\(\frac{10}{6}\)

Answer: The sum of unit fractions of \(\frac{10}{6}\) is \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\)

Another way:
Break apart \(\frac{10}{6}\) as 5 parts of \(\frac{1}{6}\) and 5 parts of \(\frac{11}{6}\)

Question 7.
\(\frac{11}{100}\)

Answer: The sum of unit fractions of \(\frac{11}{100}\) is \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\)

Another way:
Break apart \(\frac{11}{100}\) as 5 parts of \(\frac{1}{100}\), 4 parts of \(\frac{1}{100}\) and 2 parts of \(\frac{1}{100}\)

Question 8.
\(\frac{14}{8}\)

Answer: The sum of unit fractions of \(\frac{14}{8}\) is \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\)

Another way:
Break apart \(\frac{14}{8}\) as 5 parts of \(\frac{1}{8}\), 9 parts of \(\frac{1}{8}\)

Question 9.
Which One Doesn’t Belong? Which expression does belong with the other three?

Answer: The expression \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) does not belong to the other three.

Question 10.

Answer: Yes your friend is correct.
\(\frac{1}{10}\) + \(\frac{3}{10}\)  + \(\frac{5}{10}\)
Here the denominators are the same so you have to add the numerators.
\(\frac{1}{10}\) + \(\frac{3}{10}\)  + \(\frac{5}{10}\) = \(\frac{9}{10}\)
\(\frac{2}{10}\) + \(\frac{4}{10}\) + \(\frac{3}{10}\)
Here the denominators are the same so you have to add the numerators.
\(\frac{2}{10}\) + \(\frac{4}{10}\) + \(\frac{3}{10}\) = \(\frac{9}{10}\)

Question 11.
Number Sense
Is it possible to write \(\frac{7}{12}\) as the sum of three fractions with three different numerators and the same denominator? Explain.

Answer: Yes it is possible to write \(\frac{7}{12}\) as the sum of three fractions with three different numerators and the same denominator.
\(\frac{7}{12}\) = \(\frac{3}{12}\) + \(\frac{3}{12}\) + \(\frac{1}{12}\)

Question 12.
You have \(\frac{8}{4}\) pounds of dried pineapple. What are two different ways you can put all of the pineapples into 2 bags?

Answer:
Given that,
You have \(\frac{8}{4}\) pounds of dried pineapple.
Break apart \(\frac{8}{4}\) as 4 parts of \(\frac{1}{4}\) and 4 parts of \(\frac{1}{4}\).
The two different ways you can put all of the pineapples into 2 bags are 4 parts of \(\frac{1}{4}\).

Question 13.
DIG DEEPER!
A carpenter has 3 planks of wood. Each plank has a different thickness. When stacked, the thickness of the 3 planks is \(\frac{6}{8}\) inch. What are the possible thickness of each plank?

Answer:
Given that,
A carpenter has 3 planks of wood. Each plank has a different thickness.
When stacked, the thickness of the 3 planks is \(\frac{6}{8}\) inch.
\(\frac{6}{8}\) = \(\frac{2}{8}\) + \(\frac{3}{8}\) + \(\frac{1}{8}\)
The possible thickness of each plank are \(\frac{2}{8}\), \(\frac{3}{8}\), \(\frac{1}{8}\)

Review & Refresh

Find the product. Check whether your answer is reasonable.

Question 14.
Estimate: ___
608 × 5 = ___

Answer:
600 × 5 = 3000
The number close to 608 is 600.
Step 2:
608 × 5 = 3040
3040 is close to 3000. So, the answer is reasonable.

Question 15.
Estimate: ___
7 × 5,394 = ___

Answer:
7 × 5400 = 37,800
The number close to 5394 is 5400.
Step 2:
7 × 5394 = 37,758
37,758 is close to 37,800. So, the answer is reasonable.

Question 16.
Estimate: ___
927 × 3 = ___

Answer:
900 × 3 = 2700
The number close to 927 is 900.
Step 2:
927 × 3 = 2781
2781 is close to 2700. So, the answer is reasonable.

Lesson 8.3 Add Fractions with Like Denominators

Explore and Grow

Write each fraction as a sum of unit fractions. Use models to help.

How many unit fractions did you use in all to rewrite the fractions above? How does this relate to the sum \(\frac{3}{6}+\frac{5}{6}\) ?

Answer:

\(\frac{3}{6}+\frac{5}{6}\) = \(\frac{8}{6}\)

Construct Arguments
How can you use the numerators and the denominators to add fractions with like denominators? Explain why your method makes sense.

Answer:
To add fractions with like denominators, add the numerators and keep the same denominator. Then simplify the sum. You know how to do this with numeric fractions.
\(\frac{3}{6}+\frac{5}{6}\) = \(\frac{8}{6}\)

Think and Grow: Add Fractions

To add fractions with like denominators, add the numerators.

The denominator stays the same.

Answer:

Add the numerators of the like denominators.

Answer:
Add the numerators of the like denominators.

Show and Grow

Add.

Question 1.

Answer:
Add the numerators of the like denominators.

Question 2.

Answer:
Add the numerators of the like denominators.
6 + 2 = 8
\(\frac{6}{5}+\frac{2}{5}\) = \(\frac{8}{5}\)

Question 3.

Answer:
Add the numerators of the like denominators.
4 + 4 = 8
\(\frac{4}{8}+\frac{4}{8}\) = \(\frac{8}{8\) = 1

Apply and Grow: Practice

Add.

Question 4.

Answer:
Add the numerators of the like denominators.
3 + 2 = 5
\(\frac{3}{6}+\frac{2}{6}\) = \(\frac{5}{6}\)

Question 5.

Answer:
Add the numerators of the like denominators.
8 + 4 = 12
\(\frac{8}{2}+\frac{4}{2}\) = \(\frac{12}{2}\) = 6

Question 6.

Answer:
Add the numerators of the like denominators.
4 + 1 = 5
\(\frac{4}{5}+\frac{1}{5}\) = \(\frac{5}{5}\) = 1

Question 7.

Answer:
Add the numerators of the like denominators.
60 + 35 = 95
\(\frac{60}{100}+\frac{35}{100}\) = \(\frac{95}{100}\)

Question 8.

Answer:
The denominators are not the same. So first you have to make the common denominators and add the fraction with the number.
2 × 3/3 = 6/3
\(\frac{6}{3}+\frac{5}{3}\) = \(\frac{11}{3}\)

Question 9.

Answer:
The denominators are not the same. So first you have to make the common denominators and add the fraction with the number.
6 × 12/12 = 72/12
\(\frac{72}{12}+\frac{1}{12}\) = \(\frac{73}{12}\)

Question 10.

Answer:
Add the numerators of the like denominators.
3 + 1 + 1 = 5
3/4 + 1/4 + 1/4 = 5/4

Question 11.

Answer:
Add the numerators of the like denominators.
\(\frac{6}{8}\) + \(\frac{5}{8}\) + \(\frac{4}{8}\)
6 + 5 + 4 = 15
\(\frac{6}{8}\) + \(\frac{5}{8}\) + \(\frac{4}{8}\) = \(\frac{15}{8}\)

Question 12.

Answer:
Add the numerators of the like denominators.
43 + 16 + 10 = 69
\(\frac{43}{100}\) + \(\frac{16}{100}\) + \(\frac{10}{100}\) = \(\frac{69}{100}\)

Question 13.
You eat \(\frac{2}{10}\) of a vegetable pizza. Your friend eats \(\frac{3}{10}\) of the pizza. What fraction of the pizza do you and your friend eat together?

Answer:
Given that,
You eat \(\frac{2}{10}\) of a vegetable pizza. Your friend eats \(\frac{3}{10}\) of the pizza.
\(\frac{2}{10}\) + \(\frac{3}{10}\) = \(\frac{5}{10}\) = \(\frac{1}{2}\)
\(\frac{1}{2}\) fraction of the pizza do you and your friend eat together

Question 14.
Number Sense
A sum has 5 addends. Each addend is a unit fraction. The sum is 1. What are the addends?

Answer:
\(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) = \(\frac{5}{5}\) = 1

Question 15.
Writing
Explain how to add \(\frac{3}{4}\) and \(\frac{1}{4}\). Use a model to support your answer.

Answer:

\(\frac{3}{4}\) + \(\frac{1}{4}\) = \(\frac{4}{4}\) = 1

Think and Grow: Modeling Real Life

Example
The table shows the natural hazards studied by 100 students for a science project. What fraction of the students studied a weather-based natural hazard?

Answer:

Show and Grow

Question 16.
Use the graph above to find what fraction of the students studied an Earth-based natural hazard.

Answer:
We can find the fraction of the students who studied an Earth-based natural hazard
1 × 8 = 8
Half drop = 4
8 + 4 = 12
=  Number of students/Total number of students surveyed
= 12/100
Thus \(\frac{12}{100}\) fraction of the students who studied an Earth-based natural hazard.

Question 17.
DIG DEEPER!
A caterer needs at least 2 pounds of lunch meat to make a sandwich platter. She has \(\frac{6}{4}\) pounds of turkey and \(\frac{3}{4}\) pound of ham. Does the caterer have enough lunch meat to make a sandwich platter? Explain.

Answer:
Given that,
A caterer needs at least 2 pounds of lunch meat to make a sandwich platter. She has \(\frac{6}{4}\) pounds of turkey and \(\frac{3}{4}\) pound of ham.
\(\frac{6}{4}\) + \(\frac{3}{4}\) = \(\frac{9}{4}\)
Convert it into mixed fraction
\(\frac{9}{4}\) = 1 \(\frac{3}{4}\)
Thus the caterer does not have enough lunch meat to make a sandwich platter.

Add Fractions with Like Denominators Homework & Practice 8.3

Add

Question 1.

Answer:
Add the numerators of the like denominators.
Take the denominator as common and add the numerators.

Question 2.

Answer:
Add the numerators of the like denominators.
Take the denominator as common and add the numerators.
\(\frac{2}{2}\) + \(\frac{7}{2}\) = (2 + 7)/2 = \(\frac{9}{2}\)

Question 3.

Answer:
Add the numerators of the like denominators.
Take the denominator as common and add the numerators.
\(\frac{2}{5}\) + \(\frac{2}{5}\) = (2 + 2)/5 = \(\frac{4}{5}\)

Question 4.

Answer:
Add the numerators of the like denominators.
Take the denominator as common and add the numerators.
\(\frac{4}{10}\) + \(\frac{6}{10}\) = (4 + 6)/10 = \(\frac{10}{10}\) = 1

Question 5.

Answer:
The denominators are not the same. So first you have to make the common denominators and add the fraction with the number.
Take the denominator as common and add the numerators.
4 × 3/3 = 12/3
\(\frac{12}{3}\) + \(\frac{1}{3}\) = (12 + 1)/3 = \(\frac{13}{2}\)

Question 6.

Answer:
Add the numerators of the like denominators.
Take the denominator as common and add the numerators.
\(\frac{27}{100}\) + \(\frac{460}{100}\) = (27 + 460)/100 = \(\frac{487}{100}\)

Question 7.

Answer:
Add the numerators of the like denominators.
Take the denominator as common and add the numerators.
\(\frac{8}{4}\) + \(\frac{5}{4}\) = (8 + 5)/4 = \(\frac{13}{4}\)

Question 8.

Answer:
Add the numerators of the like denominators.
Take the denominator as common and add the numerators.
\(\frac{4}{6}\) + \(\frac{1}{6}\) = (4 + 1)/6 = \(\frac{5}{6}\)

Question 9.

Answer:
The denominators are not the same. So first you have to make the common denominators and add the fraction with the number.
Take the denominator as common and add the numerators.
10 × 12/12 = 120/12
\(\frac{120}{12}\) + \(\frac{7}{12}\) = (120 + 7)/3 = \(\frac{127}{12}\)

Question 10.

Answer:
Add the numerators of the like denominators.
Take the denominator as common and add the numerators.
\(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{2}{5}\) = (1 + 1 + 2)/5 = \(\frac{4}{5}\)

Question 11.

Answer:
Add the numerators of the like denominators.
Take the denominator as common and add the numerators.
\(\frac{38}{100}\) + \(\frac{13}{100}\) + \(\frac{21}{100}\) = (38+ 13 + 21)/100 = \(\frac{72}{100}\)

Question 12.

Answer:
Add the numerators of the like denominators.
Take the denominator as common and add the numerators.
\(\frac{8}{8}\) + \(\frac{4}{8}\) + \(\frac{2}{8}\) = (8 + 4 + 2)/8 = \(\frac{14 }{8}\)

Question 13.
You plant a sunflower seed. After 11 week, the plant is \(\frac{1}{2}\) inch tall. The next week your plant grows \(\frac{3}{2}\) inches. How tall is your plant after the second week?

Answer:
Given that,
You plant a sunflower seed. After 11 week, the plant is \(\frac{1}{2}\) inch tall. The next week your plant grows \(\frac{3}{2}\) inches.
\(\frac{1}{2}\) + \(\frac{3}{2}\) = \(\frac{4}{2}\) = 2
The plant is 2 inches tall after the second week.

Question 14.
Writing
Explain how to find the unknown addend.

Answer:
1 can be written as \(\frac{10}{10}\)
\(\frac{7}{10}\) + ? = \(\frac{10}{10}\)
? = \(\frac{10}{10}\) – \(\frac{7}{10}\)
? = \(\frac{3}{10}\)
Thus the unknown addend is \(\frac{3}{10}\)

Question 15.
DIG DEEPER!
When you double me and add \(\frac{1}{6}\), you get \(\frac{5}{6}\). What fraction am I?

Answer: \(\frac{2}{6}\)

Explanation:
If you add \(\frac{2}{6}\) twice and add \(\frac{1}{6}\) to it you get \(\frac{5}{6}\).

Question 16.
Reasoning
You eat \(\frac{2}{8}\) of a large apple at lunch and another \(\frac{4}{8}\) of it as a snack. Your friend eats \(\frac{4}{8}\) of a small apple at lunch and another \(\frac{2}{8}\) of it as a snack. Do you each eat the same amount? Explain.

Answer:
Given that,
You eat \(\frac{2}{8}\) of a large apple at lunch and another \(\frac{4}{8}\) of it as a snack. Your friend eats \(\frac{4}{8}\) of a small apple at lunch and another \(\frac{2}{8}\) of it as a snack.
\(\frac{2}{8}\) + \(\frac{4}{8}\) = \(\frac{6}{8}\)
\(\frac{2}{8}\) + \(\frac{4}{8}\) = \(\frac{6}{8}\)
Yes you and your friend eat same amount of food.

Question 17.
Modeling Real Life
The graph shows the classification of 100 species of birds in North America according to their extinction rate. What fraction of the species are classified as near threatened or vulnerable?

Answer:
• = 4 species
Near threatened = 4 × 4 = 16 species
half • = 2 species
16 + 2 = 18 species
Fraction of near threatened = number of species/total number of species of birds in North America
= 18/100
Vulnerable = 5 × 4 = 20 species
half • = 2 species
20 + 2 = 22 species
Fraction of near threatened = number of species/total number of species of birds in North America
= 22/100

Question 18.
Modeling Real Life
Use the graph above to find what fraction of not the species are critically endangered.

Answer:
• = 4 species
critically endangered = 4 × 4 = 16 species
half • = 2 species
16 + 2 = 18 species
Fraction of near threatened = number of species/total number of species of birds in North America
= 18/100

Review & Refresh

Question 19.
A pet store has 25 tanks with 32 fish in each tank. A customer buys 7 fish. How many fish does the pet store have now?

Answer:
Given,
A pet store has 25 tanks with 32 fish in each tank. A customer buys 7 fish.
\(\frac{25}{32}\) – \(\frac{7}{32}\) = \(\frac{18}{32}\)
Thus there are 18 fishes in the pet store.

Lesson 8.4 Use Models to subtract Fractions

Explore and Grow

Draw a model to show \(\frac{9}{12}\).
Answer:

Use your model to find \(\frac{9}{12}\) – \(\frac{5}{12}\). Explain your method.
Answer:

Repeated Reasoning
Write two fractions that have a difference of \(\frac{7}{12}\). Explain your reasoning.

Answer:  \(\frac{9}{12}\) – \(\frac{2}{12}\) = \(\frac{7}{12}\)

Think and Grow: Use Models to Subtract Fractions

You can subtract fractions by taking away parts that refer to the same whole.

Answer:

Answer:

Show and Grow

Find the difference. Explain how you used the model to subtract.

Question 1.

Answer: 5/10 = 1/2
Take away a length of 4/10 from the length of 9/10.

Question 2.

Answer:
Take away a length of 6/4 from the length of 2/4.

Apply and Grow: Practice

Find the difference. Use a model or a number line to help.

Question 3.

Answer: 4/8
Take away a length of 8/8 from the length of 4/8.

Question 4.

Answer: 8/12
Take away a length of 10/12 from the length of 2/12.

Question 5.

Answer: 3/5
Take away a length of 4/5 from the length of 1/5.

Question 6.

Answer: 6/2 = 3
Take away a length of 9/2 from the length of 3/2.

Question 7.

Answer: 10/6
Take away a length of 15/6 from the length of 5/6.

Question 8.

Answer: \(\frac{26}{100}\)
The denominators of both the fractions are the same. So subtract the numerators.
\(\frac{76}{100}\) – \(\frac{50}{100}\) = \(\frac{26}{100}\)

Question 9.
You need to walk \(\frac{3}{4}\) mile for your physical education class. So far, you have walked \(\frac{2}{4}\) mile. How much farther do you need to walk?

Answer:
Given that,
You need to walk \(\frac{3}{4}\) mile for your physical education class. So far, you have walked \(\frac{2}{4}\) mile.
\(\frac{3}{4}\) – \(\frac{2}{4}\) = \(\frac{1}{4}\)
You need to walk \(\frac{1}{4}\) miles more.

Question 10.
Number Sense
Which expressions have a difference of \(\frac{4}{5}\) ?

Answer:
5/5 – 1/5 = 4/5
10/5 – 6/5 = 4/5
6/5 – 3/5 = 3/5
9/5 – 5/5 = 4/5
i, ii, iv has the difference of \(\frac{4}{5}\)

Question 11.
Structure
Write the subtraction equation represented by the model.

Answer: \(\frac{7}{8}\) – \(\frac{4}{8}\) = \(\frac{3}{8}\)

Question 12.
Writing
Explain why the numerator changes when you subtract fractions with like denominators, but the denominator stays the same.

Answer:
The most simple fraction subtraction problems are those that have two proper fractions with a common denominator. That is, each denominator is the same. The process is just as it is for the addition of fractions with like denominators, except you subtract! You subtract the second numerator from the first and keep the denominator the same.

Think and Grow: Modeling Real Life

Example
A lizard’s tail is \(\frac{10}{12}\) foot long. It sheds a \(\frac{7}{12}\) foot long part of its tail to escape a predator. How long is the remaining part of the lizard’s tail?

Because each fraction represents a part of the same whole, you can take away a part.

Answer:
Given that,
A lizard’s tail is \(\frac{10}{12}\) foot long. It sheds a \(\frac{7}{12}\) foot long part of its tail to escape a predator.

Show and Grow

Question 13.
You have \(\frac{9}{8}\) cups of raisins. You eat \(\frac{2}{8}\) cup. What fraction of a cup of raisins do you have left?

Answer:
Given that,
You have \(\frac{9}{8}\) cups of raisins. You eat \(\frac{2}{8}\) cup.
\(\frac{9}{8}\) – \(\frac{2}{8}\) = \(\frac{7}{8}\)
Thus \(\frac{7}{8}\) fraction of a cup of raisins is left.

Question 14.
A large bottle has \(\frac{7}{4}\) quarts of liquid soap. A small bottle has \(\frac{3}{4}\) quart of liquid soap. How much more soap is in the large bottle than in the small bottle?

Answer:
Given that,
A large bottle has \(\frac{7}{4}\) quarts of liquid soap. A small bottle has \(\frac{3}{4}\) quart of liquid soap.
\(\frac{7}{4}\) – \(\frac{3}{4}\) = \(\frac{4}{4}\) = 1
Thus 1 more soap is in the large bottle than in the small bottle.

Question 15.
DIG DEEPER!
You need 2 cups of milk for a recipe. You have cup of \(\frac{1}{3}\) milk. How much more milk do you need? Explain.

Answer:
Given,
You need 2 cups of milk for a recipe. You have cup of \(\frac{1}{3}\) milk.
2 × \(\frac{1}{3}\) = \(\frac{2}{3}\)
Thus \(\frac{2}{3}\) more milk you need.

Use Models to subtract Fractions Homework & Practice 8.4

Find the difference. Explain how you used the model to subtract.

Question 1.

Answer:

Question 2.

Answer:

Find the difference. Use a model or a number line to help.

Question 3.

Answer: 15/10

Question 4.

Answer: 10/5

Question 5.

Answer: 8/12

Question 6.

Answer:

Question 7.

Answer: 7/4

Question 8.

Answer:
The denominators of both the fractions are the same. So subtract the numerators.
\(\frac{70}{100}\) – \(\frac{6}{100}\) = \(\frac{64}{100}\)

Question 9.
You have \(\frac{2}{3}\) yard of ribbon. You cut off \(\frac{1}{3}\) yard of the ribbon. How much ribbon do you have left?

Answer:
Given that,
You have \(\frac{2}{3}\) yard of ribbon. You cut off \(\frac{1}{3}\) yard of the ribbon.
The denominators of both the fractions are the same. So subtract the numerators.
\(\frac{2}{3}\) – \(\frac{1}{3}\) = \(\frac{1}{3}\)
\(\frac{1}{3}\) ribbon has left.

Question 10.
Structure
When using circular models to find the difference of \(\frac{4}{2}\) and \(\frac{1}{2}\), why do you shade two circles to represent \(\frac{4}{2}\)?

Answer:
The denominators of both the fractions are the same. So subtract the numerators.
\(\frac{4}{2}\) – \(\frac{1}{2}\) = \(\frac{3}{2}\)

Question 11.
YOU BE THE TEACHER
In a box of pens, \(\frac{3}{4}\) of the pens are blue. Your friend takes \(\frac{1}{4}\) of the blue pens and says that now \(\frac{2}{4}\) of the pens in the box are blue. Is your friend correct? Explain.

Answer:
Given,
In a box of pens, \(\frac{3}{4}\) of the pens are blue. Your friend takes \(\frac{1}{4}\) of the blue pens and says that now \(\frac{2}{4}\) of the pens in the box are blue.
The denominators of both the fractions are the same. So subtract the numerators.
\(\frac{3}{4}\) – \(\frac{1}{4}\) = \(\frac{2}{4}\)
Yes, your friend is correct.

Question 12.
DIG DEEPER!
Using numerators that even number, write two different subtraction equations that each have a difference of 1.

Answer: \(\frac{6}{4}\) – \(\frac{2}{4}\) = \(\frac{4}{4}\) = 1

Question 13.
Modeling Real Life
In our solar system, \(\frac{6}{8}\) of the planets have moons, and \(\frac{4}{8}\) of the planets have moons and rings. What fraction of the planets in our solar system have moons, but do not have rings?

Answer:
Given,
In our solar system, \(\frac{6}{8}\) of the planets have moons, and \(\frac{4}{8}\) of the planets have moons and rings.
The denominators of both the fractions are the same. So subtract the numerators.
\(\frac{6}{8}\) – \(\frac{4}{8}\) = \(\frac{2}{8}\)

Question 14.
Modeling Real Life
A professional pumpkin carver carves a pumpkin that weighs \(\frac{7}{10}\) ton. He carves a second pumpkin that weighs \(\frac{6}{10}\) ton. How much heavier is the first pumpkin than the second pumpkin?

Answer:
Given that,
A professional pumpkin carver carves a pumpkin that weighs \(\frac{7}{10}\) ton. He carves a second pumpkin that weighs \(\frac{6}{10}\) ton.
The denominators of both the fractions are the same. So subtract the numerators.
\(\frac{7}{10}\) – \(\frac{6}{10}\) = \(\frac{1}{10}\)
The first pumpkin is \(\frac{1}{10}\) heavier than the second pumpkin.

Review & Refresh

Find an equivalent fraction.

Question 15.
\(\frac{7}{4}\)

Answer:
The equivalent fraction of \(\frac{7}{4}\) is given below,
\(\frac{7}{4}\) × \(\frac{2}{2}\) = \(\frac{14}{8}\)

Question 16.
\(\frac{3}{5}\)

Answer:
The equivalent fraction of \(\frac{3}{5}\) is given below,
\(\frac{3}{5}\) × \(\frac{3}{3}\) = \(\frac{9}{15}\)

Question 17.
\(\frac{2}{3}\)

Answer:
The equivalent fraction of \(\frac{2}{3}\) is given below,
\(\frac{2}{3}\) × \(\frac{2}{2}\) = \(\frac{4}{6}\)

Lesson 8.5 Subtract Fractions with Like Denominators

Explore and Grow

Write each fraction as a sum of unit fractions. Use models to help.

How many more unit fractions did you use to rewrite \(\frac{4}{5}\) than \(\frac{3}{5}\)?
How does this relate to the difference \(\frac{4}{5}\) – \(\frac{3}{5}\) ?

Answer:

\(\frac{4}{5}\) – \(\frac{3}{5}\) = \(\frac{1}{5}\)

Construct Arguments
How can you use the numerators and the denominators to subtract fractions with like denominators? Explain why your method makes sense.

Answer: Steps on How to Add and Subtract Fractions with the Same Denominator. To add fractions with like or the same denominator, simply add the numerators then copy the common denominator. Always reduce your final answer to its lowest term.

Think and Grow: Subtract Fractions

To subtract fractions with like denominators, subtract the numerators. The denominator stays the same.

Answer:

Show and Grow

Subtract.

Question 1.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.

Question 2.

Answer:
First, make the denominators common and then subtract the numerators
1 can be written as \(\frac{12}{12}\)
\(\frac{12}{12}\) – \(\frac{8}{12}\) = (12 – 8)/12
= \(\frac{4}{12}\) or \(\frac{1}{3}\)

Question 3.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.
\(\frac{50}{100}\) – \(\frac{30}{100}\) = (50 – 30)/100
= \(\frac{20}{100}\) or \(\frac{1}{5}\)

Apply and Grow: Practice

Subtract.

Question 4.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.

Question 5.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.

Question 6.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.
\(\frac{12}{6}\) – \(\frac{7}{6}\) = (12- 7)/6
\(\frac{5}{6}\)

Question 7.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.
\(\frac{4}{5}\) – \(\frac{3}{5}\) = (4- 3)/5
\(\frac{1}{5}\)

Question 8.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.
\(\frac{60}{100}\) – \(\frac{43}{100}\) = (60 – 43)/100
\(\frac{17}{100}\)

Question 9.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.
\(\frac{10}{2}\) – \(\frac{2}{2}\) = (10 – 2)/2
\(\frac{8}{4}\) = 2

Question 10.

Answer:
First, make the denominators common and then subtract the numerators.
\(\frac{12}{12}\) – \(\frac{7}{12}\) = (12 – 7)/12
= \(\frac{5}{12}\)

Question 11.

Answer:
First, make the denominators common and then subtract the numerators
1 can be written as \(\frac{8}{8}\)
\(\frac{8}{8}\) – \(\frac{5}{8}\) = \(\frac{3}{8}\)

Question 12.

Answer:
First, make the denominators common and then subtract the numerators
2 can be written as \(\frac{8}{4}\)
\(\frac{8}{4}\) – \(\frac{1}{4}\) = \(\frac{7}{4}\)

Question 13.
You have 1 gallon of paint. You use \(\frac{2}{3}\) gallon to paint a wall. How much paint do you have left?

Answer:
Given that,
You have 1 gallon of paint. You use \(\frac{2}{3}\) gallon to paint a wall.
First, make the denominators common and then subtract the numerators
1 – \(\frac{2}{3}\)
1 can be written as \(\frac{3}{3}\)
\(\frac{3}{3}\) – \(\frac{2}{3}\) = \(\frac{1}{3}\)

Question 14.
Reasoning
Why is it unreasonable to get a difference of \(\frac{7}{8}\) when subtracting \(\frac{1}{8}\) from \(\frac{7}{8}\)? Use a model to support your answer.

Answer:
The difference of \(\frac{7}{8}\) when subtracting \(\frac{1}{8}\) from \(\frac{7}{8}\) is,

Question 15.
Your friend says each difference is \(\frac{3}{10}\). Is your friend correct? Explain.

Answer:

Your friend is correct.
10/10 – 7/10 = 3/10
100/100 = 70/100 = 30/100 = 3/10

Think and Grow: Modeling Real Life

Example
A flock of geese has completed \(\frac{5}{12}\) of its total migration. What fraction of its migration does the flock of geese have left to complete?

Because the total migration is 1 whole, find 1 − \(\frac{5}{12}\).

Answer:
Given,
A flock of geese has completed \(\frac{5}{12}\) of its total migration.
Because the total migration is 1 whole, find 1 − \(\frac{5}{12}\).
First, make the denominators common and then subtract the numerators.

Show and Grow

Question 16.
A runner has completed \(\frac{6}{10}\) of a race. What fraction of the race does the runner have left to complete?

Answer:
Given that,
A runner has completed \(\frac{6}{10}\) of a race.
1 – \(\frac{6}{10}\)
1 can be written as \(\frac{10}{10}\)
\(\frac{10}{10}\) – \(\frac{6}{10}\) = \(\frac{4}{10}\)
The runner has left \(\frac{4}{10}\) fraction of the race to complete.

Question 17.
A pizza buffet serves pizzas of the same size with different toppings. There is \(\frac{7}{8}\) of a vegetable pizza and \(\frac{2}{8}\) of a pineapple pizza left. How much more vegetable pizza is left than pineapple pizza?

Answer:
Given,
A pizza buffet serves pizzas of the same size with different toppings.
There is \(\frac{7}{8}\) of a vegetable pizza and \(\frac{2}{8}\) of a pineapple pizza left.
\(\frac{7}{8}\) – \(\frac{2}{8}\) = \(\frac{5}{8}\)
\(\frac{5}{8}\) more vegetable pizza is left than pineapple pizza.

Question 18.
DIG DEEPER!
Baseball practice is 1 hour long. You stretch for 7 minutes and play catch for 8 minutes. What fraction of an hour do you have left to practice?

Answer:
Given,
Baseball practice is 1 hour long. You stretch for 7 minutes and play catch for 8 minutes.
7 minutes + 8 minutes = 15 minutes
15 minutes = \(\frac{1}{4}\) hour
1 – \(\frac{1}{4}\) = \(\frac{3}{4}\)
Thus \(\frac{3}{4}\) fraction of an hour is left to practice.

Subtract Fractions with Like Denominators Homework & Practice 8.5

Subtract

Question 1.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.
\(\frac{7}{8}\) – \(\frac{3}{8}\) = \(\frac{4}{8}\)

Question 2.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.
\(\frac{5}{4}\) – \(\frac{3}{4}\) = \(\frac{2}{4}\)

Question 3.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.
\(\frac{13}{5}\) – \(\frac{6}{5}\) = \(\frac{7}{6}\)

Question 4.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.
\(\frac{5}{12}\) – \(\frac{1}{12}\) = \(\frac{4}{12}\)

Question 5.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.
\(\frac{9}{6}\) – \(\frac{4}{6}\) = \(\frac{5}{6}\)

Question 6.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.
\(\frac{11}{3}\) – \(\frac{7}{3}\) = \(\frac{4}{3}\)

Question 7.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.
\(\frac{10}{10}\) – \(\frac{4}{10}\) = \(\frac{6}{10}\)

Question 8.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.
\(\frac{20}{2}\) – \(\frac{8}{2}\) = \(\frac{12}{2}\)

Question 9.

Answer:
The denominators of the above fraction are the same so you have to subtract the numerators.
\(\frac{36}{100}\) – \(\frac{21}{100}\) = \(\frac{15}{100}\)

Question 10.

Answer:
First, make the denominators common and then subtract the numerators.
1 can be written as 5/5.
\(\frac{5}{5}\) – \(\frac{3}{5}\) = \(\frac{2}{5}\)

Question 11.

Answer:
First, make the denominators common and then subtract the numerators.
2 can be written as 8/4
\(\frac{8}{4}\) – \(\frac{2}{4}\) = \(\frac{6}{4}\)

Question 12.

Answer:
First, make the denominators common and then subtract the numerators
3 can be written as 24/8.
\(\frac{24}{8}\) – \(\frac{15}{8}\) = \(\frac{9}{8}\)

Question 13.
A family eats \(\frac{2}{3}\) of a tray of lasagna. What fraction of the tray of lasagna is left?

Answer:
Given,
A family eats \(\frac{2}{3}\) of a tray of lasagna.
1 – \(\frac{2}{3}\)
1 can be written as \(\frac{3}{3}\)
\(\frac{3}{3}\) – \(\frac{2}{3}\) = \(\frac{1}{3}\)
Therefore \(\frac{1}{3}\) fraction of the tray of lasagna is left.

Question 14.
Writing
Explain how finding is \(\frac{7}{10}-\frac{4}{10}\) similar to finding 7 – 4.

Answer:
Yes \(\frac{7}{10}-\frac{4}{10}\) similar to finding 7 – 4. Because the denominators of the fractions are the same.
\(\frac{7}{10}-\frac{4}{10}\) = \(\frac{3}{10}\)

Question 15.
Open-Ended
The model shows equal parts of a 1 whole. Write a subtraction problem whose answer is shown.

Answer:
By seeing the above figure we can write the subtraction problem.
1 – \(\frac{3}{8}\)

Question 16.
Modeling Real Life
you fill \(\frac{2}{4}\) of your plate with vegetables. What fraction of your plate does not contain vegetables?

Answer:
Given,
you fill \(\frac{2}{4}\) of your plate with vegetables.
1 – \(\frac{2}{4}\)
1 can be written as \(\frac{4}{4}\)
\(\frac{4}{4}\) – \(\frac{2}{4}\) = \(\frac{2}{4}\)
Thus \(\frac{2}{4}\) fraction of your plate does not contain vegetables.

Question 17.
Modeling Real Life
A group of students designs a rectangular playground. They use \(\frac{2}{8}\) of the playground for a basketball court and \(\frac{3}{8}\) of the playground for a soccer field. How much space is left?

Answer:
Given,
A group of students designs a rectangular playground.
They use \(\frac{2}{8}\) of the playground for a basketball court and \(\frac{3}{8}\) of the playground for a soccer field.
\(\frac{2}{8}\) + \(\frac{3}{8}\) = \(\frac{5}{8}\)
1 – \(\frac{5}{8}\) = \(\frac{3}{8}\)
Thus \(\frac{3}{8}\) space is left.

Review & Refresh

Find the quotient and the remainder

Question 18.
34 ÷ 7 = ___R___

Answer: 4R6

Explanation:
34 ÷ 7 = \(\frac{34}{7}\)
\(\frac{34}{7}\) = 4R6
Thus the quotient is 4 and the remainder is 6.

Question 19.
28 ÷ 3 = ___R___

Answer: 9 R1

Explanation:
28 ÷ 3 = \(\frac{28}{3}\)
\(\frac{28}{3}\) = 9 R1
Thus the quotient is 9 and the remainder is 1.

Lesson 8.6 Model Fractions and Mixed Numbers

Explore and Grow

Draw a model to show 1 + 1 + \(\frac{2}{3}\).

Use your model to write the sum as a fraction.

Answer:

Repeated Reasoning
How can you write a fraction greater than 1 as the sum of a whole number and a fraction less than 1? Explain.

Answer:
\(\frac{3}{2}\)  = 1 \(\frac{1}{2}\)
The fraction 1 \(\frac{1}{2}\) the whole fraction is greater than 1 and the fraction is less than 1.

Think and Grow: Write Fractions and Mixed Numbers

A mixed number represents the sum of a whole number and a fraction less than 1.

Answer:

Example
Write \(\frac{5}{2}\) as a mixed number.

Find how many wholes are in \(\frac{5}{2}\) and how many halves are left over.

Answer:

Show and Grow

Question 1.
Write 3\(\frac{1}{4}\) as a fraction. Use a model or a number line to help.

Answer:

Question 2.
Write \(\frac{9}{6}\) as a mixed number. Use a model or a number line to help.

Answer:
\(\frac{9}{6}\) can be written as \(\frac{3}{2}\)
Now convert \(\frac{3}{2}\) into the mixed fraction
\(\frac{3}{2}\) = 1 \(\frac{1}{2}\)

Apply and Grow: Practice

Write the mixed number as a fraction.

Question 3.
3\(\frac{4}{5}\)

Answer: \(\frac{19}{5}\)

Explanation:
Step 1
Multiply the denominator by the whole number
5 × 3 = 15
Step 2
Add the answer from Step 1 to the numerator
15 + 4 = 19
Step 3
Write an answer from Step 2 over the denominator
19/5

Question 4.
2\(\frac{1}{3}\)

Answer: \(\frac{7}{3}\)

Explanation:
Step 1
Multiply the denominator by the whole number
3 × 2 = 6
Step 2
Add the answer from Step 1 to the numerator
6 + 1 = 7
Step 3
Write an answer from Step 2 over the denominator
7/3

Question 5.
6\(\frac{7}{12}\)

Answer: \(\frac{79}{12}\)

Explanation:
Step 1
Multiply the denominator by the whole number
12 × 6 = 72
Step 2
Add the answer from Step 1 to the numerator
72 + 7 = 79
Step 3
Write an answer from Step 2 over the denominator
79/12

Question 6.
1\(\frac{82}{100}\)

Answer: \(\frac{182}{100}\)

Explanation:
Step 1
Multiply the denominator by the whole number
100 × 1 = 100
Step 2
Add the answer from Step 1 to the numerator
100 + 82 = 182
Step 3
Write an answer from Step 2 over the denominator
\(\frac{182}{100}\)

Question 7.
11\(\frac{3}{8}\)

Answer: \(\frac{91}{8}\)

Explanation:
Step 1
Multiply the denominator by the whole number
8 × 11 = 88
Step 2
Add the answer from Step 1 to the numerator
88 + 3 = 91
Step 3
Write an answer from Step 2 over the denominator
91/8

Question 8.
9\(\frac{5}{10}\)

Answer: \(\frac{95}{10}\)

Explanation:
Step 1
Multiply the denominator by the whole number
10 × 9 = 90
Step 2
Add the answer from Step 1 to the numerator
90 + 5 = 95
Step 3
Write an answer from Step 2 over the denominator
95/10

Write the fraction as a mixed number or a whole number.

Question 9.
\(\frac{9}{8}\)

Answer: 1 \(\frac{1}{8}\)

Explanation:
9÷8=1R1
\(\frac{9}{8}\) = 1 \(\frac{1}{8}\)

Question 10.
\(\frac{19}{3}\)

Answer: 6 \(\frac{1}{3}\)

Explanation:
19÷3=6R1
\(\frac{19}{3}\) = 6 \(\frac{1}{3}\)

Question 11.
\(\frac{38}{5}\)

Answer: 7 \(\frac{3}{5}\)

Explanation:
38÷5=7R3
\(\frac{38}{5}\) = 7 \(\frac{3}{5}\)

Question 12.
\(\frac{22}{10}\)

Answer: 2 \(\frac{1}{5}\)

Explanation:
11÷5=2R1
\(\frac{22}{10}\) = 2 \(\frac{1}{5}\)

Question 13.
\(\frac{460}{100}\)

Answer: 4 \(\frac{3}{5}\)

Explanation:
23÷5=4R3
\(\frac{460}{100}\) = 4 \(\frac{3}{5}\)

Question 14.
\(\frac{20}{4}\)

Answer: 5

Explanation:
4 divides 20 five times.
\(\frac{20}{4}\) = 5

Compare

Question 15.

Answer: =

Explanation:
\(\frac{3}{2}\) can be written as 1 \(\frac{1}{2}\)
1 × 2 + 1 = 3
So, 1 \(\frac{1}{2}\) = \(\frac{3}{2}\)

Question 16.

Answer: >

Explanation:
3\(\frac{3}{12}\) can be written as \(\frac{39}{12}\)
\(\frac{39}{12}\) > \(\frac{15}{12}\)
So, 3\(\frac{3}{12}\) > \(\frac{15}{12}\)

Question 17.

Answer: <

Explanation:
\(\frac{21}{6}\) can be written as 3 \(\frac{3}{6}\) or 3 \(\frac{1}{2}\)
So, 3 \(\frac{1}{2}\) < 4
\(\frac{21}{6}\) < 4

Question 18.
Which One Doesn’t Belong? Which expression does not Belong to the other three?

Answer:
3 \(\frac{2}{3}\) = \(\frac{11}{3}\)
\(\frac{9}{3}\) + \(\frac{3}{3}\) = \(\frac{12}{3}\)
\(\frac{3}{3}\) + \(\frac{3}{3}\) +\(\frac{3}{3}\) + \(\frac{2}{3}\) = \(\frac{11}{3}\)
\(\frac{11}{3}\)
So, the second expression does not belong to the other three expressions.

DIG DEEPER!
Find the unknown Number

Question 19.

Answer: 2

Explanation:
\(\frac{8}{6}\) is 4÷3=1R1
\(\frac{8}{6}\) = 1 \(\frac{2}{6}\)
So, the unknown number is 2.

Question 20.

Answer: 3

Explanation:
\(\frac{35}{4}\) = 8 R 3
8 \(\frac{3}{4}\) = \(\frac{35}{4}\)
So, the unknown number is 3.

Question 21.

Answer: 10

Explanation:
12 × 10 + 9 = 129
\(\frac{129}{12}\) = 10 \(\frac{9}{12}\)
So, the unknown number is 10.

Think and Grow: Modeling Real Life

Example
A construction worker needs nails that are \(\frac{9}{4}\) inches long. Which size of nails should the worker use?

Write \(\frac{9}{4}\) as a mixed number.

Answer:
Given,
A construction worker needs nails that are \(\frac{9}{4}\) inches long.
Convert from improper fraction to the mixed fraction.

Show and Grow

Question 22.
You need screws that are \(\frac{13}{8}\) inches long to build a birdhouse. Which size of screws should you use?

Answer:
Given,
You need screws that are \(\frac{13}{8}\) inches long to build a birdhouse.
Convert from improper fraction to the mixed fraction.
\(\frac{13}{8}\) = 1 \(\frac{5}{8}\)
8 × 1 + 5 = 13
So, you should use 1 \(\frac{5}{8}\) inches of screws.

Question 23.
You and your friend each measure the distance between two bean bag toss boards. You record the distance as 3\(\frac{3}{5}\) meters. Your friend records the distance as \(\frac{18}{5}\) meters. Did you and your friend record the same distance? Explain.

Answer:
Given that,
You and your friend each measure the distance between two bean bag toss boards.
You record the distance as 3\(\frac{3}{5}\) meters. Your friend records the distance as \(\frac{18}{5}\) meters.
3\(\frac{3}{5}\)
5 × 3 + 3 = 18
3\(\frac{3}{5}\) = \(\frac{18}{5}\)
Yes you and your friend record the same distance.

Question 24.
DIG DEEPER!
You use a \(\frac{1}{3}\)-cup scoop to measure 3\(\frac{1}{3}\) cups of rice. How many times do you fill the scoop?

Answer:
Given,
You use a \(\frac{1}{3}\)-cup scoop to measure 3\(\frac{1}{3}\) cups of rice.
\(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) = \(\frac{10}{3}\)
You need to measure 10 times to fill the scoop.

Question 25.
DIG DEEPER!
A sunflower plant is \(\frac{127}{10}\) centimeters tall. A snapdragon plant is 8\(\frac{9}{10}\) centimeters tall. Which plant is taller? Explain.

Answer:
Given that,
A sunflower plant is \(\frac{127}{10}\) centimeters tall. A snapdragon plant is 8\(\frac{9}{10}\) centimeters tall.
8\(\frac{9}{10}\) = \(\frac{89}{10}\)
\(\frac{127}{10}\) is greater than \(\frac{89}{10}\)
So, sunflower plant is taller.

Model Fractions and Mixed Numbers Homework & Practice 8.6

Write a mixed number as a fraction.

Question 1.
1\(\frac{7}{10}\)

Answer: \(\frac{17}{10}\)

Explanation:
Step 1
Multiply the denominator by the whole number
10 × 1 = 10
Step 2
Add the answer from Step 1 to the numerator
10 + 7 = 17
Step 3
Write an answer from Step 2 over the denominator
=17/10

Question 2.
1\(\frac{5}{6}\)

Answer: \(\frac{11}{6}\)

Explanation:
Step 1
Multiply the denominator by the whole number
6 × 1 = 6
Step 2
Add the answer from Step 1 to the numerator
6 + 5 = 11
Step 3
Write an answer from Step 2 over the denominator
11/6

Question 3.
2\(\frac{2}{3}\)

Answer: \(\frac{8}{3}\)

Explanation:
Step 1
Multiply the denominator by the whole number
3 × 2 = 6
Step 2
Add the answer from Step 1 to the numerator
6 + 2 = 8
Step 3
Write an answer from Step 2 over the denominator
8/3

Question 4.
4\(\frac{1}{2}\)

Answer: \(\frac{9}{2}\)

Explanation:
Step 1
Multiply the denominator by the whole number
2 × 4 = 8
Step 2
Add the answer from Step 1 to the numerator
8 + 1 = 9
Step 3
Write an answer from Step 2 over the denominator
9/2

Question 5.
3\(\frac{2}{8}\)

Answer: \(\frac{13}{4}\)

Explanation:
Step 1
Multiply the denominator by the whole number
8 × 3 = 24
Step 2
Add the answer from Step 1 to the numerator
24 + 2 = 26
Step 3
Write an answer from Step 2 over the denominator
26/8

Question 6.
9\(\frac{8}{12}\).

Answer: \(\frac{29}{3}\)

Explanation:
Step 1
Multiply the denominator by the whole number
12 × 9 = 108
Step 2
Add the answer from Step 1 to the numerator
108 + 8 = 116
Step 3
Write an answer from Step 2 over the denominator
116/12 = \(\frac{29}{3}\)

write the fraction as a mixed number or a whole number.

Question 7.
\(\frac{7}{5}\)

Answer: 1 \(\frac{2}{5}\)

Explanation:
Given the expression \(\frac{7}{5}\)
We have to convert the improper fraction to the mixed fraction.
7 ÷ 5=1R2
\(\frac{7}{5}\) = 1 \(\frac{2}{5}\)

Question 8.
\(\frac{10}{3}\)

Answer: 3 \(\frac{1}{3}\)

Explanation:
Given the expression \(\frac{10}{3}\)
We have to convert the improper fraction to the mixed fraction.
10÷3=3R1
\(\frac{10}{3}\) = 3 \(\frac{1}{3}\)

Question 9.
\(\frac{15}{4}\)

Answer: 3 \(\frac{3}{4}\)

Explanation:
Given the expression \(\frac{15}{4}\)
We have to convert the improper fraction to the mixed fraction.
15÷4=3 R 3
\(\frac{15}{4}\) = 3 \(\frac{3}{4}\)

Question 10.
\(\frac{32}{6}\)

Answer: 5 \(\frac{1}{3}\)

Explanation:
Given the expression \(\frac{32}{6}\)
We have to convert the improper fraction to the mixed fraction.
\(\frac{32}{6}\) = \(\frac{16}{3}\)
16÷3=5R1
\(\frac{32}{6}\) = 5 \(\frac{1}{3}\)

Question 11.
\(\frac{75}{8}\)

Answer: 9 \(\frac{3}{8}\)

Explanation:
Given the expression \(\frac{75}{8}\)
We have to convert the improper fraction to the mixed fraction.
75÷8=9R3
\(\frac{75}{8}\) = 9 \(\frac{3}{8}\)

Question 12.
\(\frac{40}{10}\)

Answer: 4

Explanation:
Given the expression \(\frac{40}{10}\)
We have to convert the improper fraction to the mixed fraction.
\(\frac{40}{10}\) = \(\frac{4}{1}\) = 4
Thus \(\frac{40}{10}\) = 4

Compare

Question 13.

Answer: <

Explanation:
We have to convert the improper fraction to the mixed fraction.
5 \(\frac{1}{2}\) = \(\frac{11}{2}\)
\(\frac{11}{2}\) < \(\frac{15}{2}\)

Question 14.

Answer: =

Explanation:
We have to convert the improper fraction to the mixed fraction.
\(\frac{27}{12}\) = \(\frac{27}{12}\)

Question 15.

Answer:

Explanation:
We have to convert the improper fraction to the mixed fraction.
6 \(\frac{7}{8}\) = \(\frac{55}{8}\)
\(\frac{55}{8}\) > \(\frac{50}{8}\)

Question 16.
Number Sense
Complete the number line.

Answer:

Question 17.
Modeling Real Life
You need pencil lead that is \(\frac{12}{10}\) millimeters thick to complete an art project. Which size of pencil lead should you use?

Answer:
Given,
You need pencil lead that is \(\frac{12}{10}\) millimeters thick to complete an art project.
1 \(\frac{1}{10}\) = \(\frac{11}{10}\)
1 \(\frac{2}{10}\) = \(\frac{12}{10}\)
1 \(\frac{4}{10}\) = \(\frac{14}{10}\)
You should use 2nd pencil lead.

Question 18.
DIG DEEPER!
You have a \(\frac{1}{4}\)-cup measuring cup and a \(\frac{1}{2}\)-cup measuring cup. What are two ways you can 2\(\frac{3}{4}\) cups of water?

Answer:
Given,
You have a \(\frac{1}{4}\)-cup measuring cup and a \(\frac{1}{2}\)-cup measuring cup.
\(\frac{1}{4}\) + \(\frac{1}{2}\) = \(\frac{3}{4}\)
2\(\frac{3}{4}\) – \(\frac{3}{4}\) = 2

Review & Refresh

Question 19.
67 × 31 = ___

Answer:
Multiply the two numbers 67 and 31.
67 × 31 = 2077

Question 20.
83 × 47 = ___

Answer:
Multiply the two numbers 83 and 47.
83 × 47 = 3901

Lesson 8.7 Add Mixed Numbers

Use model to find 2\(\frac{3}{8}\) + 1\(\frac{1}{8}\).

Answer: 3 \(\frac{1}{2}\)

Explanation:
Add the fractional parts and then the whole numbers.
Rewriting our equation with parts separated
=2+3/8+1+1/8
Solving the whole number parts
2+1=3
Solving the fraction parts
3/8+1/8=4/8
Reducing the fraction part, 4/8,
4/8=1/2
Combining the whole and fraction parts
3+1/2=3 1/2

Construct Arguments
How can you use the whole number parts and the fractional parts to add mixed numbers with like denominators? Explain why your method makes sense.

Answer: To add mixed numbers, we first add the whole numbers together, and then the fractions. If the sum of the fractions is an improper fraction, then we change it to a mixed number.

Think and Grow: Add Mixed Numbers

To add mixed numbers, add the fractional parts and add the whole number parts. Another way to add mixed numbers is to rewrite each number as a fraction, then add.

Answer:

Example
Find 4\(\frac{2}{8}\) + 2\(\frac{7}{8}\).

Answer:

Apply and Grow: Practice

Add.

Question 3.
5\(\frac{1}{3}\) + 3\(\frac{2}{3}\) = ___

Answer: 9

Explanation:
Add the fractional parts and then the whole numbers.
Rewriting our equation with parts separated
=5+1/3+3+2/3
Solving the whole number parts
5+3=8
Solving the fraction parts
1/3+2/3=33
Reducing the fraction part, 3/3,
3/3=1/1
Simplifying the fraction part, 1/1,
1/1=1
Combining the whole and fraction parts
8+1=9

Question 4.
2\(\frac{8}{12}\) + 7\(\frac{5}{12}\) = ___

Answer: 10 \(\frac{1}{12}\)

Explanation:
Add the fractional parts and then the whole numbers.
Rewriting our equation with parts separated
=2+8/12+7+5/12
Solving the whole number parts
2+7=9
Solving the fraction parts
8/12+5/12=13/12
Simplifying the fraction part, 13/12,
13/12=1 1/12
Combining the whole and fraction parts
9+1+1/12=10 1/12

Question 5.
4 + 1\(\frac{1}{2}\) = ___

Answer: 5 \(\frac{1}{2}\)

Explanation:
Add the fractional parts and then the whole numbers.
Rewriting our equation with parts separated
=4+1+1/2
Solving the whole number parts
4+1=5
Combining the whole and fraction parts
5+1/2=5 1/2

Question 6.

Answer: 5 \(\frac{2}{100}\)

Explanation:
Add the fractional parts and then the whole numbers.
Rewriting our equation with parts separated
=78/100+124/100 + 3
Solving the fraction parts
78/100+124/100=202/100
3 + 202/100 = 5 \(\frac{2}{100}\)

Question 7.

Answer: 16 \(\frac{3}{8}\)

Explanation:
Add the fractional parts and then the whole numbers.
8 + 5 + 2 = 15
\(\frac{4}{8}\) + \(\frac{3}{8}\) + \(\frac{4}{8}\) = (4 + 4 + 3)/8 = \(\frac{11}{8}\)
\(\frac{11}{8}\) = 1 \(\frac{3}{8}\)
15 + 1\(\frac{3}{8}\) = 16 \(\frac{3}{8}\)

Question 8.

Answer: 24 \(\frac{2}{5}\)

Explanation:
Add the fractional parts and then the whole numbers.
10 + 9 + 4 = 23
\(\frac{4}{5}\) + \(\frac{2}{5}\) + \(\frac{1}{5}\) = \(\frac{7}{5}\)
Convert it into the mixed fraction.
\(\frac{7}{5}\) = 1 \(\frac{2}{5}\)
23 + 1 \(\frac{2}{5}\) = 24 \(\frac{2}{5}\)

Question 9.
Number Sense
Explain how to use the addition properties to find mentally. Then find the sum.

Answer: 16 \(\frac{3}{4}\)

Explanation:
Add the fractional parts and then the whole numbers.
6 + 8 + 1 = 15
\(\frac{3}{4}\) + \(\frac{2}{4}\) + \(\frac{1}{4}\) = \(\frac{6}{4}\)
Convert it into the mixed fraction.
\(\frac{6}{4}\) = 1 \(\frac{2}{4}\)
15 + 1 \(\frac{2}{4}\) = 16 \(\frac{2}{4}\)

Question 10.
DIG DEEPER!
When adding mixed numbers, is it always necessary to write the sum as a mixed number? Explain.

Answer: To add mixed numbers, we first add the whole numbers together, and then the fractions. If the sum of the fractions is an improper fraction, then we change it to a mixed number.

Question 11.
DIG DEEPER!
Find the unknown number.

Answer:
Let the unknown number be x.
4 \(\frac{5}{6}\) + x = 8 \(\frac{3}{6}\)
x = 8 \(\frac{3}{6}\) – 4 \(\frac{5}{6}\)
x = 3 \(\frac{2}{3}\)

Think and Grow: Modeling Real Life

Example
You pick 2\(\frac{3}{4}\) pounds of cherries. Your friend picks 1\(\frac{2}{4}\) pounds of cherries. How many pounds of cherries do you and your friend pick in all?

Add the amounts of cherries you and your friend each pick.

Answer:
You pick 2\(\frac{3}{4}\) pounds of cherries. Your friend picks 1\(\frac{2}{4}\) pounds of cherries.

Show and Grow

Question 12.
Before noon, 2\(\frac{3}{8}\) inches of snow falls in a city. Afternoon, 4\(\frac{6}{8}\) inches of snow falls. How many inches of snow falls in the city that day?

Answer:
Given that,
Before noon, 2\(\frac{3}{8}\) inches of snow falls in a city. Afternoon, 4\(\frac{6}{8}\) inches of snow falls.
2\(\frac{3}{8}\) + 4\(\frac{6}{8}\)
2 + 4 = 6
\(\frac{3}{8}\) + \(\frac{6}{8}\) = \(\frac{9}{8}\)
Convert it into the mixed fraction.
\(\frac{9}{8}\) = 1 \(\frac{1}{8}\)
1 \(\frac{1}{8}\) inches of snow falls in the city that day.

Question 13.
DIG DEEPER!
A student driver must practice driving at night for a total of at least 10 hours. Has the student met the nighttime driving requirement yet?

Answer:
2 \(\frac{1}{2}\) + 3 \(\frac{1}{2}\) + 2 \(\frac{1}{2}\)
First add the whole numbers
2 + 3 + 2 = 7
\(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) = 1 \(\frac{1}{2}\)
7 + 1 \(\frac{1}{2}\) = 8 \(\frac{1}{2}\)

Add Mixed Numbers Homework & Practice 8.7

Add.

Question 1.

Answer: 12 \(\frac{4}{5}\)

Explanation:
Add the fractional parts and then the whole numbers.
4 + 8 = 12
Add the fractions
\(\frac{1}{5}\) + \(\frac{3}{5}\) = \(\frac{4}{5}\)
Now add the fractions and thw whole numbers
12 + \(\frac{4}{5}\) = 12 \(\frac{4}{5}\)

Question 2.

Answer: 20 \(\frac{3}{8}\)

Explanation:
Add the fractional parts and then the whole numbers.
10 + 9 = 19
Add the fractions
\(\frac{5}{8}\) + \(\frac{6}{8}\) = \(\frac{11}{8}\)
Convert it into the mixed fraction.
\(\frac{11}{8}\) = 1 \(\frac{3}{8}\)
Now add the fractions and the whole numbers
19 + 1 \(\frac{3}{8}\) = 20 \(\frac{3}{8}\)

Question 3.

Answer: 8 \(\frac{1}{3}\)

Explanation:
Add the fractional parts and then the whole numbers.
2 + 6 = 8
Now add the fractions and the whole numbers
\(\frac{1}{3}\) + 8 = 8 \(\frac{1}{3}\)

Question 4.

Answer:

Explanation:
Add the fractional parts and then the whole numbers.
3 + 4 = 7
\(\frac{10}{12}\) + \(\frac{10}{12}\) = \(\frac{20}{12}\)
Convert it into the mixed fraction.
\(\frac{20}{12}\) = 1 \(\frac{8}{12}\)
Now add the fractions and the whole numbers
7 + 1 \(\frac{8}{12}\) = 8 \(\frac{8}{12}\)

Question 5.

Answer: 9 \(\frac{2}{6}\)

Explanation:
Add the fractional parts and then the whole numbers.
Convert it into the mixed fraction.
\(\frac{11}{6}\) = 1 \(\frac{5}{6}\)
7 + 1 = 8
\(\frac{3}{6}\) + \(\frac{5}{6}\) = \(\frac{8}{6}\)
Now add the fractions and the whole numbers
8 + \(\frac{8}{6}\)
\(\frac{8}{6}\) = 1 \(\frac{2}{6}\)
8 + 1 \(\frac{2}{6}\) = 9 \(\frac{2}{6}\)

Question 6.

Answer: 15 \(\frac{1}{4}\)

Explanation:
Add the fractional parts and then the whole numbers.
Rewriting our equation with parts separated
=8+70/100+6+55/100
Solving the whole number parts
8+6=14
Solving the fraction parts
70/100+55/100=125/100
Reducing the fraction part, 125/100,
125/100=5/4
Simplifying the fraction part, 5/4,
5/4=1 1/4
Combining the whole and fraction parts
14+1+1/4= 15 \(\frac{1}{4}\)

Add

Question 7.

Answer: 11

Explanation:
Add the fractional parts and then the whole numbers.
5 + 3 + 2 = 10
Now add the fractional part,
3/4 + 1/4 = 1
10 + 1 = 11

Question 8.

Answer: 12 \(\frac{1}{2}\)

Explanation:
Add the fractional parts and then the whole numbers.
Add the whole numbers
1 + 1 + 9 = 11
\(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) = 1 \(\frac{1}{2}\)
Combining the whole and fraction parts
11 + 1 \(\frac{1}{2}\) = 12 \(\frac{1}{2}\)

Question 9.

Answer: 9 \(\frac{2}{10}\)

Explanation:
Add the fractional parts and then the whole numbers.
3 + 5 = 8
\(\frac{4}{10}\) + \(\frac{2}{10}\) + \(\frac{6}{10}\) = \(\frac{12}{10}\)
Convert it into the mixed fraction.
\(\frac{12}{10}\) = 1 \(\frac{2}{10}\)
Combining the whole and fraction parts
8 + 1 \(\frac{2}{10}\) = 9 \(\frac{2}{10}\)

Question 10.
Structure
Find 7\(\frac{4}{5}\) + 8\(\frac{2}{5}\) two different ways. Which way do you prefer? Why?

Answer:

Explanation:
Add the fractional parts and then the whole numbers.
7\(\frac{4}{5}\) + 8\(\frac{2}{5}\)
Add the fractional parts and then the whole numbers.
7 + 8 = 15
\(\frac{4}{5}\) + \(\frac{2}{5}\) = \(\frac{6}{5}\)
Convert it into the mixed fraction.
\(\frac{6}{5}\) = 1 \(\frac{1}{5}\)
15 + 1 \(\frac{1}{5}\) = 16 \(\frac{1}{5}\)

Question 11.
Modeling Real Life
A homeowner has two strings of lights. One is 8\(\frac{1}{3}\) yards long. The other is 16\(\frac{2}{3}\) yards long. He connects the strings of lights. How long will the string of lights be in all?

Answer:
Given,
A homeowner has two strings of lights. One is 8 \(\frac{1}{3}\) yards long. The other is 16 \(\frac{2}{3}\) yards long. He connects the strings of lights.
8 \(\frac{1}{3}\) + 16 \(\frac{2}{3}\) = 24 \(\frac{3}{3}\)
\(\frac{3}{3}\) = 1
24 + 1 = 25

Question 12.
DIG DEEPER!
You can play the song “Mary Had a Little Lamb” by striking three glasses filled with water to make the tone. The first glass needs 1\(\frac{3}{4}\) cups, the second glass needs 1\(\frac{1}{2}\) cups, and the third glass needs 1\(\frac{1}{4}\) cups of water. How much water do you need in all?

Answer:
Given that,
You can play the song “Mary Had a Little Lamb” by striking three glasses filled with water to make the tone. The first glass needs 1\(\frac{3}{4}\)cups, the second glass needs 1\(\frac{1}{2}\) cups, and the third glass needs 1\(\frac{1}{4}\) cups of water.
1\(\frac{1}{2}\) + 1\(\frac{1}{4}\) + 1\(\frac{3}{4}\)
1 + 1 + 1 = 3
\(\frac{1}{2}\) + \(\frac{1}{4}\) + \(\frac{3}{4}\) = 1 \(\frac{1}{2}\)
3 + 1 \(\frac{1}{2}\) = 4 \(\frac{1}{2}\)
Therefore you need 4 \(\frac{1}{2}\) cups of water.

Review & Refresh

Write the first six numbers in the pattern. Then describe another feature of the pattern.

Question 13.
Rule: Add 11.
First number: 22

Answer:
The first number is 22 you need to add 11 to it.
22 + 11 = 33
33 + 11 = 44
44 + 11 = 55
55 + 11 = 66
66 + 11 = 77
77 + 11 = 88

Question 14.
Rule: Multiply by 4.
First number: 7

Answer:
The first number is 7. You need to multiply by 4.
7 × 4 = 28
28 × 4 = 112
112 × 4 = 448
448 × 4 = 1792
1792 × 4 = 7168
7168 × 4 = 28672

Lesson 8.8 Subtract Mixed Numbers

Explore and Grow

Use a model to find 2\(\frac{3}{8}\) – 1\(\frac{1}{8}\).

Answer:
2\(\frac{3}{8}\) – 1\(\frac{1}{8}\).
First subtract the whole numbers
2 – 1 = 1
\(\frac{3}{8}\) – \(\frac{1}{8}\) = \(\frac{2}{8}\)
Combine the whole numbers and fractions.
1 \(\frac{2}{8}\) = 1 \(\frac{1}{4}\)

Construct Arguments
How can you use the whole number parts and the fractional parts to subtract mixed numbers with like denominators? Explain why your method makes sense.

Answer:
First, you have to subtract the whole number parts and then subtract the fraction parts with like denominators.
You can subtract the mixed fractions by using the number line or model.

Think and Grow: subtract Mixed Numbers

To subtract mixed numbers, subtract the fractional parts and subtract the whole number parts. Another way to subtract mixed numbers is to rewrite each number as a fraction, then subtract.

Answer:

Example
Find 5\(\frac{3}{6}\) – 4\(\frac{5}{6}\).

Answer:

Show and Grow

Subtract

Question 1.
5\(\frac{4}{5}\) – 1\(\frac{2}{5}\) = ____

Answer:
There are enough fifths.
Subtract the whole numbers
5 – 1 = 4
\(\frac{4}{5}\) – \(\frac{2}{5}\) =\(\frac{2}{5}\)
4 + \(\frac{2}{5}\) = 4 \(\frac{2}{5}\)
Thus, 5\(\frac{4}{5}\) – 1\(\frac{2}{5}\) = 4 \(\frac{2}{5}\)

Question 2.
7\(\frac{1}{3}\) – 2\(\frac{2}{3}\) = _____

Answer:
There are not enough thirds.
7\(\frac{1}{3}\) = 6 \(\frac{3}{3}\) + \(\frac{1}{3}\) = 6\(\frac{4}{3}\)
Subtract the whole numbers
6 – 2 = 4
\(\frac{4}{3}\) – \(\frac{2}{3}\) = \(\frac{2}{3}\)
4 + \(\frac{2}{3}\) = 4 \(\frac{2}{3}\)

Question 3.

Answer:
There are enough twelfths.
Subtract the whole numbers
15 – 4 = 11
\(\frac{10}{12}\) – \(\frac{8}{12}\) = \(\frac{2}{12}\)
11 + \(\frac{2}{12}\) = 11 \(\frac{2}{12}\)

Question 4.

Answer:
There are enough eighths.
\(\frac{6}{8}\) – \(\frac{6}{8}\) = 0
Subtract the whole numbers
6 – 3 = 3
3 + 0 = 3

Question 5.

Answer:
There are not enough tenths.
5 \(\frac{7}{10}\) can be written as 4 \(\frac{17}{10}\)
4 \(\frac{17}{10}\) – 1 \(\frac{9}{10}\)
Subtract the whole numbers
4 – 1 = 3
Subtract the fractional parts
\(\frac{17}{10}\) – \(\frac{9}{10}\) = \(\frac{8}{10}\)
3 + \(\frac{8}{10}\) = 3 \(\frac{8}{10}\)

Question 6.

Answer:
There are not enough hundreds.
11 \(\frac{50}{100}\) can be written as 10 \(\frac{150}{100}\)
Subtract the whole numbers
10 – 7 = 3
Subtract the fractional parts
\(\frac{150}{100}\) – \(\frac{85}{100}\) = \(\frac{65}{100}\)
3 + \(\frac{65}{100}\) = 3 \(\frac{65}{100}\)

Question 7.

Answer:
There are not enough sixths.
8 can be written as 7 \(\frac{6}{6}\)
Subtract the whole numbers
7 – 1 = 6
Subtract the fractional parts
\(\frac{6}{6}\) – \(\frac{3}{6}\) = \(\frac{3}{6}\)
6 + \(\frac{3}{6}\) = 6 \(\frac{3}{6}\)

Question 8.

Answer:
There are not enough fourths.
10 can be written as 9 \(\frac{4}{4}\)
Subtract the whole numbers
9 – 9 = 0
Subtract the fractional parts
\(\frac{4}{4}\) – \(\frac{3}{4}\) = \(\frac{1}{4}\)
0 + \(\frac{1}{4}\)  = \(\frac{1}{4}\)

Question 9.
YOU BE THE TEACHER
Your friend says the difference of 9 and 2\(\frac{3}{5}\) is 7\(\frac{3}{5}\). Is your friend correct? Explain.

Answer:
9 – 2\(\frac{3}{5}\) = 7 \(\frac{3}{5}\)
Thus by this we can say that your friend is correct.

Question 10.
Writing
Explain how adding and subtracting mixed numbers are similar and different.

Answer:
Any mixed number can also be written as an improper fraction, in which the numerator is larger than the denominator.
Subtracting mixed numbers is very similar to adding them.
Write both fractions as equivalent fractions with a denominator. Then subtract the fractions.

Question 11.
DIG DEEPER!
Write two mixed numbers with like denominators that have a sum of 5\(\frac{2}{3}\) and a difference of 1.

Answer:
5\(\frac{2}{3}\) = 3 \(\frac{1}{3}\) + 2\(\frac{1}{3}\)
Now if you subtract the same fraction you need to get the difference as 1.
3 \(\frac{1}{3}\) – 2\(\frac{1}{3}\)
3 – 2 = 1
\(\frac{1}{3}\) – \(\frac{1}{3}\) = 0
So, 3 \(\frac{1}{3}\) – 2\(\frac{1}{3}\) = 1

Think and Grow: Modeling Real Life

Example
A replica of the Eiffel Tower is 6 inches tall. It is 2\(\frac{2}{5}\) inches taller than a replica of the Space Needle. How tall is the replica of the Space Needle?
Find the difference between the height of the Eiffel Tower replica, 6 inches, and 2\(\frac{2}{5}\) inches.

Answer:
Given,
A replica of the Eiffel Tower is 6 inches tall. It is 2\(\frac{2}{5}\) inches taller than a replica of the Space Needle.

Show and Grow

Question 12.
A cook has a 5-pound bag of potatoes. He uses 2\(\frac{1}{3}\) pounds of potatoes to make a casserole. How many pounds of potatoes are left?

Answer:
Given,
A cook has a 5-pound bag of potatoes. He uses 2\(\frac{1}{3}\) pounds of potatoes to make a casserole.
5 – 2\(\frac{1}{3}\)
4 \(\frac{3}{3}\) – 2\(\frac{1}{3}\)
Subtract the whole numbers
4 – 2 = 2
Subtract the fractional parts
\(\frac{3}{3}\) – \(\frac{1}{3}\) = \(\frac{2}{3}\)
2 \(\frac{2}{3}\)
Thus 2 \(\frac{2}{3}\) pounds of potatoes are left.

Question 13.
A half-marathon is 13\(\frac{1}{10}\) miles long. A competitor runs 9\(\frac{6}{10}\) miles. How many miles does the competitor have left to run?

Answer:
Given,
A half-marathon is 13\(\frac{1}{10}\) miles long. A competitor runs 9\(\frac{6}{10}\) miles.
13\(\frac{1}{10}\) – 9\(\frac{6}{10}\)
12 \(\frac{11}{10}\) – 9\(\frac{6}{10}\)
Subtract the whole numbers
12 – 9 = 3
\(\frac{11}{10}\) – \(\frac{6}{10}\) = \(\frac{5}{10}\)
3 + \(\frac{5}{10}\) = 3 \(\frac{1}{2}\)
The competitor has left 3 \(\frac{1}{2}\) miles to run.

Question 14.
DIG DEEPER!
You want to mail a package that weighs 18\(\frac{2}{4}\) ounces. The weight limit is 13 ounces, so you remove 4\(\frac{3}{4}\) ounces of items from the package. Does the lighter package meet the weight requirement? If not, how much more weight do you need to remove?

Answer:
Given that,
You want to mail a package that weighs 18\(\frac{2}{4}\) ounces.
The weight limit is 13 ounces, so you remove 4\(\frac{3}{4}\) ounces of items from the package.
18\(\frac{2}{4}\) – 4\(\frac{3}{4}\) = 13 \(\frac{3}{4}\)
13 \(\frac{3}{4}\) – 13 = \(\frac{3}{4}\)
Thus you need to remove \(\frac{3}{4}\) ounces more.

Subtract Mixed Numbers Homework & Practice 8.8

Subtract

Question 1.

Answer: 5 \(\frac{1}{2}\)

Explanation:
Rewriting our equation with parts separated
=10+3/4−5−1/4
Solving the whole number parts
10−5=5
Solving the fraction parts
3/4−1/4=2/4
Reducing the fraction part, 2/4,
2/4=1/2
Combining the whole and fraction parts
5+1/2=5 1/2

Question 2.

Answer: 6

Explanation:
Rewriting our equation with parts separated
9 + 1/3 – 3 – 1/3
9 – 3 = 6
So, 9 \(\frac{1}{3}\) – 3 \(\frac{1}{3}\) = 6

Question 3.

Answer: 4 \(\frac{2}{3}\)

Explanation:
Rewriting our equation with parts separated
=6+7/12−1−11/12
Solving the whole number parts
6−1=5
Solving the fraction parts
7/12−11/12=−4/12
Reducing the fraction part, 4/12,
−4/12=−1/3
Combining the whole and fraction parts
5−1/3=4 2/3

Question 4.

Answer: 6 \(\frac{43}{50}\)

Explanation:
Rewriting our equation with parts separated
=15+6/100−8−20/100
Solving the whole number parts
15−8=7
Solving the fraction parts
6/100−20/100=−14/100
Reducing the fraction part, 14/100,
−14/100=−7/50
Combining the whole and fraction parts
7−7/50=6 43/50

Question 5.

Answer: 1 \(\frac{2}{3}\)

Explanation:
Rewriting our equation with parts separated
=4+3/6−2−5/6
Solving the whole number parts
4−2=2
Solving the fraction parts
3/6−5/6=−2/6
Reducing the fraction part, 2/6,
−2/6=−1/3
Combining the whole and fraction parts
2−1/3=1 2/3

Question 6.

Answer: 1 \(\frac{3}{5}\)

Explanation:
20 – 19 = 1
\(\frac{4}{5}\) – \(\frac{1}{5}\) = \(\frac{3}{5}\)
1 + \(\frac{3}{5}\) = 1 \(\frac{3}{5}\)

Subtract.

Question 7.

Answer: 2 \(\frac{3}{5}\)

Explanation:
Rewriting our equation with parts separated
=5+6/10−3
Solving the whole number parts
5−3=2
Combining the whole and fraction parts
2+6/10=2 6/10

Question 8.

Answer: 10 \(\frac{1}{2}\)

Explanation:
Rewriting our equation with parts separated
=13−2−1/2
Solving the whole number parts
13−2=11
Combining the whole and fraction parts
11−1/2=10 1/2

Question 9.

Answer: 3 \(\frac{1}{4}\)

Explanation:
Rewriting our equation with parts separated
=18−14−6/8
Solving the whole number parts
18−14=4
Combining the whole and fraction parts
4−6/8=3 2/8

Question 10.
Reasoning
Explain why you rename 4\(\frac{1}{3}\) when finding 4\(\frac{1}{3}\) – \(\frac{2}{3}\) .

Answer:
4\(\frac{1}{3}\) – \(\frac{2}{3}\)
4 can be written as 3 \(\frac{3}{3}\)
3 \(\frac{3}{3}\) – \(\frac{2}{3}\)
3 + \(\frac{3}{3}\) – \(\frac{2}{3}\)
3 + \(\frac{1}{3}\) = 3 \(\frac{1}{3}\)
So, 4\(\frac{1}{3}\) – \(\frac{2}{3}\) = 3 \(\frac{1}{3}\)

Question 11.
DIG DEEPER!
Find the unknown number.

Answer:
Let the unknown number be x.
10 \(\frac{3}{12}\) – x = \(\frac{4}{12}\)
10 \(\frac{3}{12}\) –  \(\frac{4}{12}\) = x
9 \(\frac{15}{12}\) –  \(\frac{4}{12}\) = x
x = 9 \(\frac{11}{12}\)
Thus the unknown number is 9 \(\frac{11}{12}\).

Question 12.
Modeling Real Life
A rare flower found in Indonesian rain forests can grow wider than a car tire. How much wider is the flower than a car tire that is 1\(\frac{11}{12}\) feet wide?

Answer:
Given,
A rare flower found in Indonesian rain forests can grow wider than a car tire.
3 – 1\(\frac{11}{12}\)
2 \(\frac{12}{12}\) – 1\(\frac{11}{12}\)
= 1 \(\frac{1}{12}\)

Question 13.
Modeling Real Life
Your tablet battery is fully charged. You use \(\frac{32}{100}\) of the charge listening to music, and \(\frac{13}{100}\) of the charge playing games. What fraction of the charge remains on your tablet battery?

Answer:
Given,
Your tablet battery is fully charged. You use \(\frac{32}{100}\) of the charge listening to music, and \(\frac{13}{100}\) of the charge playing games.
\(\frac{32}{100}\) – \(\frac{13}{100}\) = \(\frac{19}{100}\)
Thus \(\frac{19}{100}\) fraction of the charge remains on your tablet battery.

Review & Refresh

Divide. Then check your answer.

Question 14.

Answer:
Divide 84 by 5
84/5 = 16.8

Question 15.

Answer:
Divide 51 by 4.
51/4 = 12.75

Question 16.

Answer:
Divide 89 by 8.
89/8 = 11.125

Lesson 8.9 Problem Solving: Fractions

Explore and Grow

Make a plan to solve the problem.

The table shows the tusk lengths of two elephants. Which elephant’s tusks have a greater total length? How much greater?

Answer:
Male Elephant = 4 1/12 + 4 3/12 = 8 4/12
Female Elephant = 4 + 3 7/12 = 7 7/12
The Right Tusk of a Male Elephant is greater than Female Elephant.
The left tusk of a Male Elephant is greater than Female Elephant.
Thus the total length of the Male Elephant is greater than Female Elephant.

Make Sense of Problems
A \(\frac{7}{12}\)-foot long piece of one of the male elephant’s tusks breaks off. Does this change your plan to solve the problem? Will this change the answer? Explain.

Answer:
A \(\frac{7}{12}\)-foot long piece of one of the male elephant’s tusks breaks off.
8 4/12 – 7 7/12 = 3/4
No, if \(\frac{7}{12}\)-foot long piece of one of the male elephant’s tusks breaks off it will not change the answer. Still, the Male Elephant is greater than Female Elephant.

Think and Grow: Problem Solving: Fractions

Example
A family spends 2\(\frac{2}{4}\) hours traveling to a theme park, 7\(\frac{1}{4}\) hours at the theme park, and 2\(\frac{3}{4}\) hours traveling home. How much more time does the family spend at the theme park than traveling?

Understand the Problem

What do you know?

• The family spends 2\(\frac{2}{4}\) hours traveling to the theme park, 7\(\frac{1}{4}\) hours at the theme park, 2\(\frac{3}{4}\) hours traveling home.
  What do you need to find?
• You need to find how much more time the family spends at the theme park than the traveling.

Make a plan

How will you solve it?

• Add 2\(\frac{2}{4}\) and 2\(\frac{3}{4}\) to find how much time the family spends traveling.
• Then subtract the sum from 7\(\frac{1}{4}\) to find how much more time they spend at the theme park.

Solve
So, the family spends ___ more hours at the theme park than traveling.

Show and Grow

Question 1.
Explain how you can check your answer in each step of the example above.

Answer:

So, the family spends 2 more hours at the theme park than traveling.

Apply any and Grow: Practice

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

Answer:

• The family spends 2\(\frac{2}{4}\) hours traveling to the theme park, 7\(\frac{1}{4}\) hours at the theme park, 2\(\frac{3}{4}\) hours traveling home.
  What do you need to find?
• You need to find how much more time the family spends at the theme park than the traveling.

Question 2.
You are making a sand art bottle. You fill \(\frac{1}{6}\) of the bottle with pink sand, \(\frac{3}{6}\) with red sand, and \(\frac{2}{6}\) with white sand. How much of the bottle is filled?

Answer:
Given that,
You are making a sand art bottle. You fill \(\frac{1}{6}\) of the bottle with pink sand, \(\frac{3}{6}\) with red sand, and \(\frac{2}{6}\) with white sand.
\(\frac{1}{6}\) + \(\frac{3}{6}\) + \(\frac{2}{6}\) = \(\frac{1}{6}\)
Thus \(\frac{1}{6}\) of the bottle is filled.

Question 3.
Your friend has \(\frac{1}{8}\) of a photo album filled with beach photographs and \(\frac{4}{8}\) of the album filled with photos of friends. What fraction of the photo album is left?

Answer:
Given that,
Your friend has \(\frac{1}{8}\) of a photo album filled with beach photographs and \(\frac{4}{8}\) of the album filled with photos of friends.
\(\frac{1}{8}\) + \(\frac{4}{8}\) = \(\frac{5}{8}\)
\(\frac{8}{8}\) – \(\frac{5}{8}\) = \(\frac{3}{8}\)
Thus \(\frac{3}{8}\) fraction of the photo album is left.

Understand the problem. Then make a plan. How will you solve? Explain.

Question 4.
In Race A, an Olympic swimmer swims 100 meters in 62\(\frac{25}{100}\) seconds. In Race B, she cuts 2\(\frac{38}{100}\) seconds off her Race A time. How many seconds does she need to cut off her Race B time to swim 100 meters in 58\(\frac{45}{100}\) seconds?

Answer:
Given,
In Race A, an Olympic swimmer swims 100 meters in 62\(\frac{25}{100}\) seconds. In Race B, she cuts 2\(\frac{38}{100}\) seconds off her Race A time.
62\(\frac{25}{100}\) – 2\(\frac{38}{100}\) = 59 \(\frac{87}{100}\)
59 \(\frac{87}{100}\) – 58\(\frac{45}{100}\) = 1 \(\frac{42}{100}\)
She need 1 \(\frac{42}{100}\) to cut off her Race B time to swim 100 meters in 58\(\frac{45}{100}\) seconds.

Question 5.
A semi-truck has 2 fuel tanks that each hold the same amount of fuel. A truck driver fills up both tanks and uses \(\frac{3}{4}\) tank of gasoline driving to his first stop. He uses \(\frac{2}{4}\) tank of gasoline driving to his second stop. How much gasoline does he have left?

Answer:
Given that,
A semi-truck has 2 fuel tanks that each hold the same amount of fuel. A truck driver fills up both tanks and uses \(\frac{3}{4}\) tank of gasoline driving to his first stop. He uses \(\frac{2}{4}\) tank of gasoline driving to his second stop.
\(\frac{3}{4}\) + \(\frac{2}{4}\) = \(\frac{5}{4}\)
2 – \(\frac{5}{4}\) = \(\frac{3}{4}\)
Thus \(\frac{3}{4}\) gasoline has left.

Question 6.
A bootlace worm holds the record as the longest animal at 180 feet long. How much longer is it than 2 blue whales combined?

Answer:
Given,
A bootlace worm holds the record as the longest animal at 180 feet long.
1 blue whale = 85 \(\frac{8}{12}\)
2 blue whales = 85 \(\frac{8}{12}\) + 85 \(\frac{8}{12}\) = 171 \(\frac{1}{3}\)
180 – 171 \(\frac{1}{3}\)
179 \(\frac{3}{3}\) – 171 \(\frac{1}{3}\) = 8 \(\frac{2}{3}\)

Think and Grow: Modeling Real Life

Example
You walk \(\frac{1}{10}\) kilometer on Monday, \(\frac{3}{10}\) kilometer on Tuesday, and \(\frac{5}{10}\) kilometer on Wednesday. You continue the pattern on Thursday and Friday. How many kilometers do you walk in all?
Think: What do you know? What do you need to find? How will you solve?

Step 1: Identify the pattern.

Step 2: Use the pattern to find the distances you walk on Thursday and Friday.

Step 3: Add all of the distances.

.

Answer:
Step 1: Identify the pattern.

Step 2: Use the pattern to find the distances you walk on Thursday and Friday.

Step 3: Add all of the distances.

So, you walk 2 \(\frac{5}{10}\) kilometers in all.

Show and Grow

Question 7.
You save \(\frac{1}{4}\) dollar the first week, \(\frac{2}{4}\) dollar the next week, and dollar \(\frac{3}{4}\) dollar the following week. You continue the pattern for 3 more weeks. How much money do you save after 6 weeks?

Answer:
You save \(\frac{1}{4}\) dollar the first week, \(\frac{2}{4}\) dollar the next week, and dollar \(\frac{3}{4}\) dollar the following week. You continue the pattern for 3 more weeks.
\(\frac{1}{4}\), \(\frac{2}{4}\), \(\frac{3}{4}\), \(\frac{4}{4}\), \(\frac{5}{4}\), \(\frac{6}{4}\)
You save \(\frac{6}{4}\) dollar after 6 weeks.

Problem Solving: Fractions Homework & Practice 8.9

Question 1.
An older washing machine uses 170\(\frac{3}{10}\) liters of water per load. A new, high-efficiency, washing machine uses 75\(\frac{7}{10}\) fewer liters than the older washing machine. How many liters of water will the high-efficiency washing machine use for 2 loads of laundry?

Answer:
Given,
An older washing machine uses 170\(\frac{3}{10}\) liters of water per load. A new, high-efficiency, washing machine uses 75\(\frac{7}{10}\) fewer liters than the older washing machine.
75\(\frac{7}{10}\) + 75\(\frac{7}{10}\) = 151\(\frac{2}{5}\)
170\(\frac{3}{10}\) – 151\(\frac{2}{5}\) = 18 \(\frac{9}{10}\)

Question 2.
A student jumps 40 \(\frac{5}{12}\) inches for the high jump. On his second try, he jumps 1\(\frac{8}{12}\) inches higher. He can tie the school record if he raises the bar another 3\(\frac{10}{12}\) inches and successfully jumps over it. What is the school record for the high jump?

Answer:
Given,
A student jumps 40 \(\frac{5}{12}\) inches for the high jump.
On his second try, he jumps 1\(\frac{8}{12}\) inches higher.
He can tie the school record if he raises the bar another 3\(\frac{10}{12}\) inches and successfully jumps over it.
40 \(\frac{5}{12}\) + 1 \(\frac{8}{12}\) = 42 \(\frac{1}{12}\)
40 \(\frac{5}{12}\) + 3\(\frac{10}{12}\) = 44 \(\frac{3}{12}\)
44 \(\frac{3}{12}\) is the school record for the high jump.

Question 3.
You are shipping three care packages. The first package weighs 10\(\frac{1}{10}\) pounds. The second weighs 5\(\frac{7}{10}\) pounds, and the third weighs 25\(\frac{8}{10}\) pounds. What is the total weight of the packages?

Answer:
Given,
You are shipping three care packages. The first package weighs 10\(\frac{1}{10}\) pounds.
The second weighs 5\(\frac{7}{10}\) pounds, and the third weighs 25\(\frac{8}{10}\) pounds.
10\(\frac{1}{10}\) + 5\(\frac{7}{10}\) + 25\(\frac{8}{10}\) = 41 \(\frac{6}{10}\)
The total weight of the packages is 41 \(\frac{6}{10}\) pounds.

Question 4.
A person’s arm span is approximately equal to the person’s height. How tall is this fourth grader according to his arm span?

Answer:
Given,
A person’s arm span is approximately equal to the person’s height.
By using the pattern we can find the arm span of the fourth-grader i.e., 1 \(\frac{7}{12}\)

Question 5.
Writing
Write and solve a two-step word problem with mixed numbers that can be solved using addition or subtraction.

Answer:
I have 5 \(\frac{8}{12}\) episodes of my favorite series download onto my computer. I Downloaded some yesterday and \(\frac{7}{12}\) of the episodes this morning. The download speed was really slow. What fraction of the episodes did I download yesterday?
5 \(\frac{8}{12}\) – \(\frac{7}{12}\) = 5 \(\frac{1}{12}\) = \(\frac{61}{12}\)

Question 6.
Modeling Real Life
Your friend walks \(\frac{2}{10}\) mile to school each day. She walks the same distance home. How many miles does she walk to and from school in one 5-day school week?

Answer:
Given,
Your friend walks \(\frac{2}{10}\) mile to school each day. She walks the same distance home.
\(\frac{2}{10}\) + \(\frac{2}{10}\) = \(\frac{4}{10}\)
5 × \(\frac{4}{10}\) = \(\frac{20}{10}\) = 2
Thus she walk to and from school in one 5-day school week is 2 miles.

Question 7.
DIG DEEPER!
A store sells cashews in \(\frac{2}{3}\)-pound bags. You buy some bags and repackage the cashews into 1-pound bags. What is the least number of bags you should buy so that you do not have any cashews left over?

Answer:
Given,
A store sells cashews in \(\frac{2}{3}\)-pound bags. You buy some bags and repackage the cashews into 1-pound bags.
1 – \(\frac{2}{3}\) = \(\frac{1}{3}\)
Thus \(\frac{1}{3}\) pound of cashews left over.

Review & Refresh

Compare.

Question 8.

Answer: >

Explanation:
\(\frac{8}{12}\) = \(\frac{4}{6}\)
\(\frac{4}{6}\) > \(\frac{1}{6}\)

Question 9.

Answer: <

Explanation:
First, make the denominators common.
\(\frac{9}{10}\) = \(\frac{18}{20}\)
\(\frac{14}{8}\) = \(\frac{35}{20}\)
\(\frac{18}{20}\) < \(\frac{35}{20}\)

Question 10.

Answer: >

Explanation:
First, make the denominators common.
\(\frac{3}{4}\)
\(\frac{1}{2}\) × 2/2 = \(\frac{2}{4}\)
\(\frac{3}{4}\) > \(\frac{2}{4}\)

Add and Subtract Fractions Performance Task 8

The notes on sheet music tell you what note to play and how long to hold each note. The table shows how long you hold some notes compared to the length of one whole note.

1. a. Complete the table by writing equivalent fractions.

Answer:

A whole note is nothing but 1 so the fraction is 8/8.
1/2 note is nothing but 4/8.
1/4 note is nothing but 2/8.

b. Each group of notes represents one measure. What is the sum of the values of the notes in each measure?

Answer:

c. Draw the missing note to complete each measure.

Answer:

d. Draw one measure of notes where the sum of the values is 1. Show your work.
___________

Answer:

e. Write the fraction represented by the sum of the notes. Then write the fraction as a sum of fractions in two different ways.

Answer:
= \(\frac{1}{8}\) + \(\frac{4}{8}\) + \(\frac{2}{8}\) = \(\frac{7}{8}\)

Add and Subtract Fractions Activity

Three In a Row: Fraction Add or Subtract

Directions:

1. Players take turns.
2. On your turn, spin both spinners. Choose whether to add or subtract.
3. Add or subtract the mixed number and fraction. Cover the sum or difference.
4. If the sum or difference is already covered, you lose your turn.
5. The first player to get three in a row wins!

Answer:
1 \(\frac{1}{8}\) + \(\frac{3}{8}\) = 1 + \(\frac{1}{8}\) + \(\frac{3}{8}\) = 1 \(\frac{4}{8}\)
3 \(\frac{7}{8}\) + \(\frac{8}{8}\) = 3 + \(\frac{7}{8}\) + 1 = 4 \(\frac{7}{8}\)
2 \(\frac{5}{8}\) + \(\frac{4}{8}\) = 2 + \(\frac{5}{8}\) + \(\frac{4}{8}\) = 3 \(\frac{1}{8}\)

Add and Subtract Fractions Chapter Practice 8

8.1 Use Models to Add Fractions

Find the sum. Explain how you used the model to add.

Question 1.

Answer: 5/6

Question 2.

Answer:

Find the sum. Use a model or a number line to help.

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:
Denominators are the same so add the numerators.
\(\frac{45}{100}\) + \(\frac{10}{100}\) + \(\frac{9}{100}\) = \(\frac{64}{100}\)

8.2 Decompose Fractions

Write the fraction as a sum of unit fractions.

Question 6.
\(\frac{2}{12}\)

Answer:
The unit fraction for \(\frac{2}{12}\) is \(\frac{1}{12}\) + \(\frac{1}{12}\)

Question 7.
\(\frac{3}{3}\)

Answer: The unit fraction for \(\frac{3}{3}\) is \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\)

Write the fraction as a sum of fractions in two different ways.

Question 8.
\(\frac{5}{8}\)

Answer:
The unit fraction for \(\frac{5}{8}\) is \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\)

Question 9.
\(\frac{6}{100}\)

Answer:
The unit fraction for \(\frac{6}{100}\) is \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\)

Question 10.
\(\frac{90}{100}\)

Answer:
\(\frac{90}{100}\) = 9/10
The unit fraction for \(\frac{9}{10}\) is \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\)

Question 11.
\(\frac{4}{5}\)

Answer:
The unit fraction for \(\frac{4}{5}\) is \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\)

8.3 Add Fractions with Like Denominators

Add

Question 12.

Answer:
Denominators are the same so add the numerators.
\(\frac{5}{10}\) + \(\frac{10}{10}\) = \(\frac{15}{10}\)

Question 13.

Answer:

Denominators are the same so add the numerators.
\(\frac{1}{3}\) + \(\frac{1}{3}\) = \(\frac{2}{3}\)

Question 14.

Answer:
Denominators are the same so add the numerators.
\(\frac{1}{8}\) + \(\frac{6}{8}\) = \(\frac{7}{8}\)

Question 15.

Answer:
Denominators are the same so add the numerators.
\(\frac{7}{4}\) + \(\frac{3}{4}\) = \(\frac{11}{4}\)

Question 16.

Answer:
Denominators are the same so add the numerators.
\(\frac{2}{6}\) + \(\frac{2}{6}\) = \(\frac{4}{6}\)

Question 17.

Answer:
Denominators are the same so add the numerators.
\(\frac{8}{12}\) + \(\frac{4}{12}\) = \(\frac{12}{12}\) = 1

Question 18.
Logic
When you add two of me you get \(\frac{100}{100}\). What fraction am I?

Answer: \(\frac{50}{100}\)
If you add \(\frac{50}{100}\) two times you get \(\frac{100}{100}\)
\(\frac{50}{100}\) + \(\frac{50}{100}\) = \(\frac{100}{100}\)

8.4 Use Models to Subtract Fractions

Find the difference. Explain how you used the model to subtract.

Question 19.

Answer:

Question 20.

Answer:

Find the difference. Use a model or a number line to help.

Question 21.

Answer: 3/2

Question 22.

Answer:

Question 23.

Answer:
Denominators are the same so subtract the numerators.
\(\frac{30}{100}\) – \(\frac{21}{100}\) = (30 – 21)/100 = \(\frac{9}{100}\)

Question 24.
Modeling Real Life
A football team wins \(\frac{7}{10}\) of their games this season. They lose \(\frac{3}{10}\) of their games. How many more games does the team win than lose?

Answer:
Given that,
A football team wins \(\frac{7}{10}\) of their games this season. They lose \(\frac{3}{10}\) of their games.
\(\frac{7}{10}\) – \(\frac{3}{10}\) = \(\frac{4}{10}\)
Thus \(\frac{4}{10}\) more games the team win than lose.

8.5 Subtract Fractions with Like Denominators

Subtract.

Question 25.

Answer: \(\frac{5}{10}\)

Explanation:
Denominators are the same so subtract the numerators.
\(\frac{9}{10}\) – \(\frac{4}{10}\) = \(\frac{5}{10}\)

Question 26.

Answer: \(\frac{7}{12}\)

Explanation:
Denominators are the same so subtract the numerators.
\(\frac{14}{12}\) – \(\frac{7}{12}\) = \(\frac{7}{12}\)

Question 27.

Answer: \(\frac{24}{100}\)

Explanation:
Denominators are the same so subtract the numerators.
\(\frac{80}{100}\) – \(\frac{56}{100}\) = \(\frac{24}{100}\)

Question 28.

Answer: 3/8\(\frac{3}{8}\)

Explanation:
Denominators are the same so subtract the numerators.
1 can be written as \(\frac{8}{8}\)
\(\frac{8}{8}\) – \(\frac{5}{8}\) = \(\frac{3}{8}\)

Question 29

Answer: \(\frac{2}{3}\)

Explanation:
Denominators are the same so subtract the numerators.
1 can be written as \(\frac{3}{3}\)
\(\frac{3}{3}\) – \(\frac{1}{3}\) = \(\frac{2}{3}\)

Question 30.

Answer: \(\frac{2}{6}\)

Explanation:
Denominators are the same so subtract the numerators.
2 can be written as \(\frac{12}{6}\)
\(\frac{12}{6}\) – \(\frac{10}{6}\) = \(\frac{2}{6}\)

8.6 Model Fractions and Mixed Numbers

Write the mixed number as a fraction.

Question 31.
1 \(\frac{6}{8}\)

Answer: \(\frac{7}{4}\)

Explanation:
Step 1
Multiply the denominator by the whole number
8 × 1 = 8
Step 2
Add the answer from Step 1 to the numerator
8 + 6 = 14
Step 3
Write an answer from Step 2 over the denominator
14/8 = \(\frac{7}{4}\)

Question 32.
4 \(\frac{1}{2}\)

Answer: \(\frac{9}{2}\)

Explanation:
Step 1
Multiply the denominator by the whole number
2 × 4 = 8
Step 2
Add the answer from Step 1 to the numerator
8 + 1 = 9
Step 3
Write an answer from Step 2 over the denominator
\(\frac{9}{2}\)

Question 33.
5 \(\frac{10}{12}\)

Answer: \(\frac{35}{6}\)

Explanation:
Step 1
Multiply the denominator by the whole number
12 × 5 = 60
Step 2
Add the answer from Step 1 to the numerator
60 + 10 = 70
Step 3
Write an answer from Step 2 over the denominator
70/12 = \(\frac{35}{6}\)

Write the fraction as a mixed number or a whole number.

Question 34.
\(\frac{17}{4}\)

Answer: 4 \(\frac{1}{4}\)

Explanation:
Converting from improper fraction to the mixed fraction.
\(\frac{17}{4}\) = 4 \(\frac{1}{4}\)

Question 35.
\(\frac{30}{6}\)

Answer: 5

Explanation:
Converting from improper fraction to the mixed fraction.
6 divides 30 five times.
So, \(\frac{30}{6}\) = 5

Question 36.
\(\frac{63}{10}\)

Answer: 6 \(\frac{3}{10}\)

Explanation:
Converting from improper fraction to the mixed fraction.
\(\frac{63}{10}\) = 63 ÷ 10
= 6 \(\frac{3}{10}\)

Compare.

Question 37.

Answer: <

Explanation:
2 4/100
Step 1
Multiply the denominator by the whole number
100 × 2 = 200
Step 2
Add the answer from Step 1 to the numerator
200 + 4 = 204
Step 3
Write an answer from Step 2 over the denominator
204/100
240/100
Step 1
Multiply the denominator by the whole number
100 × 2 = 200
Step 2
Add the answer from Step 1 to the numerator
200 + 40 = 240
Step 3
Write an answer from Step 2 over the denominator
240/100
204/100 < 240/100

Question 38.

Answer: >

Explanation:
Step 1
Multiply the denominator by the whole number
3 × 8 = 24
Step 2
Add the answer from Step 1 to the numerator
24 + 2 = 26
Step 3
Write an answer from Step 2 over the denominator
26/3
26/3 > 25/3

Question 39.

Answer: =

Explanation:
25/5 = 5
5 = 5

Question 40.
Which One Doesn’t Belong? Which expression does not belong with the other three?

Answer: 20/8 does not belong with the other three.

8.7 Add Mixed Numbers

Add.

Question 41.

Answer: 9

Explanation:
Rewriting our equation with parts separated
=5+1/2+3+1/2
Solving the whole number parts
5+3=8
Solving the fraction parts
1/2+1/2=2/2
Reducing the fraction part, 2/2,
2/2=1/1
Simplifying the fraction part, 1/1,
1/1=1
Combining the whole and fraction parts
8+1=9

Question 42.

Answer: 4 1/3

Explanation:
Rewriting our equation with parts separated
=2+5/6+1+3/6
Solving the whole number parts
2+1=3
Solving the fraction parts
5/6+3/6 = 8/6
8/6 = 4/3
4/3 = 4 1/3

Question 43.

Answer: 5 5/6

Explanation:
Rewriting our equation with parts separated
=4+1+10/12
Solving the whole number parts
4+1=5
Combining the whole and fraction parts
5+10/12= 5 10/12 = 5 5/6

Question 44.

Answer: 19

Explanation:
Rewriting our equation with parts separated
=8+3/5+10+2/5
Solving the whole number parts
8+10=18
Solving the fraction parts
3/5+2/5=5/5
Simplifying the fraction part, 1/1,
1/1 = 1
Combining the whole and fraction parts
18+1=19

Question 45.

Answer: 14 1/4

Explanation:
Rewriting our equation with parts separated
=7+2/4+1+2/4
Solving the whole number parts
7+1=8
Solving the fraction parts
2/4+2/4=4/4
Reducing the fraction part, 4/4,
4/4=1/1
Simplifying the fraction part, 1/1,
1/1=1
Combining the whole and fraction parts
8+1=9
9 + 5 1/4
Rewriting our equation with parts separated
=9+5+1/4
Solving the whole number parts
9+5=14
Combining the whole and fraction parts
14+1/4=14 1/4

Question 46.

Answer: 19 5/100

Explanation:
Rewriting our equation with parts separated
=4+25/100+11+75/100
Solving the whole number parts
4+11=15
Solving the fraction parts
25/100+75/100=100/100
Reducing the fraction part, 100/100,
100/100=11
Simplifying the fraction part, 1/1,
1/1=1
Combining the whole and fraction parts
15+1=16
Rewriting our equation with parts separated
=16+3+5/100
Solving the whole number parts
16+3=19
Combining the whole and fraction parts
19+5/100=19 5/100

8.8 Subtract Mixed Numbers

Subtract

Question 47.

Answer: 3

Explanation:
Rewriting our equation with parts separated
=9+2/3-6-2/3
Solving the whole number parts
9−6=3
Solving the fraction parts
2/3−2/3=0/3
Simplifying the fraction part, 0/3,
0/3=0
Combining the whole and fraction parts
3+0=3

Question 48.

Answer: 5 2/5

Explanation:
Rewriting our equation with parts separated
=13+9/10−8−5/10
Solving the whole number parts
13−8=5
Solving the fraction parts
9/10−5/10=4/10
Reducing the fraction part, 4/10,
4/10=2/5
Combining the whole and fraction parts
5+2/5=5 2/5

Question 49.

Answer: 1/2

Explanation:
Rewriting our equation with parts separated
=3+2/8−2−6/8
Solving the whole number parts
3−2=1
Solving the fraction parts
2/8−6/8=−4/8
Reducing the fraction part, 4/8,
−4/8=−1/2
Combining the whole and fraction parts
1−1/2=1/2

Question 50.

Answer: 5 1/2

Explanation:
6 + 1/2 – 1 = 5 1/2

Question 51.

Answer: 2 3/4

Explanation:
Rewriting our equation with parts separated
=7−4−1/4
Solving the whole number parts
7−4=3
Combining the whole and fraction parts
3−1/4=2 3/4

Question 52.

Answer: 1/6

Explanation:
Rewriting our equation with parts separated
=20−19−5/6
Solving the whole number parts
20−19=1
Combining the whole and fraction parts
1−5/6=1/6

8.9 Problem Solving: Fractions

Question 53.
You give \(\frac{3}{12}\) of your bag of grapes to one friend and \(\frac{5}{12}\) of your bag to another friend. What fraction of the bag of grapes do you have left?

Answer:
Given that,
You give \(\frac{3}{12}\) of your bag of grapes to one friend and \(\frac{5}{12}\) of your bag to another friend
\(\frac{3}{12}\) + \(\frac{5}{12}\) = \(\frac{8}{12}\)
\(\frac{12}{12}\) – \(\frac{8}{12}\) = \(\frac{4}{12}\)
Thus \(\frac{4}{12}\) fraction of the bag of grapes are left.

Final Words:

Hope you are all satisfied with the solutions provided in the BIM Grade 4 Chapter 8 Add and Subtract Fractions pdf. If you have any doubts regarding the problems you can ask your doubts in the below comment box. We are ready to clarify your doubts at any time. Stay with us to get the solutions of all 4th-grade chapters.

Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure is given here in a comprehensive manner to help the students for better understanding. Must solve every problem given on the Big Ideas Math Answers Chapter 11 Convert and Display Units of Measure Grade 5. You will become perfect as you practice as many questions as you practice. Practice the problems and cross-check the answer to know your preparation level. If you feel any topic difficult, then concentrate more on those topics. Every topic is important to get a good score in the exam. Download Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure PDF without any cost.

Big Ideas Math Book 5th Grade Chapter 11 Convert and Display Units of Measure Answer Key

The list of concepts covered mainly in Convert and Display Measure are Mass and Capacity in Metric Units, Length in Metric Units, Weight in Customary Units, Length in Customary Units, Capacity in Customary Units, etc. Don’t skip any of the topics from the given chapter. Completely get free access to Big Ideas Math Book 5th Grade Answer Key Chapter 11 Convert and Display Units of Measure PDF. Below attached links help you to find every individual topic.

Lesson: 1 Length in Metric Units

• Lesson 11.1 Length in Metric Units
• Length in Metric Units Homework & Practice 11.1

Lesson: 2 Mass and Capacity in Metric Units

• Lesson 11.2 Mass and Capacity in Metric Units
• Mass and Capacity in Metric Units Homework & Practice 11.2

Lesson: 3 Length in Customary Units

• Lesson 11.3 Length in Customary Units
• Length in Customary Units Homework & Practice 11.3

Lesson: 4 Weight in Customary Units

• Lesson 11.4 Weight in Customary Units
• Weight in Customary Units Homework & Practice 11.4

Lesson: 5 Capacity in Customary Units

• Lesson 11.5 Capacity in Customary Units
• Capacity in Customary Units Homework & Practice 11.5

Lesson: 6 Make and Interpret Line Plots

• Lesson 11.6 Make and Interpret Line Plots
• Make and Interpret Line Plots Homework & Practice 11.6

Lesson: 7 Problem Solving: Measurement

• Lesson 11.7 Problem Solving: Measurement
• Problem Solving: Measurement Homework & Practice 11.7

Chapter – 11: Convert and Display Units of Measure

• Convert and Display Units of Measure Performance Task 11
• Convert and Display Units of Measure Activity
• Convert and Display Units of Measure Chapter Practice
• Convert and Display Units of Measure Practice 1-11
• Convert and Display Units of Measure STEAM Performance Task

Lesson 11.1 Length in Metric Units

Explore and Grow

Work with a partner. Find 3 objects in your classroom and use a meter stick to measure them. Record your measurements in the table.

Answer:
1 centimeter is 0.1 times as long as 1 millimeter.
1 meter is 0.01 times as long as 1 centimeter.
1 meter is 0.001 times as long as 1 millimeter.

Structure
How can you convert a metric length from a larger unit to a smaller unit? How can you convert a metric length from a smaller unit to a larger unit?
Answer:
We can convert a metric length from a larger unit to a smaller unit by Multiplying.
Example: There are 1000 meters in one kilometer. Then the answer is  5km = 5000 meters. (5 × 1000)
We can convert a metric length from a smaller unit to a larger unit by Dividing.
Example: one meter is equal to 0.001 km.  1 meter = 0.001 km ( 1m/1000=0.001km)

Think and Grow: Convert Metric Lengths

You can use powers of 10 to find equivalent measures in the metric system.

Key Idea
When finding equivalent metric lengths, multiply to convert from a larger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit.

Example
Convert 6 centimeters to millimeters.
Answer:
There are 10 millimeters in 1 centimeter.

Explanation:
Because you are converting from a larger unit to a smaller unit, multiply.
6 × 10 = 60
So, 6 centimeters is 60 millimeters.

Example
Convert 14,000 meters to kilometers.
Answer: There are 1,000 meters in 1 kilometer.

Explanation:
Because you are converting from a smaller unit to a larger unit, divide.
14,000 ÷ 1000 = 14.
So, 14,000 meters is 14 kilometers.

Show and Grow

Convert the length.

Question 1.
8.5 km = 8500 m.

Answer:
8.5 × 1000 = 8500.

Explanation:
Convert from kilometers to meters.
We know that,
1 km= 1000m
8.5 km = 8.5 × 1000 = 8500 m

Question 2.
180 cm = 1.8 m
Answer: 180/100 = 1.8 m

Explanation:
Convert from centimeters to meters.
1 m = 100 cm
1 cm = 1/100 m
180 cm = 180/100 = 1.8 m

Apply and Grow: Practice

Convert the length.

Question 3.
150 m = 0.15 km
Answer:
150 m = 0.15 km

Explanation:
Convert from meters to kilometers.
(Divide the meter value by 1000)
150m/1000 = 0.15 km

Question 4.
90 cm = 900 mm
Answer: 90 cm = 900 mm

Explanation:
Convert from centimeters to millimeters.
multiply the length value (i.e., cm value) by 10
90cm × 10 = 900 mm

Question 5.
0.03 m = 3 cm.
Answer: 0.03 m = 3 cm

Explanation:
Convert from meter to centimeter
Multiply the length value by (i.e., m value ) by 100
0.03 m × 100 = 3cm

Question 6.
0.6 km = 60,000 cm
Answer: 0.6 km = 60,000 cm

Explanation:
Convert from kilometers to centimeters
multiply the length value (i.e., km value by 100000)
0.6km × 100000 = 60,000 cm

Question 7.
800 mm = 0.8 m
Answer: 800 mm = 0.8 m

Explanation:
Convert from millimeters to meters
Divide the length value(i.e., mm value by 1000)
800/1000 = 0.8 m

Question 8.
700 cm = 0.007 km
Answer: 700 cm = 0.007 km

Explanation:
Convert from centimeters to meters
Divide the length value (i.e., cm value by 100000)
700/100000 = 0.007 km

Compare.

Question 9.

Answer:
0.02 m = 20 mm
multiply the length value (i.e., m value by 1000)
0.02 × 1000 = 20mm
3mm = 0.003 m
divide the length value(i.e., mm value by 1000)
3/1000 = 0.003 m
0.02 m < 3 mm
Question 10.

Answer:
0.025 km = 25000 mm
multiply the km value by 1e+6
3,500 mm = 0.0035 km
divide the length mm value by 1e+6

Question 12.

The giant anteater has the longest tongue in relation to its body size of any mammal. Its tongue is about 0.6 meter long. How many centimeters long is its tongue?

Answer:
The giant anteater has the longest tongue in relation to its body size of any mammal. Its tongue is about 0.6 meter long. Its tongue is about 60 centimeters long.

Explanation:
(0.6 meter = 60 centimeters) multiply the length value with 100.  i.e., (0.6 × 100 = 60)

Question 13.
Number Sense
The length of an object can be written as b millimeters or c kilometers. Compare the values of b and c. Explain your reasoning.
Answer:
The length of an object can be written as b millimeters or c kilometers
Let us assume that b = 2mm,  c = 2km
By comparing the b and c values
c value is greater than b
kilometers is greater than millimeters  ( 1km = 1000000 mm , 1mm = 1 × 10 ^ -6 km).

Question 14.
Writing
Why does the decimal point move to the left when converting from a smaller measure to a larger measure?

Answer:
As we move from a smaller unit to a larger unit, the number of larger units required will be less. Therefore the decimal point will always move to the left when you want to make a number smaller. Therefore the decimal point will always move to the right when you want to make the number Bigger.

Think and Grow: Modeling Real Life

Example
The base of Mauna Kea extends about 5.76 kilometers below sea level. What is the total height of the volcano in meters?

Convert the distance below sea level to meters.
Answer: There are 1000 meters in 1 kilometer.

Explanation:
Given,
The base of Mauna Kea extends about 5.76 kilometers below sea level.
5.76 × 1000 = 5,760
So, the volcano extends 5,760 meters below sea level.
Adding below sea level and above sea level
Given in question distance of above sea level = 4,200
The distance of below sea level = 5,760
Adding both values 4,200 + 5,760 = 9,960
So, the total height of the volcano is about 9,960 meters.

Show and Grow

Question 15.
A pool is 3.65 meters deep. A diving board is 100 centimeters above the surface of the water. What is the distance from the diving board to the bottom of the pool in centimeters?
Answer: Given pool depth = 3.65 meters
Explanation: The diving board is above the surface of water = 100 centimeters
Converting 3.65 meters into centimeters ( Since, 1m = 100 cm )
3.65 meters = 365 centimeters ( Multiply the meters value by 100 )
3.65 × 100 = 365 cm
The distance from the diving board to the bottom of the pool = 365 + 100 = 465 cm

Question 16.
You hike 1.6 kilometers from a cabin to a lookout. You plan to hike the same way back. On your way back, you stop after 1,050 meters to look at a map. How many meters have you hiked so far? How many kilometers are you from the cabin?
Answer: Given, that hike from a cabin toa lookout = 1.6 km

Explanation:
on the way you stopped after = 1,050 meters
so, 1.6 km = 1600 meters
1600 m + 1,050 m = 2,650 meters
Therefore, 2,650 meters have you hiked so far
Therefore , 550 meters from the cabin  ( 1600m – 1050m = 550m )
Converting 550 meters to kilometers = 0.55 km ( divide the meter value by 1000).
Therefore,0.55 km from the cabin.
Question 17.
DIG DEEPER!
You can take one of two routes to school. Which route is longer? How much longer? Write your answer two different ways.

Answer: Here, we are taking one route to school i.e., (Route A)

Explanation: From Route A and Route B the longer route is “Route A”.
So, we are taking “Route A” values.
Here 1.3km = 1300 meters (1.3km × 1000 = 1300 meters)
[Since we know that  1kilometer(km)  = 1000metres] 0.6 km = 600 meters (0.6km × 1000 = 600 meters)
So, we are adding1.3km + 0.6km
= 1300m + 600m
= 1900 meters
(OR)
Method (2): Here, we are having two routes:- Route A and Route B.
From the question, We observed that
We have to find out the longer route from Route A and Route B.
The value of Route A is 1.3km and 0.6km
The value of Route B is  625m and 800m
Now add both the routes A and B
We are converting the Route A value from “Kilometers to Meters”
Here (1.3km = 1300metres and 0.6km = 600metres)
By Adding we get 1300m+600m = 1900m
Now take Route B = 800m + 625m = 1425m
By comparing both Route A and Route B, “Route A is longer than Route B”.

Length in Metric Units Homework & Practice 11.1

Convert the length

Question 1.
0.8 cm = __ mm
Answer: 0.8 cm = 8 millimeters (mm)

Explanation:
We have to convert from centimeters to millimeters
1 mm = 0.1 cm
Multiply the 0.8 with 10  (0.8 × 10 =8)

Question 2.
7 m = _ km
Answer: 7 m =  0.007 km

Explanation:
Convert from meters to kilometers
1 km = 1000 m
Divide the length value by 1000 ( 7/1000 =  0.007)

Question 3.
6.4 km = ___ m
Answer: 6.4 km = 6400 m

Explanation:
Convert from kilometers to meters
1 km = 1000 m
Multiply the length value by 1000 (6.4 × 1000 = 6400)

Question 4.
1,300 mm = __ cm
Answer: 1,300 mm = 130 cm

Explanation:
Convert from millimeters to centimeters.
1 mm = 0.1 cm
Divide the length value by 10 ( 1300/10 = 130)

Question 5.
91,000 cm = ___ km
Answer: 91,000 cm = 0.91 km

Explanation:
Convert from centimeters to kilometers.
1 cm = 1e – 5
Divide the length value by 100000 ( 91000/100000 = 0.91)

Question 6.
20,000 mm = ___ km
Answer: 20,000 mm = 0.02 km

Explanation:
Convert from millimeters to kilometers
Multiply the value in mm by the conversion factor 1.0E-6.
So, 20000 mm times 1.0E-6 is equal to 0.02 km.

Compare

Question 7.

Answer: 1.6 m is greater than 16 cm

Explanation:
16cm = 0.16 m
16cm/100 = 0.16m
1.6 m = 1.6m × 100 = 160 cm

Question 8.

Answer:
300 mm = 0.3 m
1mm = 0.001 m ( divide the 300mm by 1000 )
0.3 m = 300 mm
1m = 1000mm ( multiply the 0.3m by 1000 )

Question 9.

Answer: 0.045 km = 45,000 mm

Explanation:
Convert from kiometers to millimeters
1km = 1000000 mm
45 mm = 4.5 × 10 ^ -5 km ( it is spelled as 10 to the power of -5)  (or)   4.5 e^-5

Question 10.
Dolphins can hear sounds underwater that are 24 kilometers away. How many meters away can dolphins hear sounds underwater?
Answer:
Given,
Dolphins can hear sounds underwater that are 24 kilometers away.
24000 meters away dolphins can hear sounds underwater.

Question 11.
Reasoning
How can you convert 7.8 meters to kilometers by moving the decimal point? Explain your reasoning.
Answer:
Converting 7.8 meters to kilometers
7.8 meters = 0.0078 kilometers.

Explanation:
7.8 m / 1000 = 0.0078 km ( Divide the meter value by 1000 ) ( 1km = 1000 m )
To convert from meters to kilometers, divide the meter value by 1000
since , 1km = 1000m
divide the whole meter value by 1000, put a decimal point at the end of the number and then move it three places to the left.
(But in question we have the decimal number that is 7.8  so, that is why we have moved the decimal point to the fourth number from left).

Question 12.
YOU BE THE TEACHER
Your friend divides by 100 to convert a length from meters to centimeters. Is your friend correct? Explain.
Answer:
No, it is not correct.

Explanation:
Converting a length from meters to centimeters, We have to multiply the length value by 100.

Question 13.
Which One Doesn’t Belong? Which measurement does not belong with the other three?

Answer:
5,000 cm measurement does not belong with the other three.

Explanation:
500,000 mm = 500 m
500 m = 0.5km
But, 5000 cm = 50m (Here the value 50 m is didn’t belong with given values in question)

Question 14.
Modeling Real Life
A small chunk of ice called a growler breaks away from an ice burg. The growler sticks out of the water 840 millimeters and is 3.5 meters deep in the water. What is the total height of the growler in meters?
Answer:
Converting 840 millimeters into meters

Explanation:
840 mm = 0.84 meter
( Divide the length value by 1000)
840/1000 = 0.84 meter
Total Height of the growler = 0.84 m × 3.5 m (Multiply 0.84m and 3.5m)
= 2.94 meters.

Question 15.
DIG DEEPER!
A spaceship’s route from Earth to the moon is 384,400 kilometers long. The spaceship travels 500,000 meters. How many kilometers does it have left to travel?
Answer:
The Spaceship has left to travel from Earth to the Moon = 500 kilometers.

Explanation:
According, to the question
We are converting 500,000 meters to Kilometers ( 500,000 meters = 500 kilometers)
So, the spaceship has left to travel is 500 kilometers.

Review & Refresh

Write the fraction in the simplest form.

Question 16.
\(\frac{2}{8}\)
Answer: \(\frac{2}{8}\) = \(\frac{1}{4}\)

Question 17.
\(\frac{10}{100}\)
Answer: \(\frac{10}{100}\) = \(\frac{1}{10}\)

Question 18.
\(\frac{24}{16}\)
Answer: \(\frac{24}{16}\) = \(\frac{3}{2}\)

Lesson 11.2 Mass and Capacity in Metric Units

Explore and Grow

Use a balance and weights to help you complete the statement.
Answer: 1 kilogram is 0.001 times as much as 1 gram.

Structure
How can you convert kilograms to grams? How can you convert grams to kilograms?

Use a 1-liter beaker to help you complete the statement.
Answer: 1 liter is 0.001 times as much as 1 milliliter.

Structure
How can you convert liters to milliliters? How can you convert milliliters to liters?
Answer: Converting liters to milliliters ( 1 liter = 1000 milliliters )

Explanation:
multiply the volume (i.e., liter value by 1000 )
For example :-  0.01 liter = 10 ml
0.1 liter = 100 ml
1 liter = 1000 ml
Converting milliliters to liters ( 1 milliliters = 0.001 liters)
Divide the volume value ( i.e., liter value by 1000)
1/1000 = 0.001 liter .

Think and Grow: Convert Metric Measures

Key Idea
When finding equivalent metric masses or capacities, multiply to convert from a larger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit.

Example
Convert 12.4 grams to milligrams.
Answer: There are 1000 milligrams in 1 gram.

Explanation:
Because you are converting from a larger unit to a smaller unit, multiply.
12.4 × 1000 = 12400
So, 12.4 grams is 12400 milligrams.

Example
Convert 18,000 milliliters to liters.
Answer:
There are 1000 milliliters in 1 liter.
Because you are converting from a smaller unit to a larger unit, divide.
18,000 ÷ 1000 = 18 liters .

So, 18,000 milliliters is 18 liters.

Show and Grow

Convert the mass.

Question 1.
8 kg = ___ g
Answer: 8 kg = 8000 g (8 × 1000 = 8000g)

Explanation:
Convert from kilograms to grams
1 kg = 1000 g
8 kg = 8 × 1000 g = 8000 g

Question 2.
3,800 mg = __ g
Answer: 3,800 mg = 3.8 g
Explanation:
Convert from milligrams to grams
Divide the mass value ( mg value) by 1000
( 3800/1000 = 3.8 g )

Convert the capacity.

Question 3.
22,000 mL = __ L
Answer: 22,000 mL = 22 L
Explanation:
Convert from milliliters to liters.
Divide the volume value ( mL value) by 1000
( 22000/1000 = 22 L )

Question 4.
4.6 L = __ mL
Answer: 4.6 L = 4600 mL

Explanation:
Convert from liters to milliliters
Multiply the volume value ( L  value) by 1000
4.6 × 1000 = 4600 mL

Apply and Grow: Practice

Convert the mass.

Question 5.
5,000 g = ___ kg
Answer: 5,000 g = 5 kg

Explanation:
Convert from grams to kgs
Divide the mass value ( g value) by 1000
1000 grams = 1 kg
5000/1000 = 5kg

Question 6.
67 g = ___ mg
Answer: 67 g = 67000 mg

Explanation:
Convert from grams to milligrams
1 g = 1000 mg
Multiply the mass value ( g value ) by 1000
67 × 1000 = 67000 mg

Question 7.
0.2 kg = __ mg
Answer: 0.2 kg = 200000 mg

Explanation:
Multiply the mass value ( kg value) by 1e+6

Question 8.
30,000 mg = __ kg
Answer: 30,000 mg = 0.03 kg

Explanation:
Divide the mass value ( mg value ) by 1e+6

Convert the capacity.

Question 9.
8 L = ___ mL
Answer: 8 L = 8000 mL  ( 8 × 1000 = 8000 mL )

Explanation:
Convert from liters to milliliters
1L = 1000 mL
( Multiply the volume ( L ) value by 1000)
8 liters = 8 × 1000 ml = 8000 ml

Question 10.
70 mL = ___ L
Answer: 70 mL = 0.07 L

Explanation:
Convert from milliliters to liters
Divide the volume ( mL ) value by 1000
70/1000 = 0.07 L

Question 11.
1.200 mL = __ L
Answer: 1.200 mL = 0.0012 L

Explanation:
Convert from milliliters to liters
Divide the volume ( mL ) value by 1000
1.200/1000 = 0.0012 L

Question 12.
0.4 L = ___ mL
Answer: 0.4 L = 400 mL

Explanation:
Convert from milliliters to liters
Multiply the volume ( L ) value by 1000
( 0.4 × 1000 = 400 mL )

Question 13.
What is the mass of the pumpkin in kilograms?

Answer:
Given, the mass of the pumpkin = 6,000 grams
According to the question, we have to find out the mass of pumpkin in kilograms.
Converting the 6,000 grams into kilograms = 6 kilograms

Explanation:
Divide the mass ( grams ) value by 1000
[1 kilogram = 1000 grams] , [ 6 kilogram = 6,000 grams ]
(6000/1000 = 6 kilograms )
So, the mass of pumpkin in kilograms is 6 kilograms.

Question 14.
Which One Doesn’t Belong? Which one does not have the same capacity as the other three?

Answer:
Here , 2000 ml = 2L
2L = 2000 ml
2 × 10³ ml =2000 ml
But 2 ml = 0.002 L

Explanation:
So, the 2ml does not have the same capacity as the other three

Question 15.
DIG DEEPER!
Order the masses from least to greatest. Explain how you converted the masses.

Answer: Order the masses from least to greatest is
14000 mg , 0.039 kg  ,  56 g , 0.14 kg

Explanation:
0.039 kg = 39 grams
0.14 kg = 140 grams
56 g = 0.056 kg
14,000 mg = 14 grams.

Think and Grow: Modeling Real Life

Example
You have a 5-kilogram bag of dog food. You give your dog 50 grams of food each day. How many days does the bag of food last?

Answer: Convert the mass of the bag to grams.

Explanation:
There are 1000 grams in 1 kilogram.
5 × 1000 = 5000
So, the bag contains 5000 grams of dog food.
Divide the amount of dog food in the bag by the amount you give your dog each day.
5000 ÷ 50 =100
So, the bag lasts for 100 days.

Show and Grow

Question 16.
You have 6 liters of juice to make frozen treats. You pour 30 milliliters of juice into each treat mold. How many treats can you make?
Answer: We can make 200 treats.

Explanation:
We have 6 Liters of juice
6 Liters = 6000 milliliters
From the formula ( 1 liter = 1000 milliliter )
30 milliliters of juice is poured into each treat mold
so , 6000 / 30 = 200
so, we can make 200 treats.

Question 17.
Your goal is to eat no more than 2.3 grams of sodium each day. You record the amounts of sodium you eat. How many more milligrams of sodium can you eat and not exceed your limit?

Answer: Given 2.3 grams of sodium you have to eat each day

Explanation:
convert 2.3 grams into milligrams
2.3 grams = 2300 milligrams ( multiply the value of the gram by 1000 )
subtract the sodium you eat values
2300 – 210 – 250 – 690 = 1150
so, you can take 1150 more milligrams of sodium.

Question 18.
Which contains more juice, 3 of the bottles, or 32 of the juice boxes? How much more? Write your answer in milliliters.

Answer: 1 bottle of juice contains = 2 L
1 juice box contains = 200 mL

Explanation:
from the question, we have to find 3 juice bottles quantity and 32 juice boxes quantity in milliliters.
1 L = 1000 mL ( from formula )
2L = 2000 mL
for 3 juice bottles = 3 × 2000 = 6000 ml
for 32 juice boxes = 32 × 200 = 6400 ml
so, 6400 – 6000 = 400 ml
400 mL is more
Therefore, 32 juice boxes contain more juice than 3 juice bottles.

Mass and Capacity in Metric Units Homework & Practice 11.2

Convert the mass

Question 1.
9 g = 9000 mg
Answer: 9 g = 9000 mg

Explanation:
Convert from grams to milligrams
1 g = 1000 mg
9 g = 9000 mg ( multiply the g value by 1000 )

Question 2.
78 g = 0.078 kg
Answer: 78 g = 0.078 kg

Explanation:
Convert from grams to kilograms.
1 g = 0.001 kg
78 g = 0.078 kg ( divide the g value by 1000 )

Question 3.
260,000 mg = _0.26_ kg
Answer: 260,000 mg = 0.26 kg

Explanation:
Convert from milligrams to kilograms.
1 mg = 1e + 6
260,000 mg = 0.26 kg

Question 4.
0.148 kg = 148000 mg
Answer: 0.148 kg = 148000 mg

Explanation:
Convert from kilograms to milligrams
1kg = 1000000 mg
0.148 kg = 148000 mg

Convert the capacity

Question 5.
600 mL = 0.6 L
Answer: 600 mL = 0.6 L

Explanation:
Convert from milliliters to liters.
1mL = 0.001 L
600 mL = 0.6 L
divide the mL by 1000

Question 6.
3 L = 3000 mL
Answer: 3 L = 3000 mL

Explanation:
Convert from liters to milliliters.
1 L = 1000 mL
3 L = 3000 mL ( multiply the L value by 1000 )

Question 7.
0.21L = 210 mL
Answer: 0.21 L = 210 mL

Explanation:
Convert from liters to milliliters.
1 L = 1000 mL
0.21 L = 210 mL ( multiply the L value by 1000 )

Question 8.
35 mL = 0.035 L
Answer: 35 mL = 0.035 L

Explanation:
Convert from milliliters to liters.
1 mL = 0.001 L
35 mL = 0.035 L
divide the mL value by 1000

Question 9.
There are 3.2 liters of iced tea in a pitcher. How many milliliters of iced tea are in the pitcher?
Answer: Given that iced tea in a pitcher = 3.2 Liters
we have to find out iced tea in the pitcher in milliliters

Explanation:
Convert from liters to milliliters.
3.2 Liters = 3200 milliliters
1 Liter = 1000 milliliter
3.2 Liters = 3200 milliliters ( multiply the Liters value by 1000 )
so, therefore 3200 milliliters of iced tea are in the pitcher.

Question 10.
YOU BE THE TEACHER
Your friend says that 0.04 kilogram is less than 4 × 10⁵ milligrams. Is your friend correct? Explain.
Answer: 0.04 kilogram = 40,000 mg
4 × 10⁵ mg = 0.4 kg

Explanation:
yes, your friend is correct
0.04 kg is less than 4 × 10⁵ mg
Question 11.
Number Sense
How does the meaning of each prefix relate to the metric units of mass and capacity?

Answer: The metric system is the system of measurement primarily used in science and in countries outside of the united states.

Explanation:
The metric system includes units of length ( meters ), mass ( grams ), and capacity (liters).
from the given question we have to relate each prefix to the metric units of mass and capacity is:-
metric units of mass of prefix kilo are:-  kilo is the prefix of the kilogram(kg),  kilogram (kg)=1000 grams
Milli is the prefix of milligram(mg) , milligram(mg) = 0.001 gram
metric units of the capacity of prefix kilo is:- kilo is the prefix of Kiloliter(KL), Kiloliter (KL) = 1000 liters
Milli is the prefix of Milliliter(mL), Milliliter (mL) = 0.001 liters

Question 12.
Modeling Real Life
You have 9 kilograms of corn kernels. You put 450 grams of corn kernels in each bag. How many bags can you make?
Answer: we can make 20 bags.

Explanation:
Given that you have 9 kilograms of corn kernels
convert 9 kilograms to grams = 9 kilograms = 9000grams
you put 450 grams of corn kernels in each bag.
we have to find out the how many bags we can make
so, divide the 9000 grams by 450 grams = 9000/450 = 20
so, we can make 20 bags.

Question 13.
DIG DEEPER!
Your teacher has one of each of the beakers shown. You need to measure exactly 2 liters of liquid for an experiment. What are three different ways you can do this?

Answer: We have 3 beakers as shown in figure with 400ml , 600ml , 1L

Explanation:
We have to measure exactly 2 Liters of liquid for each beaker  ( 2L = 2000 ml )
The three different ways we can do this is :-
for first beaker = 400ml × 5 = 2000ml
for second beaker = 600ml × 2 + 400ml × 2
= 1200ml + 800ml = 2000ml
for third beaker = 1 L + 1 L = 2 L

Review & Refresh

Question 14.
Newton rides to the store in a taxi. He owes the driver $12. He calculates the driver’s tip by multiplying $12 by 0.15. How much money does he pay the driver, including the tip?
Answer:
Given that newton rides to the store in a taxi.
He owes the driver $12.
so, he multiplies the drivers tip by $12 by 0.15
$12 × 0.15 + $12 = 13.8
so, newton paid the driver including a tip is 13.8

Lesson 11.3 Length in Customary Units

Explore and Grow

Work with a partner. Use a yardstick to draw 3 lines on a whiteboard that are 1 yard, 2 yards, and 3 yards in length. Then measure the lengths of the lines in feet and in inches. Record your measurements in the table:-
Table values are:-
1  Length(yards) = 3 (feet) ,  36(inches)
2  Length(yards) = 6 (feet) , 72(inches)
3  Length(yards) = 9 (feet) , 108(inches)

Answer:
1 foot is 12 times as long as 1 inch.
1 yard is 3 times as long as 1 foot.
1 yard is 3 × 12 times as long as 1 inch.

Structure
How can you convert a customary length from a larger unit to a smaller unit? How can you convert a customary length from a smaller unit to a larger unit?
Answer:
When converting customary units of measure from a larger unit to a smaller unit, multiply the larger unit by its smaller equivalent unit.
when converting customary units of measure from a smaller unit to a larger unit, divide the smaller unit by its larger equivalent unit.

Think and Grow: Convert Customary Lengths

Key Idea
When finding equivalent customary lengths, multiply to convert from a larger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit.

Example
Convert 3 miles to yards.
Answer: There are 1760 yards in 1 mile.

Explanation:
Because you are converting from a larger unit to a smaller unit, multiply.
3 × 1760 = 5280
So, 3 miles is 5280 yards.

Example
Convert 42 inches to feet and inches.
Answer: There are 12 inches in 1 foot.

Because you are converting from a smaller unit to a larger unit, divide.

Answer:
There are 12 inches in 1 foot
so, 42 inches is 3 feet 6 inches ( 42 / 12 = 3.5 )

Show and Grow

Convert the length.

Question 1.

Answer:
6 1/2 ft = 78 inches

Explanation:
Convert from feet to inches
1 foot = 12 inches
6 feet = 6 × 12 = 72 inches
1/2 ft = 6 inches
72 + 6 = 78 inches
multiply the ft value by 12
6 1/2 ft = 78 inches

Question 2.
94 in. = ft in.
Answer: 94 in = 7 ft 10 in

Explanation: divide the inch value by 12

Apply and Grow: Practice

Convert the length.

Question 3.

Answer:  3 × 3/4 ft = 45 in.

Explanation: multiply the ft value by 12

Question 4.
60 in. = _5_ ft
Answer:- 60 in = 5 f

Explanation:
divide the in value by 12

Question 5.
375 ft = __ yd
Answer: 375 ft = 125 yd

Explanation: divide the ft value by 3

Question 6.

Answer: 12 × 2/3 yd = 38 feet

Explanation:
Convert from yards to feet.
1 yard = 3 feet
multiply the yd value by 3

Question 7.
51 in. = __ ft___in.
Answer: 51 in = 4 feet 3 inches

Explanation:
Convert from inches to feet.
divide the 51-inch value by 12

Question 8.
5 yd = __ in.
Answer: 5 yd = 180 inches

Explanation:
Convert from yards to inches.
1 yard = 36 inches
multiply the yd value by 36
5 yards = 5 × 36 = 180 inches

Compare.

Question 9.

Answer: 7 × 1/3 yd = 22 ft

Explanation:
Convert from yards to feet.
multiply the yd value by 3
22 ft = 7.333 yd
divide the ft value by 3

Question 10.

Answer: 54 in = 4 feet 6 inches

Explanation:
Convert from inches to feet.
divide the inch value by 12
4 ft 8 in = 56 inches
multiply the length value by 12

Question 11.

Answer: 216 in = 6 yards

Explanation:
Convert from inches to yards.
divide the in value by 36
6 yd = 216 inches
multiply the  yd value by 36

Question 12.
A dugong is 8\(\frac{1}{3}\) feet long. How many inches long is the dugong?

Answer: A dugong is 8 × 1/3 feet long
8 × \(\frac{1}{3}\) feet = 32 inches

Explanation:
Therefore 32 inches long is the dugong.

Question 13.
DIG DEEPER!
Order the lengths from shortest to longest. Explain how you converted the lengths.

Answer:
1)  5 × \(\frac{1}{2}\) =\(\frac{5}{2}\) feet
5/2 feet = 30 inches
multiply the feet value by 12
2) 5 feet 3 inches = 63 inches
multiply the 5 feet 3 inches value by 12
3) 5 × \(\frac{2}{3}\) feet = 40 inches
multiply the feet value by 12
4)  5 × \(\frac{3}{4}\) feet = 45 inches
multiply the feet value by 12
So, order from shortest to longest = 5 × 1/2 , 5 × 2/3 , 5 × 3/4 , 5 feet 3 inches .

Think and Grow: Modeling Real Life

Example
A golfer uses a device to determine that his golf ball is 265 feet from a hole. After his next shot, his ball is 15 feet short of the hole. How many yards did the golfer hit his ball?

Because the golfer’s ball is 15 feet short of the hole after his next shot, subtract 265 from 15 to find how many feet the golfer hit his ball.
265 – 15 = _250_ feet

Answer: 265 – 15 = 250 feet

Explanation:
There are 3 feet in 1 yard.
250/3 = 83.33 yards
= 83 × \(\frac{1}{3}\) yards.

Show and Grow

Question 14.
A tree is 27 feet tall. After the tree is struck by lightning, it is 96 inches shorter. How many feet tall is the tree after it is struck by lightning?
Answer:
Given a tree is 27 feet tall. After the tree is struck by lightning, it is 96 inches shorter
we have to find the feet of the tree after it is struck by lightning.
27 feet = 324 inches
Subtract 324 – 96 = 228 inches
converting 228 inches to feet ( i.e., 228 inches = 19 feet )
So, therefore after the tree is struck by lightning its feet tall = 19 feet

Question 15.
DIG DEEPER!
The rope ladder is 2\(\frac{1}{2}\) yards tall. Each knot is made using 16 inches of rope. How many feet of rope are used to make the ladder? Explain.
Answer: 22 feet of rope are used to make the ladder.

Explanation:
2 yards = 6 feet
1 knot is 16 inches
Total 12 knots
12 × 16 = 16 feet ,  16 + 16 = 22 feet.

Question 16.
DIG DEEPER!
The Chesapeake Bay Bridge is 4\(\frac{3}{10}\) miles long. Road work begins 1,200 yards from one end of the bridge and ends 2 miles from the other end of the bridge. How many yards long is the road work?
Answer: 11760 yards

Explanation:
Given,
The Chesapeake Bay Bridge is 4\(\frac{3}{10}\) miles long.
Road work begins 1,200 yards from one end of the bridge and ends 2 miles from the other end of the bridge.
1760 × 4 = 7,040
1760 × 2 = 3,520
given 1200 yards
so, 7040 + 3520 + 1200 = 11760 yards  ( since 1 mile = 1760 yards )

Length in Customary Units Homework & Practice 11.3

Convert the length.

Question 1.
2\(\frac{1}{3}\) yd = __ in.
Answer:- 2 × \(\frac{1}{3}\) yd = 84 in

Explanation:-
Convert from yards to inches
1 yard = 36 inches
Multiply the yd value by 36

Question 2.
5 mi = __ yd.
Answer: 5 mi = 8800 yards

Explanation:
Convert from miles to yards
1 mile = 1760 yards
multiply  the mi value by 1760
5 miles = 5 × 1760 yards
5 mi = 8800 yards

Question 3.
3\(\frac{1}{3}\) yd = __ ft
Answer:
Convert from yards to feet.
multiply the yd value by 3
3 × 1/3 yd = 1 yd
1 yd = 3 feet

Question 4.
27 in. = __ ft __ in.
Answer: 27 in = 2 feet 3 inches

Explanation:
Convert from inches to feet.
divide the 27 inches value by 12

Question 5.
108 in. = __ yd
Answer: 108 in = 3 yards

Explanation:
Convert from inches to yards
1 yard = 36 inches
divide the in value by 36

Question 6.
34 in. = __ ft
Answer: 34 in = 2 feet 10 inches

Explanation:
Convert from inches to feet
1 foot = 12 inches
Divide the in value by 12

Compare.

Question 7.

Answer:
5 × 3/4 ft = 45 inches
65 in = 5 feet 5 inches ( divide the in value by 12 )

Question 8.

Answer:
19 in = 1 feet 7 inches
1 ft 5 in = 17 inches

Question 9.

Answer:
2 mi = 10560 feet
10,650 ft = 2.017 miles

Question 10.
A football player runs 93 yards. How many feet does he run?

Answer:
Given a football player runs 93 yards
we have to find how many feet does he run
convert 93 yards to feet
93 yards = 279 feet
So, therefore a football player runs 279 feet

Question 11.
Precision
Write whether you would use multiplication or division for each conversion.

Answer:
yards to feet:- 1 yard = 3 feet ( multiply the yard value by 3 )
miles to inches:- 1 mile = 63360 inches ( multiply the mile value by 63360 )
feet to miles:- 1 feet = 0.000189 mile ( divide the feet value by 5280 )
inches to feet :- 1 inch = 0.0833 feet ( divide the inch value by 12 )
miles to yards:- 1 mile = 1760 yards ( multiply the mile value by 1760 ).

Question 12.
Reasoning
Match each measurement with the best customary unit of measure.

Answer:
the height of jump = feet
length of a crayon = inches
length of river = miles
length of football field = yards.

Question 13.
Modeling Real Life
How long is the velociraptor in yards?

Answer: we have to find the value of velociraptor in yards

Explanation:
Given velociraptor in ft = 28 ft
Converting 28 ft into yards = 28 ft = 9.333 yards
Divide the ft value by 3.

Question 14.
DIG DEEPER!
You wrap a cube-shaped box with ribbon as shown. The ribbon is wrapped around all of the faces of the cube. You use 9 inches of ribbon for the bow. How many inches of ribbon do you use altogether? Explain.

Answer: Cube sides = 6

Explanation:
one side height = 1 feet 9 inches
so, 12 + 9 = 21 inches
6 × 21 inches = 126 inches
9 inches for the bow
so, 126 + 9 = 135 inches
Therefore 135 inches of ribbon is used altogether.

Review & Refresh

Find the quotient.

Question 15.
3,200 ÷ 40 = 80
Answer: 3,200 ÷ 40 = 80

Question 16.
5,400 ÷ 9 = _600__
Answer: 5,400 ÷ 9 = 600

Question 17.
600 ÷ 20 = _30_
Answer: 600 ÷ 20 = 30

Lesson 11.4 Weight in Customary Units

Explore and Grow

Work with a partner. Use the number line to help you complete each statement.

The vehicle weighs _2000_ pounds.
Answer: 2000 pounds

Explanation:
1 US ton = 2000 pounds

The whale shark weighs _15 US_ tons.
Answer: 15 US tons
Explanation: divide the 30,000 by 2000

Structure
How can you convert tons to pounds? How can you convert pounds to tons?
Answer:
we can convert tons to pounds by multiply the ton value by 2000 (i.e., 1 US ton = 2000)
we can convert pounds to tons by dividing the pound value by 2000 (i.e., 1 pound = 0.0005 us ton)

Think and Grow: Convert Customary Weights

Key Idea
When finding equivalent customary weights, multiply to convert from a larger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit.

A
Answer: 4 × 1/4 tons = 2000 pounds

Explanation:
There are 2000 pounds in 1 ton.
so, 4 × 1/4 tons = 2000 pounds.

A
Answer: 40 ounces = 2.5 pounds

Explanation:
Convert from ounces to pounds
divide the ounces value by 16
40 / 16 = 2.5
so, 40 ounces is 2.5 pounds.

Show and Grow

Convert the weight.

Question 1.
9 T = __ lb
Answer: 9 T = 19841.604 lb

Explanation:
Convert from tonns to pounds.
multiply the T value by 2205.

Question 2.
6\(\frac{1}{2}\) lb = __ oz
Answer: 6 × \(\frac{1}{2}\) lb = \(\frac{6}{2}\) = 3

Explanation:
Convert from pounds to ounces
3 lb = 48 oz
multiply the lb value by 16

Question 3.
6,000 lb = __ T
Answer: 6,000 lb = 3 US tons

Explanation:
Convert from pounds to tonn
divide the lb value by 2000

Question 4.
80 oz = __ lb
Answer: 80 oz = 5 lb

Explanation:
Convert from ounces to pounds.
divide the oz value by 16

Apply and Grow: Practice

Convert the weight.

Question 5.
10,000 lb = __ T
Answer: 10,000 lb = 4.536 T

Explanation:
divide the lb value by 2205.

Question 6.
8 lb = __ oz
Answer: 8 lb = 128 oz

Explanation:
Convert from pounds to ounces.
multiply the lb value by 16

Question 7.
240 oz = __ lb
Answer: 240 oz = 15 lb

Explanation:
Convert from ounces to pounds
divide the oz value by 16

Question 8.
7\(\frac{1}{4}\) T = ___ lb
Answer: 7 × \(\frac{1}{4}\) = 1.75
1.75 T = 3858.09 lb

Explanation:
Convert from tonnes to pounds
multiply the T value by 2205.

Question 9.
150 oz = ___ lb __ oz
Answer: 150 oz = 9.375 lb  150 oz

Explanation:
Convert from pounds to ounces
divide the oz value by 16

Question 10.
32,000 oz = __ T
Answer: 32,000 oz = 1 US ton

Explanation:
Convert from pounds to tonn
divide the oz value by 32000

Compare.

Question 11.

Answer: 30 T = 60000 lb

Explanation:
multiply the T value by 2000
6,000 lb = 3 US tons
divide the lb value by 2000

Question 12.

Answer: 53 oz = 3.312 lb

Explanation:
divide the oz value by 16
3 × 1/2 lb = 1.5 lb
1.5 lb = 0.00068 t
divide the lb value by 2205

Question 13.

Answer:
8 T = 256000 oz

Explanation:
multiply the oz value by 32000
224,000 oz = 7 US tons
divide the oz value by 32000

Question 14.
What is the weight of the hippopotamus in tons?

Answer:
Given the weight of hippopotamus = 4000 pounds
convert 4000 pounds to tons
4000 pounds = 2 US tons
divide the pound’s value by 2000
so, the weight of hippopotamus in tons = 2 US tons

Question 15.
Reasoning
Compare 10 pounds and 165 ounces using mental math. Explain.

Answer:
0 pounds = 160 ounces
multiply the value of the pound by 16
165 ounces = 10.3125 pounds
divide the value of the ounce by 16
By comparing both the values 165 ounces is greater than 10 pounds.

Question 16.
Number Sense
Which measurements are equivalent to 60 ounces?

Answer:
3 × 3/4 lb = 36 oz
3 × 1/2 lb = 56 oz
3 lb 12 oz = 60 oz
3 lb 4 oz = 52 oz

Explanation:
3 lb 12 oz measurement is equivalent to 60 ounces (oz)

Think and Grow: Modeling Real Life

Example
A newborn baby boy weighs 122 ounces. A newborn baby girl weighs 6 pounds 4 ounces. Which baby weighs more? How much more?

Convert the weight of the boy to pounds and ounces.

Answer: There are 16 ounces in 1 pound.

Explanation:
Given boy weighs = 122 ounces
122 / 16 = 7.625
= 2 – 6 × 16 + 4 = 100 ounces
so, 122 >100
Boy weigh is more than girl weigh = 22 ounces more

Show and Grow

Question 17.
Which box of cereal weighs more? How much more?

Answer:
1/2 pounds = 8 ounces
17 ounces = 1.062 pounds

Explanation:
17 ounces box of cereal weighs more
0.562 much more

Question 18.
A male rhinoceros weighs 2\(\frac{1}{4}\) tons. Which rhinoceros weighs more? How much more? Write your answer as a fraction in simplest form.

Answer: male rhinoceros = 2 × 1/4 = 2/4 = 1/2 tons

Explanation:
1/2 tons = 1000 pounds ( converting tons to pounds)
Given in figure female rhinoceros = 3,500 lb
3,500 lb = 1.75 US tons ( converting pounds to tons )
Female rhinoceros weigh more than male rhinoceros
1.75 tons – 1/2 tons => 1.75 – 0.5 = 1.25 tons
1.25 tons weigh is more
we can write 1.25 in simplest form as, we have 2 digits after the decimal point so multiply both numerator and denominator by 100, so that there is no decimal point in the numerator.
1.25 × 1001 × 100 = 125100
125 / 25100 / 25 = 54
simplest form of 1.25 = 5/4

Question 19.
DIG DEEPER!
Can all of the passengers listed in the table ride the boat at once? Explain.

Answer: Yes, all passengers who are listed on the table can ride the boat at once.

Explanation:
Add all the passenger weights 91+184+150+248+170+215+132+145+265+126+259+175  = 2260 pounds
we have to convert 2260 pounds to tons
2260 pounds = 1.13 US tons  ( divide the pounds value by 2000 ).

Weight in Customary Units Homework & Practice 11.4

Convert the weight.

Question 1.
10 T = __ lb
Answer: 10 T = 20000 lb

Explanation:
Convert from tonn to pounds
1 tonn = 2000 pounds
multiply the T value by 2000

Question 2.
32 oz = ___ lb
Answer: 32 oz = 2 pounds

Explanation:
Convert from ounces to pounds
divide the oz value by 16

Question 3.
48,000 lb = __ T
Answer:  48,000 lb = 24 US tons

Explanation:
Convert from pounds to tons
divide the lb value by 2000

Question 4.
50 lb = __ oz
Answer: 50 lb = 800 oz

Explanation:
Convert from pounds to ounces.
multiply the mass value by 16

Question 5.
5\(\frac{3}{4}\)T = __ lb
Answer: 5 × \(\frac{3}{4}\) = 15/4 =3.75 T
3.75 t = 8267.1957671958 lb

Question 6.
8\(\frac{1}{2}\) lb = __ oz
Answer: 8 × \(\frac{1}{2}\) = 8/2 = 4 lb
4 lb = 64 ounces

Explanation:
Convert from pounds to ounces.
multiply the lb value by 16

Question 7.
168 oz = __ lb __ oz
Answer: 168 oz = 10.5 lb 168 oz

Explanation:
Convert from ounces to pounds.
divide the oz value by 16

Question 8.
96,000 oz = __ T
Answer: 96,000 0z = 2.7216 T

Explanation:
Convert from ounces to the ton.
96,000 0z = 2.7216 T

Compare

Question 9.

Answer: 16 lb = 0.01 T
32,000 T = 64000000 lb

Question 10.

Answer: 128 oz = 8 lb

Explanation:
divide the oz value by 16
8 × 1/4 lb = 8/4 = 2 lb
2 lb = 32 oz
multiply the lb value by 16

Question 11.

Answer:
11 T = 388013.581 oz
multiply the T value by 35274
384,000 oz = 10.886 T
divide the oz value by 35274

Question 12.
A newborn puppy weighs 3 pounds 5 ounces. What is the weight of the puppy in ounces?
Answer:
Given a new born puppy weighs 3 pounds 5 ounces
we have to find the weight of the puppy in ounces
3 pounds 5 ounces = 1500 grams
convert 1500 grams to ounces
1500 grams = 52.911 ounces
divide the value of the gram by 28.35
The weight of puppy in ounces = 28.35

Question 13.
Number Sense
How many tons are equal to 500 pounds? Write your answer as a fraction in simplest form.

Answer: 500 pounds = 0.25 US tons

Explanation:
divide the value of the pound by 2000
when 0.25 reduced to the simplest form is (25/25)(100/25) = 14

Open-Ended
Complete the statement.

Question 14.
__ pounds > 72 ounces

Answer: 4.6 pounds > 72 ounces

Explanation:
4.6 pounds = 73.6 ounces
multiply the pound’s value by 16

Question 15.
13 tons < __ pounds
Answer: 13 tons < 27000 pounds

Explanation:
Convert from tons to pounds
1 ton = 2000 pounds
divide the value of the pound by 2000.

Question 16.
Modeling Real Life
An employee at a juice cafe uses 10 ounces of kale and \(\frac{3}{4}\) pound of apples to make a drink. Does the employee use more kale or apples? How much more?
Answer: Given that an employee at a juice cafe uses of kale = 10 ounces
and he uses pound of apples to make a drink = 3/4 pounds

Explanation:
converting 10 ounces to pounds = 0.625 pound
divide the value of the ounce by 16
converting 3/4 pounds to ounces = 12 ounces
12 ounces  is greater than 0.625 pounds
The employee uses more apples than kale
0.125 is more.

Question 17.
Modeling Real Life
You have a 3-pound bag of clay. You use 8 ounces of clay to make an ornament. How many ornaments can you make using all of the clay?
Answer:
Given that you have a 3 pound bag of clay
you use 8 ounces of clay to make an ornament.
we have to find out the how many ornaments you can make using all of the clay
Converting 3 pounds to ounces is
3 pounds = 48 ounces ( multiply the pounds value by 16 )
you have used the 8 ounces of clay to make an ornament
so, divide the 48 / 8 = 6
Therefore, we can make 6 ornaments by using all of the clay.

Review & Refresh

Find the product. Check whether your answer is reasonable.

Question 18.

Answer: Multiply the value 145 × 12 = 1740

Question 19.

Answer: multiply the value 561 × 87 = 48,807

Question 20.

Answer: multiply the value 823 × 65 = 53,495

Lesson 11.5 Capacity in Customary Units

Explore and Grow

Describe the relationship between cups and fluid ounces (fl oz). Then complete the table.

1 cup is _8 US_ times as much as 1 fluid ounce.
Answer:
Relationship between cups and fluid ounces is :-
A cup of water happens to equal both 8 fluid ounces ( in volume ) and 8 ounces( in weight) ,
so you might naturally assume that 1 cup equals to 8 ounces of weight universally in recipes.

Explanation:
About table values
1 capacity (cups ) = 8 US fluid ounces    ( multiply the cups value by 8 )
2 capacity ( cups ) = 16 US fluid ounces
3 capacity ( cups ) = 24 US fluid ounces
4 capacity ( cups ) = 32 US fluid ounces
Structure
How can you convert cups to fluid ounces? How can you convert fluid ounces to cups?

Answer:
We can convert cups to fluid ounces by multiplying the value of the cup by 8
1 cup = 8 fluid ounces
We can convert fluid ounces to cups by dividing the value of the fluid ounce by 8
1 fluid ounce = 0.125 US cup .

Think and Grow: Convert Customary Capacities

Key Idea
When finding equivalent customary capacities, multiply to convert from a larger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit.

Show and Grow

Convert the capacity

Question 1.
9 gal = __ qt
Answer: 9 gal = 36 Us liquid qt

Explanation:
Convert from gal to quart
1 gal = 4 quart
multiply the gal value by 4

Question 2.
20 pt = __ c.
Answer: 20 pt = 48.038 c

Explanation:
Convert from pints to cups
multiply the pt value by 2.402

Question 3.
42 pt = __ qt
Answer: 42 pt = 25.2199 qt

Explanation:
Convert from pints to quarts
divide the pt value by 1.665

Question 4.
68 qt = __ gal
Answer: 68 qt = 17 gal

Explanation:
Convert from quarts to gal
divide the qt value by 4

Apply and Grow: Practice

Convert the capacity.

Question 5.
7 c = fl oz
Answer: 7 c = 56 US fl oz

Explanation:
Convert from cups to fluid ounces
multiply the c value by 8

Question 6.
6 pt = __ qt
Answer: 6 pt = 3.60285 qt

Explanation:
Convert from pints to quarts
1 pint = 0.5 quart
divide the pt value by 1.665

Question 7.
16 qt = __ gal
Answer: 16 qt = 4 US liquid gal

Explanation:
Convert from quarts to gal
1 quart = 0.25 gal
divide the qt value by 4

Question 8.
15 pt = __ c
Answer: 15 pt = 36.0285 US c

Explanation:
Convert from pints to cups.
multiply the pt value by 2.402

Question 9.

Answer: 2 1/4 c = 2/4 = 1/2 c
1/2 c = 4 fl oz

Compare.

Question 11.

Answer:
14 c = 7 US liquid  pt
divide the c value by 2
10 pt = 24.019 US c
multiply the pt value by 2.402

Question 12.

Answer:
38 qt = 9.5 US liquid gal
divide the qt value by 4
8 × 1/2 = 8/2 = 4
4 gal = 16 US liquid qt
Multiply the gal value by 4

Question 13.

Answer:
4 gal = 26.6456pt
multiply the gal value by 6.661
32 pt = 4.8038 US liquid gal
divide the pt value by 6.661

Question 14.
You fill your turtle’s aquarium with 40 pints of water. How many gallons of water do you use?

Answer:
Given turtles, aquarium fill with water = 40 pints
we have to find the 40 pints of water into gallons
converting 40 pints to gallons
40 pints = 5 US liquid gallons
Divide the pints value by 8
so, therefore 5 gallons of water is used.

Question 15.
Number Sense
Newton’s water cooler contains 1\(\frac{1}{2}\) gallons of water. How many times can he fill his 16-fluid ounce canteen with water from the water cooler? Explain.
Answer:- Given newton’s water cooler contains 1 × 1/2 = 1/2 = 0.5 gallons
Explanation:-  converting 0.5 gallons = 64 US fluid ounces ( multiply the gallons value by 128 )
Given 16 fluid ounce
He can fill 4 times his 16 fluid ounce canteen with water from the water cooler
( i.e., 16 × 4 = 64 fluid ounce ) .

Question 16.
DIG DEEPER!
Order the capacities from least to greatest. Explain how you converted the capacities.

Answer:
i. 8 × 1/2 c => 8/2 = 4 c
4 c = 32 fl oz ( multiply the c value by 8 )
ii. 72 fl oz = 9 US c
divide the fl oz value by 8
iii. 7 × 3/4 c => 21/4 = 5.25 c
5.25 c = 42 fl oz
iv. 56 fl oz = 7 c
divide the fl oz value by 8
Order of capacities from least to greatest = 8 × 1/2 c , 7 × 3/4c , 56 fl oz , 72 fl oz .

Think and Grow: Modeling Real Life

Example
A car’s engine contains 4\(\frac{1}{2}\) quarts of oil. Can a mechanic use a 24-cup container to drain all of the oil?

First, convert the quarts of oil to pints.
There are __2pints in 1 quart.

Answer:
Given car engine contains = 4 × 1/2 quarts = 4/2 = 2 quarts

Explanation:
2 quarts = 4 pints
multiply the quarts value by 2
1 pint = 2 cups
converting 2 quarts to cups
2 quarts = 8 cups
multiply the quarts value by 4
So, a mechanic can use just 8 cups
8 cups are enough to drain engine oil.
Show and Grow

Question 17.
An adult has 192 fluid ounces of blood in his body. How many pints of blood are in his body?
Answer: Given an adult has 192 fluid ounces of blood in his body
we have to find the pints of blood in his body
Converting 192 fluid ounces to pints
192 fluid ounces = 12 US liquid pints
divide the value of the fluid ounce by 16
Therefore, 12 pints of blood are in his body.

Question 18.
DIG DEEPER!
You make 4\(\frac{1}{2}\) cups of soup. One serving is 12 fluid ounces. How many servings of soup do you make?
Answer:
Given 4 × 1/2 cups of soup
4 × 1/2 = 4/2 = 2 cups of soup
2 cups of soup converting to fluid ounces
2 US cups = 16 US fluid ounces
Given that serving = 12 fluid ounces
Subtract  16 fluid ounces – 12 fluid ounces = 4 fluid ounces
so, therefore you can make servings of soup in 4 fluid ounces.

Question 19.
DIG DEEPER!
A scientist has two beakers of a solution, one containing 5 cups and the other containing 1\(\frac{1}{2}\) pints. How many gallons of the solution does the scientist have? Write your answer as a fraction in simplest form.

Answer:
Given that scientist has two beakers of solution one contains 5 cups and other contains
1 × 1/2 pints.
we have to find gallons of solution
Converting 5 cups to gallons
5 cups = 0.312 US gallons
Converting 1 × 1/2 pints to gallons
1 × 1/2 => 1/2 = 0.5 pints
0.5 pints = 0.0625 US gallons
By adding both the solutions ( i.e., )
5 cups + 0.5 pints
0.312 gallons + 0.0625 gallons = 0.3745 gallons
So, the scientist has 0.3745 gallons of solution.
0.3745 in simplest form we can write as  749 / 2000.

Capacity in Customary Units Homework & Practice 11.5

Convert the capacity

Question 1.
9 pt = __ c
Answer: 9 pt = 18 c

Explanation: multiply the pt value by 2

Question 2.
72 fl oz = ___ c
Answer: 72 fl oz = 9 c

Explanation:
Convert from fluid ounces to cups.
1 fl oz = 0.125 c
divide the fl oz value by 8

Question 3.
6 c = __ fl oz
Answer: 6 c = 48 fl oz

Explanation:
Convert from cups to fluid ounces
1 cup = 6 fluid ounces
6 cups = 6 × 8 fluid ounces
multiply the c value by 8
Thus 6 c = 48 fl oz

Question 4.

Answer: 3 3/4 gal = 15 qt

Explanation:
Convert from gal to quart
1 gal = 4 quart
4  × 15/4 gal = 15 qt
multiply the gal value by 4

Question 5.

Answer: 5 1/2 qt = 11 pt

Explanation:
Convert from quarts to pints
1 quart = 2 pints

multiply the qt value by 2
5 1/2 = 11/2
11/2 × 2 = 11 pints

Question 6.
40 pt = __ gal
Answer: 40 pt = 5 gal

Explanation:
Convert from pints to gal
1 pint = 0.125 gal
40 pint = 40 × 0.125 = 5 gal
Thus 40 pt = 5 gal

Question 7.
64 qt = __ c
Answer: 64 qt = 256 c
Explanation:
Convert from quarts to cup
1 quart = 4 cups
multiply the qt value by 4

Question 8.
112 fl oz = __ pt
Answer: 112 fl oz = 7 US liquid pt
Explanation: divide the fl oz value by 16

Compare.

Question 9.

Answer:
48 qt = 12 gal
divide the qt value by 4
12 gal = 48 qt
multiply the gal value by 4
Therefore 48 qt = 12 gal

Question 10.

Answer: 24 fl oz = 3 c
divide the fl oz value by 8
3 × 1/4 c = 3/4 c = 6 fl oz
multiply the 3/4 c value by 8
Therefore 24 fl oz is greater than 3 × 1/4 c

Question 11.

Answer:
10 qt = 40 c
multiply the qt value by 4
24 c = 6 qt
divide the c value by 4
So, therefore 10 qt is greater than 24 c.

Question 12.
You buy 2 gallons of apple cider. How many cups of apple cider do you buy?

Answer:
Given that 2 gallons of apple cider
we have to find the cups of apple cider
Converting 2 gallons to Cups
2 gallons = 32 cups
multiply the gallons value by 16
So, you buy the 32 cups of apple cider.

Question 13.
Logic
Your friend makes a table of equivalent capacities. Write two pairs of customary units represented by the chart.

Answer:
We can relate the numbers as they are resembling quarts to cups relation and gallons to quarts relation.
Two pairs of the customary unit represented by the chart are :-
1 quart = 4 cups     1 gallon = 4 quarts
2 quart = 8 cups      2 gallon = 8 quarts
Question 14.
DIG DEEPER!
Which measurements are greater than 16 pints?

Answer:
Converting fluid ounces to pints
300 fluid ounces = 18.75  pints ( divide the value of the fluid ounce by 16 )
Converting cups to pints
28 cups = 14 pints ( divide the value of the cup by 2 )
Converting quarts to pints
10 quarts = 20 pints ( multiply the quarts value by 2 )
Converting gallon to pints
1 gallon = 8 pints ( multiply the gallon value by 8 )
Converting fluid ounces to pints
275 fluid ounces = 17.188 pints ( divide the value of the fluid ounce by 16 )
Converting cups to pints
35 cups = 17.5 pints ( divide the value of the cup by 2 )
Therefore, 300 fluid ounces, 10 quarts, 275 fluid ounces, 35 cups measurements are greater than 16 pints

Question 15.
Modeling Real Life
Your friend buys 8 quarts of frozen yogurt. How many cups of frozen yogurt does she buy?
Answer: Given that quart of frozen yogurt = 8

Explanation:
we have to find cups of frozen yogurt
converting 8 quarts to cups
8 quarts = 32 cups ( multiply the quarts value by 4 )
Therefore, she buys 32 cups of frozen yogurt

Question 16.
Modeling Real Life
A recipe calls for 2\(\frac{1}{4}\) cups of milk. You want to make 2 batches of the recipe. Should you buy a pint, quart, or half gallon of milk?
Answer: Given 2 × 1/4 => 2/4 = 1/2 cups of milk

Explanation: we want to make 2 batches of recipe (i.e., 2 × 1/2 = 1 cup )
1 pint = 2 cups
1 cup = 1/2 pint

Review & Refresh

Question 17.
0.5 × 0.7 = _0.35_
Answer:
multiply the 0.5 × 0.7 = 0.35

Question 18.
46.2 × 0.68 = _31.416_
Answer:
multiply the 46.2 × 0.68 = 31.416

Question 19.
1.4 × 0.3 = _0.42_
Answer:
multiply the 1.4 × 0.3 = 0.42

Lesson 11.6 Make and Interpret Line Plots

Explore and Grow
Measure and record your height to the nearest quarter of a foot. Collect the heights of all the students in your class and create a line plot of the results.


Construct Arguments
Make two conclusions from the line plot.

Think and Grow: Make Line Plots

Example
The table shows the amounts of water that 10 students use for a science experiment. Make a line plot to display the data. How many students use more than \(\frac{1}{2}\) cup?

Step 1: Write the data values as fractions with a common denominator.
The denominators of the data values are 2, 4, and 8. Because 2 and 4 are factors of 8, use a denominator of 8.

Step 2: Use a scale on a number line that shows all of the data values.
Step 3: Mark an X for each data value.

Show and Grow

Question 1.
The table shows the distance your friend swims each day for 10 days. Make a line plot to display the data.

How many days does your friend swim \(\frac{3}{4}\) mile or more?
Answer:- From the table we observed that your friend swim 3/4 miles or more than 3/4 miles in  6 days.

Apply and Grow: Practice

Question 2.
The table shows the amounts of mulch a landscaping company orders on 10 different days. Make a line plot to display the data.

What do you notice about the data?
Answer:
From the table we observed that except 1/4 and 1/2 the remaining days like 7/8 and 3/4 company use more than 1/2 ton of mulch .

Question 3.
DIG DEEPER!
Your teacher has the three packages of seeds shown. She divides the first package into bags weighing \(\frac{1}{2}\) ounce each. She divides the second package into bags weighing \(\frac{1}{4}\) ounce each. She divides the third package into bags weighing \(\frac{1}{8}\) ounce each. Find the total number of bags of seeds. Use a line plot to display the results.

Answer:
Given that we observed from figures each bag is 2 ounces
Explanation:
given 1st bag = 1/2 ounce each
2 ounces = 1/2 + 1/2 +1/2 + 1/2 = 4(1/2) = 2
4 bags
2nd bag = 1/4 ounce each
2 ounces = 1/4 + 1/4 +1/4 +1/4 + 1/4 + 1/4 + 1/4 + 1/4
= 8 (1/4) = 2
8 bags
3rd bag = 1/8 ounce each
2 ounces = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8
= 16 (1/8) = 2
16 bags
Total number of bags of seeds = 4 bags + 8 bags + 16 bags = 28 bags
Think and Grow: Modeling Real Life

Example
You record the amounts of time you skateboard each day for 8 days. Your friend skateboards the same total amount of time, but for an equal number of hours each day. How long does your friend skateboard each day?

Step 1: You and your friend skateboard the same total amount of time. Use the line graph to find the number of hours you each skateboard.

Step 2: Divide the number of hours by the number of days.

Show and Grow

Question 4.
You record the amounts of trail mix you pour into 12 bags. Your friend has the same total amount of trail mix, but equally divides it among 12 bags. How much trail mix does your friend pour into each bag?

Answer:- your friend pour trail mix into each bag is equal to the amount of trail mix you pour into the bag.

Make and Interpret Line Plots Homework & Practice 11.6

Question 1.
The table shows the amounts of time that 10 students take to land three balls in a row in a game. Make a line plot to display the data. How many pygmy marmosets weigh more than \(\frac{1}{2}\) ounce?

Answer: Here 1/2 = 0.5 ounce
Except 1/2 ounce
5/8 , 7/8 , 3/4 ounces pygmy weighs more than 1/2 ounce.

Use the table.

Question 2.
The table shows the amounts of berries required to make 10 different smoothie recipes. Make a line plot to display the data.


Answer: The most common amount of berries required is 3/4
Six times as many recipes use 3/4 cup of berries as 1/4 cup of berries
from table 4 × (3/4) = 12/4 = 3
2 × (1/4) = 2/4 = 1/2
= 3/(1/2) = 6

Question 3.
DIG DEEPER!
How many total cups of berries are needed to make one of each smoothie?
Answer: Total 2 to 3 cups of berries are needed to make one of each smoothie.

Use the line plot.

Question 4.
Modeling Real Life
The line plot shows the number of miles you run each day for 10 days. Your friend runs the same total number of miles, but runs an equal number of miles each day. How far does your friend run each day?

Answer: Your friend runs 4/5 miles each day for 10 days

Explanation: 0 + 0 + 0.5 + 0.5 + 0.5 + 1 + 1 + 1 + 1.5+ 2 = 8
He runs same miles each day = 8/10 = 0.8
0.8 = 4/5
Question 5.
DIG DEEPER!
Your cousin runs a total amount that is 6 times as far as your friend runs in one day. How far does your cousin run?
Answer: Let us assume that, If the friend runs 0.8 per day

Explanation: 0.8 = 4/5
so, cousin run 6 times more than a friend
so, 6 × 0.8 = 4.8 ( cousin runs per day is 4.8 )

Review & Refresh

Question 6.
561 ÷ 7 = 80.142
Answer: divide the 561 ÷ 7 = 80.142

Question 7.
3,029 ÷ 4 = 757.25
Answer: divide the 3,029 ÷ 4 = 757.25

Question 8.
2,814 ÷ 9 = 312.6
Answer: divide the 2,814 ÷ 9 = 312.6

Lesson 11.7 Problem Solving: Measurement

Explore and Grow

Make a plan to solve the problem.
A fruit vendor sells fruit by the pound. You have a tote that can hold up to 4 pounds. A bag of oranges weighs 2\(\frac{1}{4}\) pounds. A bag of apples weighs 28 ounces. Can your tote hold both bags of fruit? Explain.

Answer: Given that vendor sells fruit by the pound.

Explanation:
The tote can hold up to 4 pounds
A bag of oranges weighs = 2 × 1/4 = 2/4 = 1/2 pounds
A bag of apples weighs = 28 ounces
we have to find that can tote to hold both bags
Convert 28 ounces to pounds
28 ounces = 1.75 pounds ( divide the value of the ounce by 16 )
Given in question that tote can hold up to 4 pounds
so, adding 1/2 pounds and 1.75 pounds
= 1/2 pounds = 0.5
0.5 pounds + 1.75 pounds = 2.25 pounds
Therefore tote holds both the bags of fruit.

Precision
Which bag of fruit is heavier? Explain.
Answer: Bag of apple is heavier ( i.e., a bag of apple weighs 28 ounces )

Explanation:
28 ounces = 1.75 pounds
bag of orange is 0.5 pounds
1.74 > 0.5  (So, apple bag weigh is heavier)

Think and Grow: Problem Solving: Measurement

Example
A recipe calls for 2\(\frac{1}{4}\) cups of milk. You have \(\frac{1}{4}\) pint of whole milk and 1\(\frac{1}{2}\) cups of skim milk. Do you have enough milk for the recipe?

Answer: Given that , a recipe calls for 2 × 1/4 cups of milk
Explanation: 2 × 1/4 => 1/2 = 0.5 cups of milk
you have 1/4 pint of milk = 0.25 pints
0.25 pints = 0.5 cups
and 1 × 1/2 cups of skim milk => 1/2 = 0.5 cups
Recipe calls for 0.5 cups of milk
Yes, we have enough milk for the recipe.

Understand the Problem

What do you know?

• The recipe calls for 2 cups of milk.
• You have \(\frac{1}{4}\) pint of whole milk and 1\(\frac{1}{2}\) cups of skim milk.

What do you need to find?

You need to find whether you have enough milk for the recipe.
Answer: Given that recipe calls for 2 cups of milk
you have 1/4 pint of whole milk => 1/4 pint = 0.25 pint
0.25 pint = 0.5 cups
and 1 × 1/2 cups of skim milk => 1/2 cups = 0.5 cups
adding cups values => 0.5 + 0.5 = 1
So, you don’t have enough milk for the recipe .

Make a Plan
How will you solve?

• Convert \(\frac{1}{4}\) pint of whole milk to cups.
• Add the amounts of whole milk and skim milk.
• Compare the amount of milk you have to the amount needed.

Solve
Step 1: Convert \(\frac{1}{4}\) pint to cups.

Step 2: Add the amounts of whole milk and skim milk.


Answer: So, you _1.5_cups have enough milk for the recipe.
2/4 cups = 1/2
1/2 = 0.5 cups

Show and Grow

Question 1.
Explain how you can check whether the answer above is reasonable.
Answer:  By calculating we get whole milk = 0.5 cups
By calculating we get skim milk =  0.5 cups
By adding whole milk and skim milk => 0.5 + 0.5 = 1 cup

Apply and Grow: Practice

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

Question 2.
Your friend buys 1 pound of walnuts, 16 ounces of peanuts, and \(\frac{1}{2}\) pound of cashews. How many ounces do the nuts weigh in all?
Answer: Given walnuts = 1 pounds
peanuts = 16 ounces
cashews = 1/2 pounds
we have to find weight of all nuts in ounces
Explanation: walnuts = 1pounds
converting pounds to ounces
1 pounds = 16 ounces
peanuts = 16 ounces
cashews = 1/2 pounds
converting pounds to ounces
1/2 pounds = 8 ounces
Adding peanuts , cashews , walnuts weight = 16 + 8 + 16 = 40 ounces
The nuts weigh in all = 40 ounces

Question 3.
A bottle of orange juice contains 64 fluid ounces. How many cups of orange juice are in 3 bottles?

Understand the problem. Then make a plan. How will you solve? Explain.
Answer:
Given that a bottle of orange juice contains = 64 fluid ounces.
Converting 64 fluid ounces to cups
64 fluid ounces = 8 cups
8cups × 3 bottles = 8 × 3 = 24 cups

Question 4.
Your friend wants to buy curtains that hang from the top of the window to the floor. Curtain lengths are typically measured in inches. What length curtains should he buy?

Answer:
Given the length ( ft ) values in figure
we have to measure ft value in inches
5 ft = 60 inches
3 ft = 36 inches  ( He should by 60 inches and 30 inches length curtains ).

Question 5.
Your friend runs a total distance of 1 kilometer at track practice by running 100-meter hurdles. How many times does he run the hurdles?
Answer: Given your friend runs a total distance = 1 km
Convert 1 km to meters
1 km = 1000 meters
your friend practice 100 meter hurdles by running
so 100 × 10 = 1000
so , 10 times he run the hurdles

Question 6.
A trailer can carry 13\(\frac{1}{2}\) tons. It has room to carry 6 cars at once. Can the trailer carry 6 cars that each weigh 3,800 pounds? Explain.

Answer: Convert tons to pounds
13 × 1/2 tons = 13000 pounds
Given total 6 cars
each car weigh 3,800 pounds
so, 6 cars × 3,800 pounds = 6 × 3,800 = 22,800 pounds
so, the trailer cannot carry 6 cars at once

Question 7.
DIG DEEPER!
You walk your dog 4 laps around the block each day. Each block is 400 meters. How many total kilometers do you walk your dog around the block after 35 weeks?
Answer: Given, you walk your dog around the block each day = 4 laps
Each block = 400 meters

Explanation: There are 7 days in a week
given 35 weeks
4 × 400 × 7 × 35 = 392000 meters
Convert 392000 meters to km
392000 meters = 392 km
Therefore, 392 km you walk your dog around the block after 35 weeks

Think and Grow: Modeling Real Life

Example
A crew member needs to put a temporary fence around the perimeter of the rectangular football field. How many feet of temporary fencing does the crew member need?
Think: What do you know? What do you need to find? How will you solve?

Step 1: Convert the length of the field to feet.
There are __ feet in 1 yard.
120 × __ = __
The length of the field is __ feet.
Step 2: Use a formula to find the perimeter of the field.

Show and Grow

Question 8.
An artist puts a wood border around the perimeter of the rectangular mural. How many feet of wood does the artist need?

Answer: 1 yard = 3 feet
Given 10/3 yd = 3.33 yd
3.33 yd × 3 = 9.99 feet
perimeter of rectangular mural
p = ( 2 × L ) + ( 2 × W )
=  2 ×  8 + 2 × 9.99
= 16 + 19.98
= 35 feet
Artist need 35 feet of wood .

Question 9.
DIG DEEPER!
The sports jug contains 5 gallons of water. The paper cup holds 8 fluid ounces of water. How many paper cups can 3 sports jugs fill? Justify your answer.

Answer: Convert 5 gallons of water to fluid ounces

Explanation:
5 gallons = 640 fluid ounces
Given paper, cup holds = 8 fluid ounces of water
1 sport jug = 5 gallons
3 sport jugs = 3 × 5 = 15 gallons
15 gallons = 1920 fluid ounces
8 × 240 = 1920
240 paper cups can fill 3 sports jug .

Problem Solving: Measurement Homework & Practice 11.7

Understand the problem. Then make a plan. How will you solve? Explain.

Question 1.
A robotic insect has a mass of 80 milligrams. The mass of a quarter is 5.67 grams. How many more grams is the mass of a quarter than the mass of the robotic insect?

Answer: Given robotic insect mass = 80 milligrams
The mass of quarter = 5.67 grams
Convert 80 milligrams to grams
80 milligrams = 0.008 grams
subtract 5.67 grams – 0.008 grams = 5.662
Therefore the mass of quarter  5.662 grams is more than the mass of robotic insect

Question 2.
Newton pours water out of a filled 2-liter beaker. Now it only has 1,025 milliliters of water in it. How many milliliters of water did Newton pour out?
Answer: Given newton pours water out of a filled beaker = 2 Liters

Explanation:
Now it has water = 1,025 milliliters
Convert 2 Liters to millimeters
2 liters = 2000 milliliters
2000 – 975 = 1,025
Newton pour out  975 millimeters of water

Question 3.
You run 5 laps around a track. Each lap is 400 meters. How many total kilometers do you run?
Answer: Given you run 5 laps around a track
Each lap = 400 meters

Explanation:
5 × 400 = 2000 meters
convert meters to kilometers
2000 meters = 2 kilometers
Therefore you run 2 kilometers

Question 4.
Two hotel workers have a total of 30 bags of luggage each weighing 50 pounds. One worker weighs 150 pounds, and the other weighs 210 pounds. Can they transfer themselves and all of the bags in the elevator at once? Explain.

Answer:
Given in figure elevator weight limits = 2.5 tons

Explanation:
Convert 2.5 tons to pounds
2.5 tons = 5000 pounds
Given works have total 30 bags
1 bag weight = 50 pounds
30 bags weight = 50 × 30 = 1500 pounds
Given one worker weight = 150 pounds
second worker weight = 210 pounds
By adding all the values 1500 + 150 + 210 = 1860 pounds
Yes, they can transfer themselves and all of the bags in the elevator once.
Question 5.
DIG DEEPER!
You have 84 feet of streamers. You cut 24 pieces that are \(\frac{1}{2}\) each yard long. How many feet of streamers do you have left?
Answer:
Given steamers = 84 feet
24 pieces are 1/2 = 0.5 each yard long
24 × 0.5 = 12 yard long
12 yards = 36 feet
84 – 36 = 48 feet of streamers you have left .

Question 6.
Writing
Write and solve a two-step word problem involving units of measure.

Question 7.
Modeling Real Life
You want to hang a wallpaper border around the perimeter of the rectangular bathroom shown. How many yards of wallpaper border do you need?

Answer:
Given length = 6 ft , width = 1 y

Explanation:
Convert 6 ft to yd
6 ft = 2 yd
perimeter of rectangle = 2 (L + W)
= 2(2 + 1 )
= 2(3) = 6 yd
6 yd of wallpaper border you need

Question 8.
DIG DEEPER!
You need gallon of fertilizer to cover a lawn. What is the least amount of money that you can pay and have enough fertilizer?

Answer: Given one lawn fertilizer is 128 fluid ounces

Explanation:
Take 2 gallons = $ 40 × 2 = 80
Given another lawn fertilizer 16 fluid ounces
2 gallons = $ 11 × 16 = 176
80 is the least amount of money that you can pay and have enough fertilizer
128 fluid ounces is cheap when compared to 16 fluid ounces.

Review & Refresh

Divide. Then check your answer.

Question 9.

Answer: 5,343 divide by 25
5,343 ÷ 25 = 213.72

Question 10.

Answer: 2,064 divide by 24
2,064 / 24 = 86

Convert and Display Units of Measure Performance Task 11

Passenger airliners come in many different sizes. Plane A and Plane B are two different types of wide-body jet airliners.

Question 1.
The table shows some facts about Plane A.
a. The length of Plane B is 80 yards. Which is longer, Plane A or Plane B? How much longer?

Answer:- Given, length of plane B = 80 yards
We observed from the table that the length of plane A = 250 ft 2 in
Convert 250 ft 2 into yards
250 ft 2 in = 83.389 yards
So, Length of plane A = 83.389 yards
Length of plane B = 80 yards
Plane A is longer than Plane B
3.389  is longer.
b. The wingspan of Plane B is 37\(\frac{1}{12}\) feet longer than the Wingspan of Plane A. What is the wingspan of Plane B?
Answer: The wingspan of plane B = 37 × 1/2 = 36.852  inches

Question 2.
Before an airliner can take off, the pilot has to make sure it weighs less than the maximum takeoff weight.
a. Plane A weighs 404,600 pounds and can carry at most 422,000 pounds of fuel. How many pounds can the airliner hold in passengers and cargo?
b. The maximum landing weight of Plane A is 300,000 pounds less than the maximum takeoff weight. Why does an airliner weigh less at the end of a flight than at the beginning?
c. Plane A uses 20 quarts of fuel for each mile it flies. How many gallons of fuel does the plane use during a 3,200-mile flight?

Question 3.
Plane B can hold 544 passengers. Plane A can hold \(\frac{3}{4}\) of passengers that Plane B can hold.
a. How many passengers can Plane A hold?
Answer: Plane A hold 3/4 = 0.75 passengers

b. An airline estimates that each passenger weighs about 200 pounds, including carry-on baggage. How much passenger and carry-on weight does the airline estimate for Plane B?
Answer: 408 passenger and carry on weight does the airline estimate for plane B

Convert and Display Units of Measure Activity

Directions:

1. Players take turns.
2. On your turn, place a counter on a yellow hexagon.
3. Solve for the missing measurement and cover the answer with another counter. If you surround a monster, then put a counter on the monster. If you do not surround a monster, then your turn is over.
4. Continue playing until all measurements are covered.
5. The player who captures the most monsters wins!

Convert and Display Units of Measure Chapter Practice

11.1 Length in Metric Units

Convert the length.

Question 1.
4 cm = __ mm
Answer: 4 cm = 40 mm

Explanation:
Convert from centimeter to millimeter
1 cm = 10 mm
4 cm = 4 × 10 mm = 40 mm
multiply the cm value by 10

Question 2.
81 m = _8100__ cm
Answer: 81 m = 8100 cm

Explanation:
Convert from meter to centimeter.
1 m = 100 cm
multiply the m value by 100
81 m = 81 × 100 cm = 8100 cm

Question 3.
0.56 km = _56000_ cm
Answer: 0.56 km = 56000 cm

Explanation:
Convert from kilometer to centimeter.
Multiply the km value by 100000

Question 4.
9 mm = 0.009__ m
Answer: 9 mm = 0.009 m
Explanation:-
Convert millimeter to meter.
divide the mm value by 1000

Compare.

Question 5.

Answer:- 73 m = 0.073 kilometer
Explanation:- divide the m value by 1000
Answer:- 7.3 km = 7300 m
Explanation:- multiply the km value by 1000

Question 6.

Answer:
0.6 cm = 0.006 m
divide the cm value by 100
0.06 m = 6 cm
multiply the m value by 100

Question 7.

Answer:
2mm = 0.2 cm
divide the mm value by 10
0.2 cm = 2mm
multiply the cm value by 10

11.2 Mass and Capacity in Metric Units

Convert the mass.

Question 8.
3 kg = _3000__ g
Answer:
3 kg = 3000 g
Explanation:
Convert from kg to gram
1 kg = 1000 grams
multiply the kg value by 1000
3 kg = 3 × 1000 gram = 3000 gram

Question 9.
0.006g = _6__ mg
Answer: 0.006 g = 6 mg

Explanation:
Convert from grams to milligrams
multiply the g value by 1000

Question 10.
70 g = _0.07_ kg
Answer: 70 g = 0.07 kg

Explanation:
Convert from grams to kilograms
divide the g value by1000

Question 11.
29,000 mg = _0.029_ kg
Answer: 29,000 mg = 0.029 kg

Explanation:
Convert from milligrams to kilograms
divide the mg value by 1e + 6
29,000 mg = 0.029 kg

Convert the capacity.

Question 12.
400 mL = _0.4_ L
Answer: 400 mL = 0.4 L

Explanation:
Convert from milliliters to liters
divide the mL value by 1000

Question 13.
10 L = 10000 mL
Answer: 10 L = 10000 mL

Explanation:
Convert from liters to milliliters
1 L = 1000 ml
10 L = 10 × 1000 = 10000 mL
multiply the L value by 1000

Question 14.
7 mL =0.007 L
Answer: 7 mL = 0.007 L

Explanation:
Convert from milliliters to liters
divide the mL value by 1000
7 mL = 0.007 L

Question 15.
0.65 L = 650mL
Answer: 0.65 L = 650 mL

Explanation:
Convert from liters to milliliters
1 L = 1000 mL
multiply the L value by 1000
0.65 L = 0.65 × 1000 = 650 mL
So, 0.65 L = 650 mL

11.3 Length in Customary Units

Convert the length.

Question 16.
2 mi = ___ yd
Answer: 2 mi = 3520 yards

Explanation:
Convert from miles to yards
1 mi = 1760 yards
multiply the mi value by 1760
2 mi = 2 × 1760 yards = 3520 yards

Question 17.
14\(\frac{2}{3}\) yd = ___ ft
Answer: 14 × 2/3 yd = 28 ft

Question 18.
103 in. = __ ft __ in.
Answer: 103 in = 8 ft 7 in

Explanation:
Convert from inches from feet.
divide the 103 in value by 12

Question 19.
2,340 in. = yd
Answer: 2,340 in = 65 yd

Explanation:
Convert from inches to yards
divide the 2,340 in value by 36

Compare.

Question 20.

Answer: 5 × 2/3 yd = 10 ft
17 ft = 5.667 yd

Explanation:
Convert yards to feet.
divide the 17 ft value by 3

Question 21.

Answer: 67 in = 5 feet 7 inches

Explanation:
divide the in value by 12
5 ft 10 in = 70 in
multiply the 5 ft 10 in value by 12

Question 22.

Answer:
16 mi = 84480 ft
multiply the mi value by 5280
84,000 ft = 15.909 mi
divide the ft value by 5280

Weight in Customary Units

Convert the weight.

Question 23.

Answer: 4/2 T = 2 (By solving 4/2 we get 2)
so we take 4/2 as 2
1 T = 2000 lb
2 T = 4000 lb

Question 24.
100,000 lb = ___ T
Answer: 100,000 lb = 45.359237 T

Explanation:
100,000 lb × 0.00045359237 = 45.359237 T

Convert the weight.

Question 25.
217 oz = __ lb __ oz
Answer: 217 oz = 13 lb 9 oz

Question 26.
956 oz = __ lb
Answer:  956 oz = 59 lb

Compare.

Question 27.

Answer: 5×1/4 T = 2755 lb
15,000 lb = 6.696 T

Question 28.

Answer: 258 oz = 16.125 lb
divide the oz value by 16
17 lb 12 oz = 284 oz
multiply the lb oz value by 16

Question 29.

Answer: 192,000 oz = 6 T
7 T = 250,880 oz

Question 30.
Number Sense
Which measurements are equivalent to 52 ounces?

Answer: 3 lb 4 oz measurement is equivalent to 52 ounces.

11.5 Capacity in Customary Units

Convert the capacity.

Question 31.
18 qt = __ pt
Answer: 18 qt = 29.9762706 pt

Explanation:
1qt equals to 1.6653484 pt
1.6653484 × 18pt = 29.9762706 pt

Question 32.

Answer: 24 fl oz

Explanation:
4 × 3/4c , by solving this we get 12/4c=3c
from formula= 1c = 8 floz
3c = 8 fl oz × 3c = 24 floz

Question 33.
72 pt = __ gal
Answer: 72 pt = 9 gal

Explanation:
1 pt = 0.125 gal
72 pt = 0.125 × 72 = 9 gal

Question 34.
81 qt = __ gal
Answer: 81 qt = 20.25 gal

Explanation:
1 qt = 0.25 gallons
81 qt = 81 × 0.25 = 20.25 gal

Compare.

Question 35.

Answer:
5/4 gal = 5 US qt
multiply the gal value by 4
21 qt = 5.25 US gal
divide the qt value by 4

Question 36.

Answer:
Convert from pints to cups
7/2 pt = 7 c
9 c > 7 c
3 1/2 pt < 9 c

Question 37.

Answer:–
Convert from quart to cups.
1 quart = 4 cups
4 qt = 16 c
4 qt < 20 c

Question 38.
Modeling Real Life
You have 2\(\frac{1}{4}\) gallons of apple juice. How many pints of apple juice do you have?

Answer: Given 2 × 1/4 (gallons of apple juice)
By solving 2 × 1/4 we get 1/2=>0.5 gallons
so, we have 4 pints of apple juice

Explanation:
we have to find out pints of apple juice
0.5 gallons is equal to 4 pints
from the formula multiply the gallon value (i.e., 0.5 with 8 = 0.5 × 8 = 4 pints)
11.6 Make and Interpret Line Plots

Question 39.
The table shows the amounts of clay made by 10 students. Make a line plot to display the data.

How many students made more than \(\frac{3}{4}\) cup of clay?
Answer:  3/4 = 0.75
only one student ( 7/8 )made more than 3/4 cup of clay ( i.e., 7/8 = 0.875 )

What is the most common amount of clay made?
Answer: The most common amount of clay made is 3/4

11.7 Problem Solving: Measurement

Question 40.
A recipe calls for 2\(\frac{3}{4}\) cups of fava beans. You have 1\(\frac{1}{4}\)– pint can of fava beans and \(\frac{1}{2}\) cup of cooked fava beans. Do you have enough fava beans for the recipe?

Answer: Yes, you have enough fava beans for the recipe

Explanation:
Given that a recipe calls for 2 × 3/4 = 0.5 cups of fava beans
you have 1 × 1/4 pints = 0.5 cups of fava beans ( convert 1/4 pints to cups )
and 1/2 = 0.5 cups of cooked fava beans
So, the recipe calls 0.5 cups of fava beans are equal to you have 0.5 cups of fava beans.

Convert and Display Units of Measure Practice 1-11

Question 1.
Your friend estimates that a bookcase is 2\(\frac{1}{2}\) feet wide. The actual width is \(\frac{2}{3}\) foot longer. What is the width of the bookcase?
Answer: 2 × 1/2 = 1 estimation feet
2/3 = 0.667 actual width feet
1 – 0.667 = 0.34

Question 2.
What is the product of 845 and 237?

Answer: Option C
product (Multiply) the 845 and 237 = 200,265

Explanation:  845 × 237 = 200,265

Question 3.
How many milliliters are equal to 0.6 liter?

Answer:-  Option D  (600 mL)

Explanation: 1 liter = 1000 mL
0.6 liter = 0.6L × 1000mL
= 600mL

Question 4.
Which are equivalent to ?

Answer:  6 × 3/10  is equivalent to 18 × 1/10

Explanation:
6 × 3/10 = multiply 6 with 3 we  get 18, denominator remains same
so the answer is 18 × 1/10.

Question 5.
To find 34 + (16 + 23), your friend adds 34 and 16. Then she adds 23 to the sum. Which property did she use?

Answer:-  Option B
She used the Associative property of addition.

Question 6.
An Eastern Hognose Snake is 2\(\frac{1}{2}\) feet long. It grows another foot. What is the new length of the snake in inches?

Answer: 2 × 1/2 = 1 feet

Explanation:
It grows another foot = 1
so, 1 + 1 = 2 feet
convert 2 feet to inches
2 feet = 24 inches
So, the new length of the snake is 24 inches.

Question 7.
What common factor should you divide the numerator and denominator of \(\frac{16}{24}\) by so that it is in the simplest form?

Answer: 8 is the common factor that divides the numerator and denominator of 16/24 in simplest form

Explanation:
The simplest form is nothing but if the top and bottom(i.e., numerator and denominator) have no common factors other than 1.
16/24 = solve it by 8
By solving we get 2/3.

Question 8.
A salesperson at a fabric store has 30 yards of fabric. He puts the same number of yards of fabric on each of 4 rolls for a display. How many yards of fabric does the salesperson put on each roll?

Answer:
Option B
2/15 yard

Explanation:
Given 30 yards of fabric
rolls= 4
rolls/yards = 4/30 = 2/15yard

Question 9.
Descartes estimates 96.3 × 42 by rounding each number to the nearest ten. What is Descartes’s estimate?

Answer: Option D (4,000)

Explanation: Here we have to multiply the given number 96.3 × 42
96.3 ~ 100 (96.3 is the nearest value to 100)
42~40 (42 is the nearest value to 40)
so, multiply both the values 100 × 40 = 4000

Question 10.
The fifth-grade classes are making a mural to hang in the front hallway of the school.

Part A Each class creates a square for the mural that has side lengths of \(\frac{1}{2}\) meter. What is the area of each square?

Answer: area of square =s×s
1/2 × 1/2 = 0.5 × 0.5 = 0.25 meters
Part B
There are 12 classes. What is the area of the entire mural? Explain.
12 × 0.25 = 3 meters

Question 11.
Which expressions have a quotient of 4.6?

Answer: All expressions have a quotient of 4.6 except 15.64÷34 does not have a quotient of 4.6

Explanation: we can find out the quotient value by this method
quotient = Dividend ÷ divisor  (i.e., from the above question we are taking one value                                                                                      124.2 ÷ 27 = 4.6)

Question 12.
What is the quotient of 5 and \(\frac{1}{8}\) ?

Answer:- The quotient of 5 and 1/8 = 40
Explanation:- Divide the 5 and 1/8

Question 13.
You need thirty 5-foot pieces of string for a project. A store sells string by the yard. How many yards of string will you need to buy?
Answer:- 11.655

Explanation: Given foot pieces = 35
1 foot = 0.333 yard
1 yard = 3 foot or 3 feet
we have to find yards of string.
foot pieces × yards = 35 × 0.333
= 11.655

Question 14.
In which equations does k = \(\frac{3}{4}\) ?

Answer:  Option D
3/6 × 3/2 =k

Explanation:
we have equated k value as 3/4
so, by solving 3/6 × 3/2 we get 3/4

Question 15.
Newton brings 3 bags of popcorn that are all the same size to a club. There are 12 people at the club. Each person eats the same amount of popcorn and all of the popcorn is eaten. What fraction of a bag of popcorn does each person eat?


Answer: Bags = 3 ,  People = 12
so, divide 3/12 = 1/4
Option A is the answer

Question 16.
Evaluate

Answer:
Convert the decimal values to fractions
4.5 = 9/2
13.68 = 342/25
13.70 = 137/10
15.70 = 157/10

Question 17.
What is the sum of \(\frac{5}{6}\) and \(\frac{1}{4}\) ? 
Answer: Option D
5/6 + 1/4 = 13/12

Question 18.
What is 40,071 written in word form?
A. four thousand, seventy-one
B. four hundred, seventy-one
C. forty thousand, seventy-one
D. forty thousand, seven hundred ten
Answer: Option C

Forty thousand, seventy-one

Convert and Display Units of Measure STEAM Performance Task

Sound is created from vibrations in the air called sound waves. In music, when you hear different pitches, it is because the sound waves are traveling at different speeds. The frequency of a pitch measures the number of sound waves per second. Higher pitches have higher frequencies, and lower pitches have lower frequencies. Frequencies are measured in Hertz.

Question 1.
A₄ is the musical note commonly used to tune instruments. The frequency of A₄ is 440 Hertz, because the sound vibrates 440 times per second.
a. The frequency of A₃ is \(\frac{1}{2}\) the frequency of A₄. The frequency of A₂ is \(\frac{1}{2}\) the frequency of A₃. What is the frequency of A₂?
Answer: frequency of A₂ = 110
b. Is the pitch of A₂ higher or lower than the pitch of A₄? Explain.
c. How can you use the frequency of A₄ to find the frequency of A₅? Explain.
d. The frequency of B₄ is 493.88 Hertz. What is the frequency of B₃?
e. A computer software program can correct the frequency of a sound so it has perfect pitch. A violin plays a note that has a frequency of 255.1 Hertz. Explain how to change the frequency so it has the pitch of B₃.

Question 2.
Use the Internet or some other resource to learn about how audio processors can help to correct a singer’s pitch, or to alter the way a song sounds. Write one interesting thing you learn.
Answer:
Auto-Tune is an audio processor introduced in 1997 by and registered trademark of Antares Audio Technologies, which uses a proprietary device to measure and alter pitch in vocal and instrumental music recording and performances. It was originally intended to correct off-key inaccuracies, allowing vocal tracks to be perfectly tuned despite originally being slightly off-pitch.
Pitch correction is an electronic effects unit or audio software that changes the highness and lowness in pitch of an audio signal so that all pitches will be notes from the equally tempered system(i.e., like the pitches on a piano). Pitch correction first detects the pitch of an audio signal (using a live pitch detection algorithm), then calculates the desired change and modifies the audio signal accordingly. The widest use of pitch corrector devices is in western popular music on vocal lines.

Question 3.
You borrow a guitar to learn how to play. Use the Guitar table to decide which guitar you should borrow.

a. Based on your height, you need a guitar that is close to 1 yard long. Which guitar is closer?
Answer: 1 yard = 36 inches
Guitar A is 37 inches
So, Guitar A is closer
b. You also need a guitar that is close to 8 pounds. Which guitar do you think you should borrow? Explain.
Answer: Guitar B you should borrow
176 ounces = 11 pounds which is closer to 8 pounds .
c. Guitar B is called a full-size guitar and Guitar A is called a \(\frac{7}{8}\)-size guitar. Is the length of Guitar A \(\frac{7}{8}\) the length of Guitar B? Explain
Answer: From the table Length of Guitar B = 40 inches
Given guitar A = 7/8 = 10.5 inches
No, the length of Guitar A is not equal to Guitar B
d. The scale length on a guitar affects the pitch. To find the scale length of a guitar, multiply the distance between the nut and the 12th fret by 2. On your guitar, that distance is 12\(\frac{3}{4}\) inches. What is the scale length of your guitar?
Answer: 9 × 12 × 2 = 216
The scale of the length of the guitar is 216

e. The strings on your guitar are \(\frac{3}{8}\) inch longer than the scale length to allow you to tune the strings to correct pitch. What are the string lengths on your guitar?
Answer:- The string length on your guitar = 3/8
3/8 = 4.5 inches
f. When you tune a string, you adjust it tighter to make the pitch higher, or looser to make pitch lower. You use a tuning instrument to help you string has a tune your guitar. It says that your A₄ string has a frequency of 436.2 Hertz. How should you adjust the string to get the pitch in tune?
Answer:- we have to adjust the string to get the pitch in tune = 440 Hertz
its  wavelength (cm) = 78.41

Conclusion:

I wish the information provided in the above article regarding the Big Ideas Math Answers Grade 5 Chapter 11 Convert and Display Units of Measure is helpful for all the students. For any queries, you can post your doubts in the below comment section. Keep in touch with us to get the latest updates of all Big Ideas Math Grade 5 Chapters.

Searching for the best material for Integers, Number Lines, and Coordinate Plane? If yes, then there is a one-stop solution for your search. We are providing the Big Ideas Math Book 6th Grade Answers Ch 8 Integers, Number Lines, and the Coordinate Plane pdf in the next sections. Follow our material and make your preparation as expected. You can easily score marks if you practice all the problems of BIM 6th Grade Answer Key which gives the step by step solution to all the problems. Scroll to the next sections to find various details like tasks, examples, answer keys, free pdf’s and so on.

Big Ideas Math Book 6th Grade Answer Key Chapter 8 Integers, Number Lines, and the Coordinate Plane

Big Ideas Math Book 6th Grade Answer Key Chapter 8 Integers, Number Lines, and the Coordinate Plane free pdf is here. Download BIM 6th Grade Chapter 8 Solution Key pdf from the below given links. If you are really worried about your preparation, then definitely you have to check this article. Because we are providing all the tips and tricks to solve the problems. Before starting your practice, understand all the concepts and learn each and every small topic, so that you can overcome all your weakess and score better marks. Follow all the concepts involving Integers, Comparing and Ordering Integers, Rational Numbers etc.

Performance Task

• Integers, Number Lines, and the Coordinate Plane STEAM Video/Performance Task
• Integers, Number Lines, and the Coordinate Plane Getting Ready for Chapter

Lesson: 1 Integers

• Lesson 8.1 Integers
• Integers Homework & Practice 8.1

Lesson: 2 Comparing and Ordering Integers

• Lesson 8.2 Comparing and Ordering Integers
• Comparing and Ordering Integers Homework & Practice 8.2

Lesson: 3 Rational Numbers

• Lesson 8.3 Rational Numbers
• Rational Numbers Homework & Practice 8.3

Lesson: 4 Absolute Value

• Lesson 8.4 Absolute Value
• Absolute Value Homework & Practice 8.4

Lesson: 5 The Coordinate Plane

• Lesson 8.5 The Coordinate Plane
• The Coordinate Plane Homework & Practice 8.5

Lesson: 6 Polygons in the Coordinate Plane

• Lesson 8.6 Polygons in the Coordinate Plane
• Polygons in the Coordinate Plane Homework & Practice 8.6

Lesson: 7 Writing and Graphing Inequalities

• Lesson 8.7 Writing and Graphing Inequalities
• Writing and Graphing Inequalities Homework & Practice 8.7

Lesson: 8 Solving Inequalities

• Lesson 8.8 Solving Inequalities
• Solving Inequalities Homework & Practice 8.8

Chapter: 8 – Integers, Number Lines, and the Coordinate Plane

• Integers, Number Lines, and the Coordinate Plane Connecting Concepts
• Integers, Number Lines, and the Coordinate Plane Chapter Review
• Integers, Number Lines, and the Coordinate Plane Practice Test
• Integers, Number Lines, and the Coordinate Plane Cumulative Practice

Integers, Number Lines, and the Coordinate Plane STEAM Video/Performance Task

STEAM Video

Designing a CubeSat
A CubeSat is a type of miniature satellite that is used for space research. Each CubeSat has the dimensions shown and a mass of no more than 1.33 kilograms.

Watch the STEAM Video “Designing a CubeSat.” Then answer the following questions.
1. For what fields of study do you think CubeSats can be used?
2. Tony says g-forces are a measure of how heavy you feel.  e table shows the g-forces on a CubeSat at three points in time. Why can g-forces be as high as 6 during a rocket launch and as low as 0 in space?

3. What would happen to a CubeSatthatcannot withstand a g-force of 6? a g-force of 0?

Performance Task

Launching a CubeSat
After completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given information about three different types of Cubesats that you can purchase.

You will determine which of the three CubeSats is the best option for a mission. Why might g-force, pressure, and temperature be important considerations for making your decision?

Integers, Number Lines, and the Coordinate Plane Getting Ready for Chapter

Chapter Exploration
Question 1.
Work with a partner. Plot and connect the points to make a picture.

Answer:

Question 2.
Create your own “dot-to-dot” picture. Use at least 20 points.
Answer:

Vocabulary
The following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.
negative numbers
opposites
inequality
quadrants

Lesson 8.1 Integers

Exploration 1

Reading and Describing Temperatures
Work with a partner. The thermometers show the temperatures in four cities.
Honolulu, Hawaii
Anchorage, Alaska
Death Valley, California
Seattle, Washington
a. Match each temperature with its most appropriate location.

Answer:
Honolulu, Hawaii  – 110 degrees Fahrenheit
Anchorage, Alaska – 0 degrees Fahrenheit
Death Valley, California – 80 degrees Fahrenheit
Seattle, Washington – 40 degrees Fahrenheit

b. What do all of the temperatures have in common?
Answer :
Measuring in degrees fahrenheit and Readings

c. What does it mean for a temperature to be below zero? Provide an example. Can you think of any other situations in which numbers may be less than zero? Maintain OversightHow does this exploration help you represent numbers less than 0?
Answer:
Temperature to be below zero means cold weather starts .
Example:
When used by weather forecasters in the U.S., it means “below 0°F”. ( It essentially means, “It’s gonna be cold; bring your mittens and a warm hat.”

d. The thermometers show temperatures on a vertical number line. How else can you represent numbers less than zero? Provide an example.
Answer:

Positive numbers are greater than 0. They can be written with or without a positive sign (+).
1 5 20 10,000

Negative numbers are less than 0. They are written with a negative sign (−).
-1 -5 -20 -10,000

Two numbers that are the same distance from 0 on a number line, but on opposite sides of 0, are called opposites. The opposite of 0 is 0.

Try It

Write a positive or negative integer that represents the situation.
Question 1.
A hiker climbs 900 feet up a mountain.
Answer:
+900, 900 feet
Explaination :
Positive numbers are greater than 0. They can be written with or without a positive sign (+).

Question 2.
You have a debt of $24.
Answer:
-24
Explaination :
Debt is an amount of money borrowed by one party from another.
Debt of $24 is represented as -24.

Question 3.
A student loses 5 points for not showing work on a quiz.
Answer:
-5
Explaination :
lose is a another meaning of negative.
Student loses 5 points is indicated as -5.

Question 4.
A savings account earns $10.
Answer:
+10
Explaination :
Earns is another vocabulary to positive.
earns $10 is represented as +10 or 10.

Graph the integer and its opposite.
Question 5.
6
Answer:
(6, -6)
Explanation:
For any given integer ‘a’, the opposite integer is found at the same distance from 0 on the number line, but on the other side.
So, the opposite integer of integer ‘a’, is ‘-a’ on the number line, but on the other side of 0.

Question 6.
-4
Answer:
(4, -4)
Explanation :
For any given integer ‘a’, the opposite integer is found at the same distance from 0 on the number line, but on the other side.
So, the opposite integer of integer ‘a’, is ‘-a’ on the number line, but on the other side of 0.

Question 7.
-12
Answer:
(12, -12)
Explanation :
For any given integer ‘a’, the opposite integer is found at the same distance from 0 on the number line, but on the other side.
So, the opposite integer of integer ‘a’, is ‘-a’ on the number line, but on the other side of 0.

Question 8.
1
Answer:
(1, -1)
Explanation :
For any given integer ‘a’, the opposite integer is found at the same distance from 0 on the number line, but on the other side.
So, the opposite integer of integer ‘a’, is ‘-a’ on the number line, but on the other side of 0.

Self-Assessment for Concepts & Skills

Solve each exercise. Then rate your understanding of the success criteria in your journal.

WRITING INTEGERS Write a positive or negative integer that represents the situation.
Question 9.
A baseball is thrown at a speed of 78 miles per hour.
Answer:
+78
Explanation :
A baseball is thrown at a speed of 78 miles per hour. So, thrown indicated +ve
+78 or 78.

Question 10.
A submarine is 3750 feet below sea level.
Answer:
-3750
Explanation :
submarine is 3750 feet below sea level. so, below indicates -ve
-3750

GRAPHING INTEGERS Graph the integer and its opposite.
Question 11.
8
Answer:
(8, -8)
Explaination :
For any given integer ‘a’, the opposite integer is found at the same distance from 0 on the number line, but on the other side.
So, the opposite integer of integer ‘a’, is ‘-a’ on the number line, but on the other side of 0.

Question 12.
– 7
Answer:
(7 -7)
Explaination :
For any given integer ‘a’, the opposite integer is found at the same distance from 0 on the number line, but on the other side.
So, the opposite integer of integer ‘a’, is ‘-a’ on the number line, but on the other side of 0.

Question 13.
11
Answer:
(11, -11)
Explaination :
For any given integer ‘a’, the opposite integer is found at the same distance from 0 on the number line, but on the other side.
So, the opposite integer of integer ‘a’, is ‘-a’ on the number line, but on the other side of 0.

Question 14.
VOCABULARY
Which of the following numbers are integers?
18, 4.1, -9, \(\frac{1}{6}\) , 1.75, 22
Answer:
An integer is defined as a number that can be written without a fractional component.

18, -9, 22

Question 15.
VOCABULARY
List three words or phrases used in real life that indicate negative integers.
Answer:

minus , below , down , debt, low.

Question 16.
WRITING
Describe the opposite of a positive integer, the opposite of a negative integer, and the opposite of zero.
Answer:
Opposite of positive integer is negative integer.
A negative integer is a whole number that has value less than zero. Negative integer are normally whole numbers, for example, -3, -5, -8, -10 etc
Opposite of negative integer is positive integer.
The positive integer are the numbers 1, 2, 3, … , sometimes called the counting numbers or natural numbers, for example , +1, 2 , +3 ……..
Opposite of zero
We do not consider zero to be a positive or negative number. So, zero (0) opposite is zero(0).

Question 17.
The world record for scuba diving is 332 meters below sea level. Write an integer that represents a new world record. Explain.
Answer:
1090 ft is represented as the new world record in scuba diving.
Explanation:
converting m to ft
1 m – 3.2808 ft
332 m – 1090 ft.

Question 18.
The indoor and outdoor temperatures are shown. The freezing point of water is 32°F. Write integers that represent how each temperature must change to reach the freezing point of water. Explain.

Answer:
Given:
Freezing point of water = 32°F
From the pic the outdoor temperature = 25°F
To reach the freezing point of water outdoor we need to increase the temperature outdoor temperature.
32°F -25°F = 7°F
Outdoor temperature should be increased by 7°F.
From the pic indoor temperature= 68°F
Similarly, to reach the freezing point of water indoor we need to decrease the indoor temperature.
68°F -32°F = 36°F
Indoor temperature should be reduced by 36°F.

Question 19.
An ion is an atom that has a positive or negative electric charge. When an ion has more protons than electrons, it has a positive charge. When an ion has fewer protons than electrons, it has a negative charge. Explain what it means for an atom to have an electric charge of zero.

Answer:
When an atom has an equal number of electrons and protons, it has an equal number of negative electric charges (the electrons) and positive electric charges (the protons). The total electric charge of the atom is therefore zero and the atom is said to be neutral.

Integers Homework & Practice 8.1

Review & Refresh

Find the volume of the prism.
Question 1.

Answer:
Given:
Length of cuboid : 4/5 mm
Width of the cuboid: 1/2 mm
Height of the cuboid: 3/8 mm
Volume of the cuboid = l*w*h
\(\frac{4}{5}\)*\(\frac{1}{2}\)*\(\frac{3}{8}\)= (4x1x3)/(5x2x8)=3/20
\(\frac{3}{20}\) cubic mm.

Question 2.

Answer:
Given:
Length of cuboid : 4/5 yd
Width of the cuboid: 5/8 yd
Height of the cuboid: 3/4 yd
Volume of the cuboid = l*w*h
\(\frac{4}{5}\)*\(\frac{5}{8}\)*\(\frac{3}{4}\)= (4x5x3)/(5x8x4)=3/8
\(\frac{3}{8}\) cubic yd.

Question 3.

Answer:
Given:
Length of cuboid : 15/4 ft
Width of the cuboid: 4/3 ft
Height of the cuboid: 8/5 ft
Volume of the cuboid = l*w*h
\(\frac{15}{4}\)*\(\frac{4}{3}\)*\(\frac{8}{5}\)= (15x4x8)/(4x3x5)=8
\(\frac{8}{1}\) cubic ft.

Factor the expression using the GCF.
Question 4.
4m + 32
Answer:
When we find all the factors of two or more numbers, and some factors are the same (“common”), then the largest of those common factors is the Greatest Common Factor. Abbreviated “GCF”.
4m + 32
divide the equation by 4
\(\frac{4m}{4}\) + \(\frac{32}{4}\)
\(\frac{4(m + 8)}{1}\)
4 is the greatest common factor.

Question 5.
18z – 22
Answer:
18z – 22
Take 2 common we get,
2 ( 9z – 11)
2 is the greatest common factor.
Explanation:
When we find all the factors of two or more numbers, and some factors are the same (“common”), then the largest of those common factors is the Greatest Common Factor. Abbreviated “GCF”.

Question 6.
38x + 80
Answer:
38x + 80
Take 2 common we get,
2 ( 19z + 40)
no more possible to simplify so
2 is the greatest common factor.
Explanation:
When we find all the factors of two or more numbers, and some factors are the same (“common”), then the largest of those common factors is the Greatest Common Factor. Abbreviated “GCF”.

Question 7.
42n – 27s
Answer:
42n – 27s
Take 3 common we get,
3 (14n – 9s)
no more possible to simplify so
3 is the greatest common factor.
Explanation:
When we find all the factors of two or more numbers, and some factors are the same (“common”), then the largest of those common factors is the Greatest Common Factor. Abbreviated “GCF”.

Question 8.
The height of a statue is 276 inches. What is the height of the statue in meters? Round your answer to the nearest hundredth.
A. 1.09 m
B. 7.01 m
C. 108.66 m
D. 701.04 m
Answer:
1 inch = 0.025 m
Height of a statue = 276 inches
convert it into meters =276 inch x 0.025 = 7.01 m
So,
B is the answer.

Concepts, Skills, & Problem Solving

OPEN-ENDED Describe a situation that can be represented by the integer. (See Exploration 1, p. 345.)
Question 9.
– 6
Answer:
The Temperature is decreased by 6 °F

Question 10.
12
Answer:
Earned bonus of 12 points

Question 11.
– 45
Answer:
Had lose of 45 coins .

WRITING INTEGERS Write a positive or negative integer that represents the situation.
Question 12.
A football team loses 3 yards.
Answer:
-3
As loses represents negative

Question 13.
The temperature is 6 degrees below zero.
Answer:
below zero indicates negative
-6 degrees

Question 14.
You earn $15 raking leaves.
Answer:
Earn represents positive
+15$

Question 15.
A person climbs 600 feet up a mountain.
Answer:
+600 feet as its up a mountain.

Question 16.
You withdraw$42 from an account.
Answer:
-42$ withdraw from my account.

Question 17.
An airplane climbs to 37,500 feet.
Answer:
An airplane climbs to +37,500 feet

Question 18.
The temperature rises 17 degrees.
Answer:
Temperature rises indicates increase +17 degrees

Question 19.
You lose 56 points in a video game.
Answer:
I lose -56 points from my video game.

Question 20.
A ball falls 350 centimeters.
Answer:
A ball falls -350 centimeters

Question 21.
You receive 5 bonus points in class.
Answer:
I receive +5 points in class.

Question 22.
MODELING REAL LIFE
On December 17, 1903, the Wright brothers accomplished the first powered flight. The plane traveled a distance of 120 feet. Write this distance as an integer.

Answer:
Distance Traveled by the plane = 120 feet.
It means +120 .

Question 23.
MODELING REAL LIFE
A stock market gains 83 points. The next day, the stock market loses 47 points. Write each amount as an integer.
Answer:
+83 = Stock Market gains 83 points.
– 47 = The next day the stock market loses 47 points.

GRAPHING INTEGERS
Graph the integer and its opposite.
Question 24.
– 5
Answer:
The opposite of -5 = +5

Question 25.
– 8
Answer:
The opposite of -8 = +8

Question 26.
14
Answer:
The opposite of 14 = -14

Question 27.
9
Answer:
The opposite of 9 = -9

Question 28.
– 14
Answer:
The opposite of -14 = +14

Question 29.
20
Answer:
The opposite of +20 = -20

Question 30.
– 26
Answer:

Question 31.
18
Answer:
The opposite of 18 is -18

Question 32.
30
Answer:
The opposite of 30 is – 30

Question 33.
– 150
Answer:
The opposite of -150 is 150

Question 34.
– 32
Answer:
The opposite of – 32 is 32

Question 35.
400
Answer:
The opposite of 400 is -400

Question 36.
YOU BE THE TEACHER
Your friend describes the positive integers. Is your friend correct? Explain your reasoning.

Answer:
No
Explanation:
The natural numbers 1, 2, 3, 4, 5, ……… are called positive integers.
Positive numbers are represented to the right of zero on the number line. Positive numbers are greater than negative numbers as well a zero.
Because zero is neither positive nor negative . Zero is a neutral number.

USING A NUMBER LINE Identify the integer represented by the point on the number line.
Question 37.
A
Answer:
The point A is marked at 5

Question 38.
B
Answer:
The point B is marked at -8

Question 39.
C
Answer:
The point C is marked at -15

Question 40.
D
Answer:
The point D is marked at 18

Question 41.
DIG DEEPER!
Low tide, represented by the integer −1, is 1 foot below the average water level. High tide is 5 feet higher than low tide.
a. What does 0 represent in this situation?
b. Write an integer that represents the average water level relative to high tide.

Answer a :
The Low Tide = -1
Average water level = 0
Explanation:
As the low tide is just below average water level . When average water level =0
Then low tide can be – 1
Answer b :
High Tide = 4
Explanation:
High tide is 5 feet higher than low tide so we get
High Tide = -1 + 5 = 4
An integer that represents the average water level relative to high tide = 4

Question 42.
REPEATED REASONING
Consider an integer n.
a. Is the opposite of n always less than 0? Explain your reasoning.
b. What can you conclude about the opposite of the opposite of n? Justify your answer.
c. Describe the meaning of −[−(−n)]. What is it equal to?
Answer a:
Only if n is a positive integer
Explanation:
The integer n is a positive integer then  only the negative integer of n is always less than 0 Positive numbers are represented to the right of zero on the number line and Negative numbers are represented to the left of zero on the number line.

Answer b :
n is a integer . opposite of n is -n and opposite of (opposite of n) = opposite of (-n)= +n

Answer c :
– x – = +
– x + = –
−[−(−n)]= means minus of minus of minus n
−[−(−n)]= – (+ n)= -n

Question 43.
In a game of tug-of-war, a team wins by pulling the flag over its goal line. The flag begins at0. During a game, the flag moves 8 feet to the right,12 feet to the left, and 13 feet back to the right.Did a team win? Explain. If not, what does each team need to do in order to win?

Answer:
Flag begins at 0
After First pull:
The flag moves 8 feet to the right means = 0 + 8 =8
After Second pull:
The flag is at 8 now then it moves 12 feet to the left .
Now the flag is at = 8 – 12 = -4
After Third pull:
Now the flag is at -4 now then it moves to 13 feet to the right
Then the flag is at = -4 + 13 = 9
Now the flag is at 9 that means to win the flag should cross goal line that means + 10
No team wins
To win the right side team the flag should move 1 or more to the right
To win the left side team the flag should move 11 or more to the left.

Lesson 8.2 Comparing and Ordering Integers

EXPLORATION 1

Seconds to Liftoff
Work with a partner. You are listening to a command center before the liftoff of a rocket. You hear the following:
“T minus 10 seconds . . . go for main engine start . . . T minus 9 . . . 8 . . . 7 . . . 6 . . . 5 . . . 4 . . . 3 . . . 2 . . . 1 . . . we have liftoff.”


a. Represent these events on a number line.
Answer:
Rocket clears launchpad tower = +6 = A Event
Launch Verification = -16 = B Event
Main Engine Start = -3 = C Event
Rocket Topping sequence complete = -110 = D Event
Launch control system enabled = -90 = E Event
Boosters ignite = 0 = F Event

b. List the events in the order they occurred. Explain your reasoning.
Answer:
1 – Rocket Topping sequence complete = -110 = D Event
2 – Launch control system enabled = -90 = E Event
3 – Launch Verification = -16 = B Event
4 – Main Engine Start = -3 = C Event
5 – Boosters ignite = 0 = F Event
6 – Rocket clears launchpad tower = +16 = A Event
As per the above number line the events which take place are ordered from left side to right side

c. Extend the number line in part(a) to show events in an astronaut’s day. Include at least five events before liftoff and at least five events after liftoff. Use the Internet or another reference source to gather information.
Answer:
1 – Rocket Topping sequence complete = -110 = D Event
2 – Launch control system enabled = -90 = E Event
3 – Launch Verification = -16 = B Event
4 – Main Engine Start = -3 = C Event
5 – Boosters ignite = 0 = F Event
6 – Rocket clears launchpad tower = +6 = A Event
7- Stage 1 Burnout = +16 = G Event
8 – Fairing Jettison = +25 = H Event
9 – Stage 1 Separation = + 30 = I Event
10 – Stage 2 Ignition = +35 = J Event
11 – Transfer to the launch pad = – 120 = K Event

Recall that on a horizontal number line, numbers to the left are less than numbers to the right. Numbers to the right are greater than numbers to the left. On a vertical number line, numbers below are less than numbers above. Numbers above are greater than numbers below.

Try It

Copy and Complete the statement using < or >.
Question 1.

Answer:
0 > -4
Explanation:
The Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller. Think what the number represents. Think what the value is.

Question 2.

Answer:
-5 < 5
Explanation:
All Positive Numbers are greater than the Negative numbers .

Question 3.

Answer:
-8 < -7
Explanation:
The Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.
With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller. Think what the number represents. Think what the value is.

Order the integers from least to greatest.
Question 4.
-2, -3, 3, 1, -1
Answer:
-3, -2, -1, 1, 3

Question 5.
4, -7, -8, 6, 1
Answer:
-8, -7, 1, 4, 6

Question 6.
In Example 3, what is the least possible integer value of the number?
Answer:

Self-Assessment for Concepts & Skills

Solve each exercise. Then rate your understanding of the success criteria in your journal.
ORDERING INTEGERS Order the integers from least to greatest.
Question 7.
6, – 4, – 1, 3, 5
Answer:
-4, -1,  3, 5, 6

Question 8.
– 7, – 9, 0, 8, – 2
Answer:
-9, -7, -2, 0, 8

Question 9.
WRITING
Explain how to determine which of two integers is greater.
Answer:

We are used to big positive numbers meaning a big value – the bigger the number, the more, or higher, or longer, or expensive, or whatever the number represents.

With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller. Think what the number represents and what the value is.

Question 10.
REASONING
The positions of four fish are shown.
a. Use red, blue, yellow, and green dots to graph the positions of the fish on a horizontal number line and a vertical number line.
b. Explain how to use the number lines from part(a) to order the positions from least to greatest.

Answer a :
The position of red fish = -4
The position of Yellow fish = -6
The position of green fish = 0
The position of Blue fish = 8


Answer b:
Least to greatest numbers are
-6, -4, 0, 8
Explanation:
From the above horizontal number line we notice that the numbers from left to right of number line  represent least to greatest numbers.

Question 11.
NUMBER SENSE
a and bare negative integers. Compare a and b. Explain your reasoning.

Answer:

b > a
Explanation:
we notice that the numbers from left to right of number line  represent least to greatest numbers.The Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.
With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller. Think what the number represents. Think what the value is..

Question 12.
The freezing temperature of nitrogen is −210°C, and the freezing temperature of oxygen is −219°C. A container of nitrogen and a container of oxygen are both cooled to −215°C. Do the contents of each container freeze? Explain.
Answer:
The temperature of liquid nitrogen can readily be reduced to its freezing point 63 K (−210 °C; −346 °F) by placing it in a vacuum chamber pumped by a vacuum pump
The temperature at which a substance freezes is called the freezing point. The freezing point of oxygen is -219°C . This means that they need to be cooled to lower temperatures to make them freeze.

Question 13.
DIG DEEPER!
The diagram shows the daily high temperatures during a school week. Was a positive Celsius temperature recorded on Tuesday? on Friday? Explain.

Answer:
No
Explanation:
The natural numbers 1, 2, 3, 4, 5, ……… are called positive integers.
Positive numbers are represented to the right of zero on the number line. Positive numbers are greater than negative numbers as well a zero.
Because zero is neither positive nor negative . Zero is a neutral number.
Therefore positive Celsius temperature recorded on Monday and Friday .

Comparing and Ordering Integers Homework & Practice 8.2

.2

Review & Refresh

Write a positive or negative integer that represents the situation.
Question 1.
You walk up 83 stairs.
Answer:
up indicates + .so it is + 83

Question 2.
A whale is 17 yards below sea level.
Answer:
Below indicates – . So it is -17

Question 3.
An organization receives a $75 donation.
Answer:
Receives indicates +. So it is +$75

Question 4.
A rock falls 250 feet off a cliff.
Answer:
Falls indicates – . So it is -250

Question 5.
What is the area of the trapezoid?

A. 6.3 ft²
B. 44.1 ft²
C. 50.4 ft²
D. 88.2 ft²
Answer:
Height of Trapezoid = 4.2ft
Base 1 of Trapezoid = 12ft
Base 2 of Trapezoid = 9 ft
Area of Trapezoid = half-height × (base1 + base2) = \(\frac{4.2}{2}\) (12 + 9)
=2.1 × 21 = 44.1 ft²

Divide. Write the answer in simplest form.
Question 6.
\(\frac{1}{5} \div \frac{1}{9}\)
Answer:
\(\frac{1}{5}\)÷latex]\frac{9}{1}[/latex]= 9/5=1.8

Question 7.
\(\frac{2}{5} \div \frac{1}{3}\)
Answer:
(2/5) /(1/3) = (2×3) /5 = 6/5=1.2

Question 8.
\(\frac{1}{4}\) ÷ 3
Answer:
\(\frac{1}{4}\)× \(\frac{1}{3}\)=\(\frac{1}{12}\) = 0.083

Question 9.
\(\frac{4}{7}\) ÷ 8
Answer:
\(\frac{4}{7}\) × \(\frac{1}{8}\)=\(\frac{1}{14}\) =0.071

Concepts, Skills, &Problem Solving

OPEN-ENDED Name an event that could occur at the given time (in seconds) in Exploration 1. Describe when the event occurs in the order of events from the exploration. (See Exploration 1, p. 351.)

Question 10.
– 300
Answer:

Question 11.
– 150
Answer:

Question 12.
10
Answer:

COMPARING INTEGERS Copy and complete the statement using < or >.
Question 13.

Answer:
3 > 0
Explanation:
All Positive Numbers are greater than the Negative numbers .

Question 14.

Answer:
-2 < 0
Explanation:
All Positive Numbers are greater than the Negative numbers .

Question 15.

Answer:
6 > -6
Explanation:
All Positive Numbers are greater than the Negative numbers .

Question 16.

Answer:
3 > -4
Explanation:
All Positive Numbers are greater than the Negative numbers .

Question 17.

Answer:
-1 < 4
Explanation:
All Positive Numbers are greater than the Negative numbers .

Question 18.

Answer:
-7 > -8
Explanation:
The Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.

Question 19.

Answer:
-3 < -2
Explanation:
The Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.

Question 20.

Answer:
-5 > – 10
Explanation:
The Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.

YOU BE THE TEACHER
Your friend compares two integers. Is your friend correct? Explain your reasoning.
Question 21.

Answer:
No My friend is wrong.
Explanation:
The Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.
-1 is nearer to 0 than -3 so -1 is greater
-3 < – 1

Question 22.

Answer:
Yes it is True .
– 7 < -3

ORDERING INTEGERS Order the integers from least to greatest.
Question 23.
0, – 1, 2, 3, – 3
Answer:
-3, -1, 0, 2, 3
Explanation:
With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .

Question 24.
– 4, – 2, – 3, 2, 1
Answer:
-4, -3, -2, 1, 2
Explanation:
With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .

Question 25.
– 2, 3, – 3, – 4, 4
Answer:
-4, -3, -2, 3, 4
Explanation:
With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .

Question 26.
5, – 11, – 9, 3, – 4
Answer:
-11, -9, -4. 3, 5
Explanation:
With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .

Question 27.
– 3, 8, 4, 0, – 13
Answer:
-13, -3, 0, 4, 8
Explanation:
With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .

Question 28.
– 7, 2, 6, – 4, 3
Answer:
-7, -4, 2, 3, 6
Explanation:
With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .

Question 29.
12, – 8, – 16, 7, 1
Answer:
-16, -8, 1, 7, 12
Explanation:
With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .

Question 30.
10, – 10, 30, – 30, – 50
Answer:
-50, -30, -10, 10, 30
Explanation:
With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .

Question 31.
– 5, 15, – 10, – 20, 25
Answer:
-20, -10, -5, 15, 25
Explanation:
With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .

Question 32.
MODELING REAL LIFE
An archaeologist discovers the two artifacts shown.
a. What integer represents ground level?
b. A dinosaur bone is 42 centimeters below ground level. Is it deeper than both of the artifacts? Explain.

Answer a :
An integer represents ground level = 0 (as it is neutral)
Answer b :
Dinosaur bone is at = – 42cms
First artifact is at =-38 cms
Second artifact is at = – 44 cms
No it not depper than both the artifacts.
Explanation:
It is in between the artifacts. as -42 lies in between -38 and -44

Question 33.
REASONING
A number is between −2 and −10. What is the least possible integer value of this number? What is the greatest possible integer value of this number?
Answer:
The numbers between -2 and -10 = -3, -4, -5, -6, -7, -8, -9
Greatest value = -3
Least Value = – 9
Explanation:
The Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.

Question 34.
NUMBER SENSE
Describe the locations of the integers m and n on a number line for each situation.
a. m < n
b. m > n
c. n > m
Answer a :
m < n where m = 1 and n = 3

Answer b :
m > n where n = -1 and m = 1

Answer c :
n > m where n = 5 and m = -5

CRITICAL THINKING Tell whether the statement is always, sometimes, or never true. Explain.

Question 35.
A positive integer is greater than its opposite.
Answer:
YES,
Explanation:
The opposite number of a positive number is negative numbers. Negative are always lesser than positive numbers.

Question 36.
An integer is less than its opposite and greater than 0.
Answer:
No
Explanation:
integer = 5
The opposite of 5 is -5
Here integer is not less than its oppositeand greater than 0 it is -5 < 5 .

Question 37.
MODELING REAL LIFE
The table shows the highest and lowest elevations for five states.

a. Order the states by their highest elevations, from least to greatest.
b. Order the states by their lowest elevations, from least to greatest.
c. What does the lowest elevation for Florida represent?
Answer a :
Florida < Louisiana <Arkansas < Tennessee < California
345< 535 < 2753 < 6643 < 14494
Answer b :
California < Louisiana < Florida < Arkansas < Tennessee
-282 < -8 < 0 < 55 < 178

Question 38.
NUMBER SENSE
Point A is on a number line halfway between −17 and 5. Point Bis halfway between Point A and 0. What integer does Point B represent?
Answer:
Point A = half way between -17 and 5 = (- 17 + 5) ÷ 2 = – 12÷2 = -6
Point B = halfway between Point A and 0 = (-6 + 0) ÷ 2= -6 ÷ 2 = – 3
Therefore Point B represent -3 integer

Question 39.
REASONING
Eleven Fahrenheit temperatures are shown on a map during a weather report. When the temperatures are ordered from least to greatest, the middle temperature is below off. Do you know exactly how many of the temperatures are represented by negative numbers? Explain.
Answer:

Question 40.
PUZZLE
Nine students each choose one integer. Here are seven of them:
5, − 8, 10, − 1, − 12, − 20, and 1.
a. When all nine integers are ordered from least to greatest, the middle integer is 1. Describe the integers chosen by the other two students.
b. When all nine integers are ordered from least to greatest, the middle integer is −3. Describe the integers chosen by the other two students.

Answer a :
Order the numbers so that 1 is in the middle:
-20, -12, -8, -1, 1, 5, 10, x, x -> The other 2 numbers must be greater than 1, as the range can be 2 < x, x being the number chosen
Answer b .
Order the numbers so that -3 is in the middle:
x, -20, -12, -8, (-3), -1, 1, 5, 10 -> The other number must be less than -3, as the range is x < – 3, x being the number chosen

Lesson 8.3 Rational Numbers

EXPLORATION 1

Locating Fractions on a Number Line
Work with a partner. Represent the events on a number line using a fraction or a mixed number.

Answer:

Integers, fractions, and decimals make up the set of rational numbers. A rational number is a number that can be written as a – b, where a and b are integers and b ≠ 0.

Try It

Graph the number and its opposite.
Question 1.
2\(\frac{1}{2}\)
Answer:
2 × \(\frac{1}{2}\) = \(\frac{2}{2}\) = 1
The opposite of 1 is -1

Question 2.
–\(\frac{4}{5}\)
Answer:
–\(\frac{4}{5}\)= – ( 4 ÷ 5) = – 0.8
The opposite of – 0.8 is 0.8

Question 3.
– 3.5
Answer:
The opposite of – 3.5 is 3.5

Question 4.
5.25
Answer:
The opposite of 5.25 is -5.25

Copy and complete the statement using < or >.
Question 5.

Answer:
–\(\frac{4}{7}\) = -0.57
–\(\frac{1}{7}\)= -0.14
– 0.57   <  -0.14

Question 6.

Answer:
–\(\frac{5}{3}\) = -1.66
–\(\frac{11}{6}\) = -1.83
-1.66 > – 1.83

Question 7.

Answer:
– 0.5  <  0.3

Question 8.

Answer:
-6.5  > – 6.75

Self-Assessment for Concepts & Skills

Solve each exercise. Then rate your understanding of the success criteria in your journal.
COMPARING RATIONAL NUMBERS Copy and complete the statement using < or >.
Question 9.

Answer:
–\(\frac{2}{3}\) = -0.66
–\(\frac{5}{9}\) = -0.55
-0.66  < -0.55

Question 10.

Answer:
–\(\frac{9}{4}\)= – 2.25
–\(\frac{19}{8}\)= -2.375
-2.25  >  -2.375

Question 11.

Answer:
-1.7   >   -2.4

Question 12.
NUMBER SENSE
Which statement is not true?
A. On a number line, −2\(\frac{1}{6}\) is to the left of −2\(\frac{2}{3}\).
B. −2 \(\frac{2}{3}\) is less than −2\(\frac{1}{6}\).
C. On a number line, −2\(\frac{2}{3}\) is to the left of −2\(\frac{1}{6}\).
Answer A :
−2\(\frac{1}{6}\) = −\(\frac{1}{3}\) = – 0.33
−2\(\frac{2}{3}\) = −\(\frac{4}{3}\) = -1.33
Explanation:

Answer B :
−2 \(\frac{2}{3}\) = − \(\frac{4}{3}\) = -1.33
−2\(\frac{1}{6}\) = −\(\frac{1}{3}\) = – 0.33
-1.33  <  – 0.33
Explanation:
The Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.

Answer C :
−2 \(\frac{2}{3}\) = − \(\frac{4}{3}\) = -1.33
−2\(\frac{1}{6}\) = −\(\frac{1}{3}\) = – 0.33
From the above number line we notice that -1.33 is left of -0.33

Question 13.
WRITING
Explain how to determine whether a number is a rational number.
Answer:
The rational number which is represented in the \(\frac{p}{q}\)form and where q is not equal to zero.
Examples :
\(\frac{2}{3}\), \(\frac{7}{3}\)

Self-Assessment for Problem Solving

Solve each exercise. Then rate your understanding of the success criteria in your journal.
Question 14.
You and your friend rappel down a cliff. Your friend descends 0.11 mile and then waits for you to catch up. You descend and your current change in elevation is −0.12 mile. Have you reached your friend? Explain.

Answer:
Distance traveled by my friend = 0.11

Question 15.
The table shows the changes in the value of a stock over a period of three days. On which day does the value of the stock change the most? Explain your reasoning.

Answer:
Change in stock is most in day 3 that is – 0.45
Explanation:
On day 1 the stock change is -0.42
On day 2 there is no stock change that is 0
On day 3 the stock change is -0.45
From 0 to -0.45 change is more

Rational Numbers Homework & Practice 8.3

Review & Refresh

Copy and complete the statement using < or >.
Question 1.

Answer:
5 < 8

Question 2.

Answer:
-4 > -7

Question 3.

Answer:
2 > -5

Question 4.

Answer:
0 > -3

Question 5.
You pay $48 for 8 pounds of chicken. Which is an equivalent rate?
A. $44 for 4 pounds
B. $28 for 4 pounds
C. $15 for 3 pounds
D. $30 for 5 pounds
Answer:
$30 for 5 pounds
Explanation:
You pay $48 for 8 pounds of chicken.
$48 = 8 Pounds
$__ = 5 Ponds.
Do Cross Multiplication
(48 × 5)÷8 = 6  × 5 = $30

Find the whole.
Question 6.
40% of what number is 24?
Answer:
40 % = 24
100 % = ?
The answer is 60.
Explanation:
Do cross multiplication we get :
100 % × 24 = 40% × ?
2400 ÷ 40 = 60.
Therefore answer is 60.

Question 7.
12% of what number is 9?
Answer:
12 % = 9
100 % = ?
The answer is 75.
Explanation:
Do cross multiplication we get :
100 % × 9 = 12% × ?
900 ÷ 12 = 75.
Therefore answer is 75.
Question 8.
48% of what number is 84?
Answer:
48 % = 84
100 % = ?
The answer is 175.
Explanation:
Do cross multiplication we get :
100 % × 84 = 48% × ?
8400 ÷ 48 = 175.
Therefore answer is 175.

Question 9.
140% of what number is 98?
Answer:
140 % = 98
100 % = ?
The answer is 70.
Explanation:
Do cross multiplication we get :
100 % × 98 = 140% × ?
9800 ÷ 140 = 70.
Therefore answer is 70.

Multiply.
Question 10

Answer:

Question 11.

Answer:

Question 12.
3.7 × 4.854
Answer:

Question 13.
2.9 × 8.8609
Answer: