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Students can grab the complete knowledge on Divide Fractions on Go Math Grade 8 Answer Key Chapter 14 Scatter Plots. This article consists of the solutions to practice problems, review tests along with answers and explanations for students to have more practice. So, the students who are in search of Go Math 8th Grade Answer Key Chapter 14 Scatter Plots can Download pdf from here. It is difficult for parents and teachers to deal with the students & give explanations for their questions. Therefore, start practicing the maths with the help of Go Math Grade 8 Answer Key.

Go Math Grade 8 Answer Key Chapter 14 Scatter Plots

We the team of ccss math answers offer the pdf of Go Math Grade 8 Answer Key Chapter 14 Scatter Plots. Get step by step solution for Go Math Grade 8 Answer Key Chapter 14 Scatter Plots here. With the help of the HMH Go Math 8th Grade Solution Key you can score good marks in the exams. If you learn the concepts you can make the question on your own and test your knowledge. Hence make use of the below links and practice the given problems from now.

Lesson 1: Scatter Plots and Association

• • Scatter Plots and Association – Page No. 436
  • Scatter Plots and Association – Page No. 437
  • Scatter Plots and Association – Page No. 438

Lesson 2: Trend Lines and Predictions

• • Trend Lines and Predictions – Page No. 442
  • Trend Lines and Predictions – Page No. 443
  • Trend Lines and Predictions – Page No. 444

Model Quiz

• • Model Quiz – Page No. 445

Mixed Review

• • Mixed Review – Page No. 446

Guided Practice – Scatter Plots and Association – Page No. 436

Bob recorded his height at different ages. The table below shows his data.

Question 1.
Make a scatter plot of Bob’s data.

Type below:
_____________

Answer:

Explanation:
As Bob gets older, his height increases along with the straight line on the
graph. So, the association is positive and linear.

Question 2.
Describe the association between Bob’s age and his height. Explain the association.
Type below:
_____________

Answer:
The association is positive and linear. Bob’s height increases as he gets older. We would see that Bob’s height eventually stops increasing if the data continued.

Question 3.
The scatter plot shows the basketball shooting results for 14 players. Describe any clusters you see in the scatter plot. Identify any outliers.

Type below:
_____________

Answer:
There is an outlier at (35,18)

Explanation:
There is a cluster in the “20 – 25” shots attempted range and a smaller cluster in the “5 – 14” shots attempted range.
There is an outlier at (35,18)

ESSENTIAL QUESTION CHECK-IN

Question 4.
Explain how you can make a scatter plot from a set of bivariate data.
Type below:
_____________

Answer:
Bivariate data – data that has two variables per observation,
An x variable and y variable.
Scatterplot – The graph displaying categorical data, with an x and y-axis.
Response Variable – the variable that is explained by the other.
Explanatory Variable – the variable which explains the other.

14.1 Independent Practice – Scatter Plots and Association – Page No. 437

Sports Use the scatter plot for 5–8.

Olympic Men’s Long Jump Winning Distances

Question 5.
Describe the association between the year and the distance jumped for the years 1960 to 1988.
Type below:
_____________

Answer:
The data shows a positive linear association. If the year increases, the winning distance increases.

Question 6.
Describe the association between the year and the distance jumped for the years after 1988.
Type below:
_____________

Answer:
Between 1996 and 2004, there was a slight increase in distance over time. The data from 1988 to 2012 will show a negative association.

Question 7.
For the entire scatter plot, is the association between the year and the distance jumped linear or nonlinear?
_____________

Answer:
The data show a rise between 1960 and 1988. The data also show a fall between 1988 and 2012. Therefore, overall, there is no linear pattern.

Question 8.
Identify the outlier and interpret its meaning.
Type below:
_____________

Answer:
The outlier is at (1968, 8.9). It represents a long jump of 8.9 meters in 1968 that exceeds the other jumps made in the surrounding years.

Question 9.
Communicate Mathematical Ideas Compare a scatter plot that shows no association to one that shows negative association.
Type below:
_____________

Answer:
Randomly scattered data points with no apparent pattern define a scatter plot with no association. Data points that fall from left to right and has data set values that increases as the other decreases define a scatter plot with a negative association.

Scatter Plots and Association – Page No. 438

For 10–11, describe a set of real-world bivariate data that the given scatter plot could represent. Define the variable represented on each axis.

Question 10.

_____________

Answer:
The x-axis represents the number of containers. The y-&is represents the price per container.

Question 11.

_____________

Answer:
The x-axis represents the number of hours spent watching tv. The y-axis represents the number of TVs owned.

FOCUS ON HIGHER ORDER THINKING

Question 12.
Multiple Representations Describe what you might see in a table of bivariate data that would lead you to conclude that the scatter plot of the data would show a cluster.
Type below:
_____________

Answer:
A cluster in a scatter plot is when there are a lot of points all grouped around the same location.
Look for points that have the same input and output values. If there are a lot of points together, you must have a cluster in your scatter plot.

Question 13.
Justify Reasoning Is it possible for a scatter plot to have a positive or negative association that is not linear? Explain.
Type below:
_____________

Answer:
Yes

Explanation:
Yes; it is possible for a scatter plot to have a positive or negative association that is not linear. The data points may have a falling or rising curve that will exhibit a nonlinear association.

Question 14.
Critical Thinking To try to increase profits, a theater owner increases the price of a ticket by $25 every month. Describe what a scatter plot might look like if x represents the number of months and y represents the profits. Explain your reasoning.
Type below:
_____________

Answer:
Initially, the number of tickets sold might decline a little, but the price increase would offset the loss in sales. That means that profits would increase, showing a positive association.
When the price would get too high, ticket sales would decline rapidly, so profits would fall giving a negative association.

Guided Practice – Trend Lines and Predictions – Page No. 442

Angela recorded the price of different weights of several bulk grains. She made a scatter plot of her data. Use the scatter plot for 1–4.

Question 1.
Draw a trend line for the scatter plot.

Type below:
_____________

Answer:

Question 2.
How do you know whether your trend line is a good fit for the data?
Type below:
_____________

Answer:
Most of the data points are close to the trend line. The trend line has about the same number of points above and below it.

Question 3.
Write an equation for your trend line.
Type below:
_____________

Answer:
y = 0.09x

Explanation:
The trend line passes through (0, 0) and (19, 1.80).
Find the slope by using the slope formula.
slope = m = (y2 – y1)/(x2 – x1) = 1.80/19 = 0.09
The line passes through the origin. So, the y-intercept is 0.
From an equation for the trend line by substituting the slope value for m and the value of the y-intercept b in the slope-intercept formula.
y = mx + b
y = 0.09x + 0
y = 0.09x

Question 4.
Use the equation for your trend line to interpolate the price of 7 ounces and extrapolate the price of 50 ounces.
Type below:
_____________

Answer:
The price for 7 and 50 ounces is $0.63 and $4.50

Explanation:
Use the equation for the trend line (y = 0.09x) to interpolate the price of 7 ounces by substituting 7 for x (y= 0.09 • 7) and solving for y.
Use the equation for the trend line (y = 0.09x) to interpolate the price of 50 ounces by substituting 50 for x (y= 0.09 • 50) and solving for y.

ESSENTIAL QUESTION CHECK-IN

Question 5.
A trend line passes through two points on a scatter plot. How can you use the trend line to make a prediction between or outside the given data points?
Type below:
_____________

Answer:
Use two points on the line. rind the slope and y-intercept. Substitute the values of the slope (m) and y-intercept (b) to form an equation using y = mx + b. Substitute the value of x for which you want to make a prediction and solve for y OR substitute your prediction for y and solve to find its value.

14.2 Independent Practice – Trend Lines and Predictions – Page No. 443

Use the data in the table for Exercises 6–10.

Question 6.
Make a scatter plot of the data and draw a trend line.

Type below:
_____________

Answer:

Question 7.
What type of association does the trend line show?
Type below:
_____________

Answer:
Negative Association

Explanation:
One data set increases – Wind Speed and the other – Wind Chill decreases. So, the trend line shows a Negative Association.

Question 8.
Write an equation for your trend line.
Type below:
_____________

Answer:
y = -0.25x + 2.5

Explanation:
Find the slope using the Slope Formula
m = (y2 – y1)/(x2 – x1) = ((-10) – 5)/(50 – 30) = -5/20 = -0.25
Find the y-intercept using the Slope-Intercept Formula
y = mx + b
-5 = -0.25(30) + b
-5 = -7.5 + b
2.5 = b
Substitute the value of m and b into the Slope-Intercept Formula to form an equation for the trend line.
y = -0.25x + 2.5

Question 9.
Make a Prediction Use the trend line to predict the wind chill at these wind speeds.
a. 36 mi/h
_________ °F

Answer:
-6.5°F

Explanation:
Use the trend line to predict the wind chill at 36mi/h
y = -0.25x + 2.5
y = -0.25(36) + 2.5
y = -9 + 2.5
y = -6.5
The wind chill at 36mi/h is -6.5ºF

Question 9.
b. 100 mi/h
_________ °F

Answer:
-22.5°F

Explanation:
Use the trend line to predict the wind chill at 100mi/h
y = -0.25x + 2.5
y = -0.25(100) + 2.5
y = -25 + 2.5
y = -22.5
The wind chill at 100mi/h is -22.5ºF

Question 10.
What is the meaning of the slope of the line?
Type below:
_____________

Answer:
The slope means that the wind chill falls about 1°F for every 4 mph increase in wind speed.

Use the data in the table for Exercises 11–14.

Question 11.
Make a scatter plot of the data and draw a trend line.

Type below:
_____________

Answer:

Question 12.
Write an equation for your trend line.
Type below:
_____________

Answer:
y = -(2/15)x + 64

Explanation:
Find the slope using the Slope Formula
m = (y2 – y1)/(x2 – x1) = (72 – 64)/(60 – 0) = 8/60 = -2/15
Find the y-intercept using the Slope-Intercept Formula at (0, 64)
y = mx + b
b = 64
Substitute the value of m and b into the Slope-Intercept Formula to form an equation for the trend line.
y = -2/15x + 64

Question 13.
Make a Prediction Use the trend line to predict the apparent temperature at 70% humidity.
Type below:
_____________

Answer:
73.3º F

Explanation:
Use the equation of the trend line. Substitute 70(for 70%) into the equation for x.
y = -(2/15)x + 64
y = -(2/15)(70) + 64
y = -140/15 + 64
y = -9.3 + 64
y = 73.3
The apparent temperature is 73.3º F

Question 14.
What is the meaning of the y-intercept of the line?
Type below:
_____________

Answer:
The y-intercept explains that at 0% humidity, the apparent temperature is 64ºF

FOCUS ON HIGHER ORDER THINKING – Trend Lines and Predictions – Page No. 444

Question 15.
Communicate Mathematical Ideas Is it possible to draw a trend line on a scatter plot that shows no association? Explain.
_____________

Answer:
No

Explanation:
It is not possible to draw a trend line on a scatter plot that shows no association. If the scatter plot shows no association, the data points have no relationships with one another. You can draw a trend line if a linear association is available.

Question 16.
Critique Reasoning Sam drew a trend line that had about the same number of data points above it as below it, but did not pass through any data points. He then picked two data points to write the equation for the line. Is this a correct way to write the equation? Explain.
_____________

Answer:
No

Explanation:
Sam did not use the correct way to write an equation.
Sam may have drawn a correct trend line but using the data points that are not on the trend line may have an incorrect equation for the line. He should use two points on that trend line to write the equation.

Question 17.
Marlene wanted to find a relationship between the areas and populations of counties in Texas. She plotted x (area in square miles) and y (population) for two counties on a scatter plot:
Kent County (903, 808)                                Edwards County (2118, 2002)
She concluded that the population of Texas counties is approximately equal to their area in square miles and drew a trend line through her points.
a. Critique Reasoning Do you agree with Marlene’s method of creating a scatter plot and a trend line? Explain why or why not.
_____________

Answer:
I do not agree with Marlene’s method of creating a scatter plot and a trend line. She did not have enough data. Marlene should have collected and plotted data for many more counties.

Question 17.
b. Counterexamples Harris County has an area of 1778 square miles and a population of about 4.3 million people. Dallas County has an area of 908 square miles and a population of about 2.5 million people. What does this data show about Marlene’s conjecture that the population of Texas counties is approximately equal to their area?
Type below:
_____________

Answer:
The data collected are only of two counties whose populations are nearly equal to their area. The fact that the populations of Harris and Dallas counties are in the millions, Marlene’s conjecture about the population of Texas counties being equivalent to their area is invalid.

Ready to Go On? – Model Quiz – Page No. 445

14.1 Scatter Plots and Association

An auto store is having a sale on motor oil. The chart shows the price per quart as the number of quarts purchased increases. Use the data for Exs. 1–2.

Question 1.
Use the given data to make a scatter plot.

Type below:
_____________

Answer:

Question 2.
Describe the association you see between the number of quarts purchased and the price per quart. Explain.
Type below:
_____________

Answer:
Negative nonlinear association

Explanation:
The association seen between the number of quarts purchased and the price per quart is negative and nonlinear. As the number of quarts rises, the price per quart decreases but you can see a data curve.

14.2 Trend Lines and Predictions

The scatter plot below shows data comparing wind speed and wind chill for an air temperature of 20 °F. Use the scatter plot for Exs. 3–5.

Question 3.
Draw a trend line for the scatter plot.

Type below:
_____________

Answer:

Question 4.
Write an equation for your trend line.
Type below:
_____________

Answer:
y = -0.35x + 12.25

Explanation:
The line passes through (10, 8.75) and (35, 0) so we can use these points to find the slope.
The slope of the line is :
Slope = m = (y2 – y1)/(x2 – x1) = (0 – 8.75)/(35 – 10) = -8.75/25 = -0.35
Find the y-intercept using the slope-intercept formula :
y = mx + b
0 = -0.35 . 35 + b
0 = -12.25 + b
b = 12.25
Substitute the slope m and the y-intercept b in the slope-intercept formula.
The equation for the trend line is :
y = mx + b
y = -0.35x + 12.25

Question 5.
Use your equation to predict the wind chill to the nearest degree for a wind speed of 60 mi/h.
________ °F

Answer:
9°F

Explanation:
y = −0.35x + 12.25
y = -0.35(60) + 12.25
y = -21 + 12.25
y = -8.75
The wind chill to the nearest degree for a wind speed of 60 mi/h is 9°F.

ESSENTIAL QUESTION

Question 6.
How can you use scatter plots to solve real-world problems?
Type below:
_____________

Answer:
Using a scatter plot, you can see positive and negative trends such as prices over time. You can also make predictions such as height at a certain age.

Selected Response – Mixed Review – Page No. 446

Question 1.
Which scatter plot could have a trend line whose equation is y = 3x + 10?

Options:
a. A
b. B
c. C
d. D

Answer:
b. B

Question 2.
What type of association would you expect between a person’s age and hair length?
Options:
a. linear
b. negative
c. none
d. positive

Answer:
c. none

Explanation:
The length of their hair reduces. This is because the length of hair changes with the growth phase of the hair follicles. When one is young, the cells of the papilla divide more rapidly, and hence the length of the hair to be long before reaching the transitional phase and then shed off in the telogen phase. The older one gets, the papilla cells do not divide as rapidly and the length of the hair shortens with age.

Question 3.
Which is not shown on the scatter plot?

Options:
a. cluster
b. negative association
c. outlier
d. positive association

Answer:
d. positive association

Explanation:
The scatter plot shows a cluster, some outliers, and a negative association.
It does not show a positive association.

Question 4.
A restaurant claims to have served 352,000,000 hamburgers. What is this number in scientific notation?
Options:
a. 3.52 × 10⁶
b. 3.52 × 10⁸
c. 35.2 × 10⁷
d. 352 × 10⁶

Answer:
b. 3.52 × 10⁸

Explanation:
100,000,000
So, 3.52 × 10⁸

Question 5.
Which equation describes the relationship between x and y in the table?

Options:
a. y = −4x
b. y = −\(\frac{1}{4}\)x
c. y = 4x
d. y = \(\frac{1}{4}\)x

Answer:
b. y = −\(\frac{1}{4}\)x

Explanation:
In order to find out the relationship between x and y, we have to use the values in the question and substitute them into the solution options.
So, y = -1/4x

Mini-Task

Question 6.
Use the data in the table.

a. Make a scatterplot of the data.

Type below:
______________

Answer:

Question 6.
b. Which data point is an outlier?
Type below:
______________

Answer:
The outlier is the point (92, 135).

Question 6.
c. Predict the number of visitors on a day when the high temperature is 102 °F.
Type below:
______________

Answer:
Based on the cluster around 100°F, I would expect that on a day with a temperature of 102 °F, the pool would have between 350 and 400 visitors.

Conclusion:

Hope our Go Math Grade 8 Answer Key Chapter 14 Scatter Plots helped you a lot. Stick to our page to get chapter-wise Answer Keys of Go Math Grade 8. You can get step by step explanations for all the questions in an easy manner.

Go Math Grade 4 Answer Key Chapter 12 Relative Sizes of Measurement Units Pdf download links are provided here for free od cost.  Do refer to them during the preparation time and learn the concepts easily. All the students who are hunting for the Go Math Grade 4 Answer Key Chapter 12 Relative Sizes of Measurement Units can download them here. So, take the help of these available pdf links and download Go Math Grade 4 Answer Key Chapter 12 pdf to understand & learn the concepts of Relative Sizes of Measurement Units in a simplistic manner.

Go Math Grade 4 Answer Key Chapter 12 Relative Sizes of Measurement Units

Go through the below-provided links and get the Go Math Grade 4 Chapter 12 Relative Sizes of Measurement Units Answer Key for better preparation and score good marks in the exams. The provided solutions to all the questions asked from Relative Sizes of Measurement Units concepts will help you in real-time calculations also. Hence, utilize these lesson-wise links and solve each and every concept related questions covered in this chapter.

Lesson 1:

• Measurement Benchmarks Page No 645
• Measurement Benchmarks Lesson Check Page No 646

Lesson 2:

• Customary Units of Length Page No. 649
• Customary Units of Length Page No. 650

Common Core

• Common Core – New – Page No. 651
• Common Core – New – Lesson Check Page No. 652

Lesson 3:

• Customary Units of Weight Page No. 655
• Customary Units of Weight Page No. 656

Common Core

• Common Core – New – Page No. 657
• Common Core – New – Page No. 658

Lesson 4:

• Customary Units of Liquid Volume Page No. 661
• Customary Units of Liquid Volume Page No. 662

Common Core

• Common Core – New – Page No. 663
• Common Core – New – Lesson Check Page No. 664

Lesson 5:

• Line Plots Page No. 667
• Line Plots Page No. 668

Common Core

• Common Core – New – Page No. 669
• Common Core – New – Lesson Check Page No. 670

Mid Chapter Checkpoint

• Mid-Chapter Checkpoint Page No. 671
• Mid-Chapter Checkpoint Page No. 672

Lesson 6:

• Investigate • Metric Units of Length Page No. 675
• Investigate • Metric Units of Length Page No. 676

Common Core

• Common Core – New – Page No. 677
• Common Core – New – Lesson Check Page No. 678

Lesson 7:

• Metric Units of Mass and Liquid Volume Page No. 680
• Metric Units of Mass and Liquid Volume Page No. 681
• Metric Units of Mass and Liquid Volume Page No. 682

Common Core

• Common Core – New – Page No. 683
• Common Core – New – Lesson Check Page No. 684

Lesson 8:

• Units of Time Page No. 687
• Units of Time Page No. 688

Common Core

• Common Core – New – Page No. 689
• Common Core – New – Lesson Check Page No. 690

Lesson 9: Problem Solving • Elapsed Time

• Problem-Solving • Elapsed Time Page No. 693
• Problem-Solving • Elapsed Time Page No. 694

Common Core

• Common Core – New – Page No. 695
• Common Core – New – Lesson Check Page No. 696

Chapter 12: Page No. 699

Chapter 12: Page No. 700

Lesson 10:

• Common Core – New – Mixed Measures Page No. 701
• Common Core – New – Mixed Measures Lesson Check Page No. 702

Lesson 11: Algebra • Patterns in Measurement Units

• Algebra • Patterns in Measurement Units Page No. 705
• Algebra • Patterns in Measurement Units Page No. 706

Common Core

• Common Core – New – Page No. 707
• Common Core – New – Page No. 708

Chapter 12: Review/Test

• Review/Test Page No. 709
• Review/Test Page No. 710
• Review/Test Page No. 711
• Review/Test Page No. 712
• Review/Test Page No. 713
• Review/Test Page No. 714
• Review/Test Page No. 719
• Review/Test Page No. 720

Common Core – New – Page No. 645

Measurement Benchmarks

Use benchmarks to choose the customary unit you would use to measure each.

Question 1.
height of a computer
foot

Question 2.
weight of a table
________

Answer: Pound

The customary unit to measure the weight of the table is Pound.

Question 3.
length of a semi-truck
________

Answer: Yard

The unit to measure the length of a semi-truck is the yard.

Question 4.
the amount of liquid a bathtub holds
________

Answer: Gallon

The customary unit to measure the amount of liquid a bathtub holds is Gallon.

Use benchmarks to choose the metric unit you would use to measure each.

Question 5.
mass of a grasshopper
________

Answer: Gram

The metric unit to measure the mass of a grasshopper is the gram.

Question 6.
the amount of liquid a water bottle holds
________

Answer: Liter

The metric unit to measure the amount of liquid a water bottle holds is Liter.

Question 7.
length of a soccer field
________

Answer: Meter

The metric unit to measure the length of a soccer field is meter.

Question 8.
length of a pencil
________

Answer: Centimeter

The metric unit to measure the length of a pencil is Centimeter.

Circle the better estimate.

Question 9.
mass of a chicken egg
a. 50 grams
b. 50 kilograms

Answer: 50 grams

The better estimate to measure the mass of a chicken egg is 50 grams.

Question 10.
length of a car
a. 12 miles
b. 12 feet

Answer: 12 feet

The better estimate to measure the length of a car is 12 feet.

Question 11.
amount of liquid a drinking glass holds
a. 8 ounces
b. 8 quarts

Answer: 8 ounces

The better estimate to measure the amount of liquid a drinking glass holds is 8 ounces.

Complete the sentence. Write more or less.

Question 12.
A camera has a length of _______ than one centimeter.

Answer: more

Explanation:

The length of a camera will greater than a centimeter. So, A camera has a length of more than one centimeter.

Question 13.
A bowling ball weighs _______ than one pound.

Answer: more

The unit of the pound is very less compared to the length of the ball.
So, A bowling ball weighs more than one pound.

Problem Solving

Question 14.
What is the better estimate for the mass of a textbook, 1 gram or 1 kilogram?
1 ________

Answer: 1 kilogram

The weight of a book will be more than a gram. So, the better estimate for the mass of a textbook is 1 kilogram.

Question 15.
What is the better estimate for the height of a desk, 1 meter or 1 kilometer?
1 ________

Answer: 1 meter

The kilometer is not suitable to measure the height of the desk. So, the better estimate for the height of a desk is 1 meter.

Common Core – New – Page No. 646

Lesson Check

Question 1.
Which is the best estimate for the weight of a stapler?
Options:
a. 4 ounces
b. 4 pounds
c. 4 inches
d. 4 feet

Answer: 4 ounces

The best estimate for the weight of a stapler is 4 ounces
So, the correct answer is option A.

Question 2.
Which is the best estimate for the length of a car?
Options:
a. 4 kilometers
b. 4 tons
c. 4 kilograms
d. 4 meters

Answer: 4 meters

The unit to measure the length of the car is meters.
Thus the answer is option D.

Spiral Review

Question 3.
Bart practices his trumpet 1 \(\frac{1}{4}\) hours each day. How many hours will he practice in 6 days?
Options:
a. 8 \(\frac{2}{4}\) hours
b. 7 \(\frac{2}{4}\) hours
c. 7 hours
d. 6 \(\frac{2}{4}\) hours

Answer: 7 \(\frac{2}{4}\) hours

Explanation:

Bart practices his trumpet 1 \(\frac{1}{4}\) hours each day.
The normal fraction for 1 \(\frac{1}{4}\) = \(\frac{5}{4}\)
In order to calculate the number of hours for 6 days, we need to multiply the fraction with 6.
6 × \(\frac{5}{4}\) = \(\frac{30}{4}\)
The mixed fraction of \(\frac{30}{4}\) is 7 \(\frac{2}{4}\) hours
So, the correct answer is otpion D.

Question 4.
Millie collected 100 stamps from different countries. Thirty-two of the stamps are from countries in Africa. What is \(\frac{32}{100}\) written as a decimal?
Options:
a. 32
b. 3.2
c. 0.32
d. 0.032

Answer: 0.32

The decimal for the fraction is \(\frac{32}{100}\) = 0.32
Thus the answer is option C.

Question 5.
Diedre drew a quadrilateral with 4 right angles and 4 sides of the same length. What kind of polygon did Diedre draw?
Options:
a. square
b. trapezoid
c. hexagon
d. pentagon

Answer: square

Explanation:

A square has got 4 sides of equal length and 4 right angles (right angle = 90 degrees).
So, the correct answer is option A.

Question 6.
How many degrees are in an angle that turns through \(\frac{1}{2}\) of a circle?
Options:
a. 60°
b. 90°
c. 120°
d. 180°

Answer: 180°

Explanation:

\(\frac{1}{2}\) × 360°
360°/2 = 180°
So, the correct answer is option D.

Page No. 649

Question 1.
Compare the size of a yard to the size of a foot.
Use a model to help.


1 yard is ____ times as long as ____ foot.
____              ____

Answer: 1 yard is three times as long as one feet.

Complete.

Question 2.
2 feet = ____ inches

Answer: 24 inches

Explanation:

1 foot = 12 inches
2 feets = 2 × 12 inches = 24 inches

Question 3.
3 yards = ____ feet

Answer: 9 feets

Explanation:

1 yard = 3 feets
3 yards = 3 × 3 = 9 feets

Question 4.
7 yards = ____ feet

Answer: 21 feets

Explanation:

1 yard = 3 feets
7 yards = 3 × 7 = 21 feets
Therefore 7 yards = 21 feets

Question 5.
4 yards = ____ feet

Answer: 12 feets

Explanation:

1 yard = 3 feet
4 yards = 4 × 3 feets = 12 feets
4 yards = 12 feets

Question 6.
10 yards = ____ feet

Answer: 30 feets

Explanation:

1 yard = 3 feets
10 yards = 10 × 3 feets = 30 feets
10 yards = 30 feets

Question 7.
7 feet = ____ inches

Answer: 84 inches

Explanation:

1 feet = 12 inches
7 feets = 7 × 12 = 84 inches

Use Symbols Algebra Compare using <, >, or =.

Question 8.
1 foot ____ 13 inches

Answer: 1 foot < 13 inches

Explanation:

We know that 1 foot = 12 inches
12 inches is less than 13 inches
So, 1 foot < 13 inches

Question 9.
2 yards ____ 6 feet

Answer: 2 yards = 6 feet

Explanation:

1 yard = 3 feets
2 yards = 2 × 3 feets = 6 feets
2 yards = 6 feet

Question 10.
6 feet ____ 60 inches

Answer: 6 feet > 60 inches

Explanation:

1 feet = 12 inches
6 feets = 6 × 12 inches = 72 inches
72 inches is greater than 60 inches
So, 6 feet > 60 inches

Question 11.
Joanna has 3 yards of fabric. She needs 100 inches of fabric to make curtains. Does she have enough fabric to make curtains? Explain. Make a table to help.
Type below:
________

Answer:

Given that, Joanna has 3 yards of fabric. She needs 100 inches of fabric to make curtains.
1 yard = 36 inches
3 yards = 36 × 3 = 108 inches
108 inches > 100 inches
So, she has enough fabric to make curtains.

Question 12.
Select the measures that are equal. Mark all that apply.
Options:
a. 4 feet
b. 12 yards
c. 36 feet
d. 480 inches
e. 15 feet
f. 432 inches

Answer: B = C = F

Explanation:

1 yard = 3 feet
12 yards = 12 × 3 = 36 feet
So, B = C

1 feet = 12 inches
36 feet = 12 × 36 inches = 432 inches
C = F
Therefore B = C = F

Page No. 650

Question 13.
Jasmine and Luke used fraction strips to compare the size of a foot to the size of an inch using fractions. They drew models to show their answers. Whose answer makes sense? Whose answer is nonsense? Explain your reasoning.
Jasmine’s Work

1 inch is \(\frac{1}{12}\) of a foot.
Luke’s Work

1 inch is \(\frac{1}{3}\) of a foot.
_______ ‘s answer makes sense

Answer: Jasmine’s answer makes sense

Question 13.
a. Apply For the answer that is nonsense, write an answer that makes sense.
Type below:
________

Answer: Luke’s answer is nonsense and Jasmine’s answer makes sense.
Because 1 foot = 12 inches. The fraction of 1 inch = \(\frac{1}{3}\) of a foot.

Question 13.
b. Look back at Luke’s model. Which two units could you compare using his model? Explain.
Type below:
________

Answer: Luke’s model will be suitable to compare the size of a foot to the size of a yard using fractions.

1 feet = 12 inches
3 feet = 36 inches
36 inches = 1 yard
So, 1 yard = \(\frac{12}{36}\)
1 yard = \(\frac{1}{3}\) feet

Common Core – New – Page No. 651

Customary Units of Length

Complete.

Question 1.
3 feet = 36 inches
Think: 1 foot = 12 inches,
so 3 feet = 3 × 12 inches, or 36 inches

Question 2.
2 yards = ____ feet

Answer: 6

Explanation:

1 yard = 3 feet
2 yards = 2 × 3 = 6 feets

Question 3.
8 feet = ____ inches

Answer: 96 inches

Explanation:

1 foot = 12 inches
8 feet = 12 × 8 = 96 inches
So, 8 feet = 96 inches

Question 4.
7 yards = ____ feet

Answer:21 feets

Explanation:

1 yard = 3 feet
7 yards = 7 × 3 feet = 21 feets
So, 7 yards = 21 feets

Question 5.
4 feet = ____ inches

Answer: 48 inches

Explanation:

1 foot = 12 inches
4 feet = 4 × 12 inches = 48 inches
So, 4 feet = 48 inches

Question 6.
15 yards = ____ feet

Answer: 45 feet

Explanation:

1 yard = 3 feet
15 yards = 15 × 3 feet = 45 feet
So, 15 yards = 45 feet

Question 7.
10 feet = ____ inches

Answer: 120 inches

Explanation:

1 foot = 12 inches
10 feet = 10 × 12 inches
10 feet = 120 inches

Compare using <, >, or =.

Question 8.
3 yards ____ 10 feet

Answer: 3 yards < 10 feet

Explanation:

1 yard = 3 feet
3 yards = 3 × 3 feet = 9 feet
9 feet is less than 10 feet
So, 3 yards < 10 feet

Question 9.
5 feet ____ 60 inches

Answer: 5 feet = 60 inches

Explanation:

1 foot = 12 inches
5 feet = 5 × 12 inches = 60 inches
So, 5 feet = 60 inches

Question 10.
8 yards ____ 20 feet

Answer: 8 yards > 20 feet

Explanation:

1 yard = 3 feet
8 yards = 8 × 3 feet = 24 feet
24 feet is greater than 20 feet
So, 8 yards > 20 feet

Question 11.
3 feet ____ 10 inches

Answer: 3 feet > 10 inches

Explanation:

1 foot = 12 inches
3 feet = 3 × 12 inches = 36 inches
36 inches is greater than 10 inches
So, 3 feet > 10 inches

Question 12.
3 yards ____ 21 feet

Answer: 3 yards < 21 feet

Explanation:

1 yard = 3 feet
3 yards = 3 × 3 feet = 9 feet
9 feet is less than 21 feet
So, 3 yards < 21 feet

Question 13.
6 feet ____ 72 inches

Answer: 6 feet = 72 inches

Explanation:

1 foot = 12 inches
6 feet = 6 × 12 inches = 72 inches
6 feet = 72 inches

Problem Solving

Question 14.
Carla has two lengths of ribbon. One ribbon is 2 feet long. The other ribbon is 30 inches long. Which length of the ribbon is longer?
2 feet ____ 30 inches

Answer: 2 feet < 30 inches

Explanation:

Carla has two lengths of ribbon. One ribbon is 2 feet long. The other ribbon is 30 inches long.
1 feet = 12 inches
2 feet = 2 × 12 inches = 24 inches
24 inches is less than 30 inches
30 inches is greater than 2 feet.
2 feet < 30 inches

Question 15.
A football player gained 2 yards on one play. On the next play, he gained 5 feet. Was his gain greater on the first play or the second play?
2 yards ____ 5 feet

Answer: 2 yards > 5 feet

Explanation:

A football player gained 2 yards on one play.
On the next play, he gained 5 feet.
1 yard = 3 feet
2 yards = 2 × 3 feet = 6 feet
The first play > The second play

Common Core – New – Page No. 652

Lesson Check

Question 1.
Marta has 14 feet of wire to use to make necklaces. She needs to know the length in inches so she can determine how many necklaces to make. How many inches of wire does Marta have?
Options:
a. 42 inches
b. 84 inches
c. 168 inches
d. 504 inches

Answer: 168 inches

Explanation:

Marta has 14 feet of wire to use to make necklaces.
1 feet = 12 inches
14 feet = 14 × 12 inches
14 feet = 168 inches
So, the correct answer is option C.

Question 2.
Jarod bought 8 yards of ribbon. He needs 200 inches to use to make curtains. How many inches of ribbon does he have?
Options:
a. 8 inches
b. 80 inches
c. 96 inches
d. 288 inches

Answer: 288 inches

Explanation:

Jarod bought 8 yards of ribbon. He needs 200 inches to use to make curtains.
1 yard = 36 inches
8 yards = 288 inches
Thus he has 288 inches of ribbon.
So, the correct answer is option D.

Spiral Review

Question 3.
Which describes the turn shown below?

Options:
a. \(\frac{1}{4}\) turn counterclockwise
b. \(\frac{1}{4}\) turn clockwise
c. \(\frac{1}{2}\) turn clockwise
d. \(\frac{3}{4}\) turn counterclockwise

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

By seeing the above figure we can say that the circle turn \(\frac{1}{4}\) in counterclockwise direction.

Question 4.
Which decimal represents the shaded part of the model below?

Options:
a. 0.03
b. 0.3
c. 0.33
d. 0.7

Answer: 0.3

Explanation:

The square is divided into 10 parts. Among them, 3 parts are shaded.
The fraction of the shaded part is \(\frac{3}{10}\)
The decimal that represents the above figure is 0.3
Thus the correct answer is option B.

Question 5.
Three sisters shared $3.60 equally. How much did each sister get?
Options:
a. $1.00
b. $1.20
c. $1.80
d. $10.80

Answer: $1.20

Explanation:

Three sisters shared $3.60 equally.
The amount that each sister get = x
x × 3 = $3.60
x = $3.60/3 = $1.20
So, the correct answer is option B.

Question 6.
Which is the best estimate for the width of your index finger?
Options:
a. 1 millimeter
b. 1 gram
c. 1 centimeter
d. 1 liter

Answer: 1 centimeter

The unit to measure the width of your index finger is 1 centimeter
The answer is option C.

Page No. 655

Question 1.
4 tons = ______ pounds

Answer: 8000 pounds

Explanation:

1 ton = 2000 pounds
4 tons = 4 × 2000 pounds = 8000 pounds
4 tons = 8000 pounds

Complete.

Question 2.
5 tons = ______ pounds

Answer: 10,000 pounds

1 ton = 2000 pounds
5 tons = 5 × 2000 pounds
5 tons = 10,000 pounds

Question 3.
6 pounds = ______ ounces

Answer: 96 ounces

1 pound = 16 ounces
6 pounds = 6 × 16 ounces
6 pounds = 96 ounces

Question 4.
7 pounds = ______ ounces

Answer: 112 ounces

1 pound = 16 ounces
7 pounds = 7 × 16 ounces
7 pounds = 112 ounces

Question 5.
6 tons = ______ pounds

Answer:

1 ton = 2000 pounds
6 tons = 6 × 2000 pounds
6 tons = 12,000 pounds

Use Symbols Algebra Compare using >, <, or =.

Question 6.
1 pound ______ 15 pounds

Answer: 1 pound < 15 pounds
1 is greater than 15.
So, 1 pound < 15 pounds

Question 7.
2 tons ______ 2 pounds

Answer: 2 tons > 2 pounds
1 ton is greater than 1 pound.
So, 2 tons > 2 pounds

Question 8.
A landscaping company ordered 8 tons of gravel. It sells the gravel in 50-pound bags. How many pounds of gravel did the company order?
______ 50-pound bags.

Answer: 16000 pounds

A landscaping company ordered 8 tons of gravel. It sells the gravel in 50-pound bags.
1 ton = 2000 pounds
8 tons = 8 × 2000 pounds = 16000 pounds

Question 9.
If you could draw a number line that shows the relationship between tons and pounds, what would it look like? Explain.

Answer:
Since 1 ton = 2000 pounds, the number line would show tick marks for every whole number from 0 to 2000. Each tick mark from 0 to 2000 would represent 1 pound. The tick mark in 2000 would represent 1 ton.

Question 10.
Write the symbol that compares the weights correctly.

160 ounces ______ 10 pounds

Answer: 160 ounces = 10 pounds
1 pound = 16 ounces
16 pounds = 10 × 16 ounces = 160 ounces
160 ounces = 10 pounds

Question 10.
600 pounds ______ 1 ton

Answer: 600 pounds < 1 ton
1 ton = 2000 pounds
600 pounds is less than 2000 pounds
600 pounds < 1 ton

Page No. 656

Question 11.
Alexis bought \(\frac{1}{2}\) pound of grapes. How many ounces of grapes did she buy?
Dan drew the number line below to solve the problem. He says his model shows that there are 5 ounces in \(\frac{1}{2}\) pound. What is his error?

Look at the way Dan solved the problem.
Draw a correct number line and solve the problem.
Find and describe his error.
So, Alexis bought ______ ounces of grapes.
Type below:
________

1 pound = 16 ounces
\(\frac{1}{2}\) pound = 8 ounces
The error of Dan is he must draw the mark till 8 but he drew till 5 ounces.

Question 11.
Look back at the number line you drew. How many ounces are in \(\frac{1}{4}\) pound? Explain.
Type below:
________

Answer: There are 4 ounces in \(\frac{1}{4}\) pound.

Common Core – New – Page No. 657

Customary Units of Weight

Complete.

Question 1.
5 pounds = 80 ounces
Think: 1 pound = 16 ounces, so
5 pounds = 5 × 16 ounces, or 80 ounces

Question 2.
7 tons = _____ pounds

Answer: 14,000 pounds

Explanation:

1 ton = 2000 pounds
7 tons = 7 × 2000 pounds = 14000 pounds
7 tons = 14000 pounds

Question 3.
2 pounds = _____ ounces

Answer: 32 ounces

Explanation:

1 pound = 16 ounces
2 pounds = 2 × 16 ounces = 32 ounces
2 pounds = 32 ounces

Question 4.
3 tons = _____ pounds

Answer: 6,000 pounds

Explanation:

1 ton = 2000 pounds
3 tons = 3 × 2000 pounds = 6000 pounds
3 tons = 6000 pounds

Question 5.
10 pounds = _____ ounces

Answer: 160 ounces

Explanation:

1 pound = 16 ounces
10 pounds = 10 × 16 ounces = 160 ounces
10 pounds = 160 ounces

Question 6.
5 tons = _____ pounds

Answer: 10,000 pounds

Explanation:

1 ton = 2000 pounds
5 tons = 5 × 2000 pounds = 10000 pounds
5 tons = 10000 pounds

Question 7.
7 pounds = _____ ounces

Answer: 112 ounces

Explanation:

1 pound = 16 ounces
7 pounds = 7 × 16 ounces = 112 ounces
7 pounds = 112 ounces

Compare using <, >, or =.

Question 8.
8 pounds _____ 80 ounces

Answer: 8 pounds > 80 ounces

Explanation:

1 pound = 16 ounces
8 pounds = 128 ounces
128 ounces is greater than 80 ounces
So, the answer is 8 pounds > 80 ounces

Question 9.
1 ton _____ 100 pounds

Answer: 1 ton > 100 pounds

Explanation:

1 ton = 2000 pounds
2000 pounds is greater than 100 pounds
1 ton > 100 pounds

Question 10.
3 pounds _____ 50 ounces

Answer: 3 pounds < 50 ounces

Explanation:

1 pound = 16 ounces
3 pounds = 3 × 16 ounces = 48 ounces
3 pounds = 48 ounces
3 pounds < 50 ounces

Question 11.
5 tons _____ 1,000 pounds

Answer: 5 tons > 1,000 pounds

Explanation:

1 ton = 2000 pounds
5 tons = 5 × 2000 pounds = 10000 pounds
10000 pounds is greater than 1000 pounds
5 tons > 1,000 pounds

Question 12.
16 pounds _____ 256 ounces

Answer: 16 pounds = 256 ounces

Explanation:

1 pound = 16 ounces
16 pounds = 16 × 16 ounces = 256 ounces
16 pounds = 256 ounces

Question 13.
8 tons _____ 16,000 pounds

Answer: 8 tons = 16,000 pounds

Explanation:

1 ton = 2000 pounds
8 tons = 8 × 2000 pounds = 16,000 pounds
8 tons = 16,000 pounds

Problem Solving

Question 14.
A company that makes steel girders can produce 6 tons of girders in one day. How many pounds is this?
6 tons = _____ pounds

Answer: 12,000 pounds

Explanation:

A company that makes steel girders can produce 6 tons of girders in one day.
1 ton = 2000 pounds
6 tons = 6 × 2000 pounds = 12000 pounds
6 tons = 12000 pounds

Question 15.
Larry’s baby sister weighed 6 pounds at birth. How many ounces did the baby weigh?
6 pounds = _____ ounces

Answer: 96 ounces

Explanation:

Larry’s baby sister weighed 6 pounds at birth.
1 pound = 16 ounces
6 pounds = 6 × 16 ounces = 96 ounces

Common Core – New – Page No. 658

Lesson Check

Question 1.
Ann bought 2 pounds of cheese to make lasagna. The recipe gives the amount of cheese needed in ounces. How many ounces of cheese did she buy?
Options:
a. 20 ounces
b. 32 ounces
c. 40 ounces
d. 64 ounces

Answer: 32 ounces

Explanation:

Ann bought 2 pounds of cheese to make lasagna.
1 pound = 16 ounces
2 pounds = 2 × 16 ounces = 32 ounces
So, the answer is option is option B.

Question 2.
A school bus weighs 7 tons. The weight limit for a bridge is given in pounds. What is this weight of the bus in pounds?
Options:
a. 700 pounds
b. 1,400 pounds
c. 7,000 pounds
d. 14,000 pounds

Answer: 14,000 pounds

Explanation:

A school bus weighs 7 tons. The weight limit for a bridge is given in pounds.
1 ton = 2000 pounds
7 tons = 7 × 2000 pounds
7 tons = 14000 pounds
So, the correct answer is option D.

Spiral Review

Question 3.
What is the measure of m∠EHG?

Options:
a. 60°
b. 100°
c. 120°
d. 130°

Answer: 120°

Explanation:

m∠EHG = m∠EHF + m∠FHG
m∠EHG = 90° + 30° = 120°
m∠EHG = 120°
The correct answer is option C.

Question 4.
How many lines of symmetry does the square below have?

Options:
a. 0
b. 2
c. 4
d. 6

Answer: 4

Explanation:

A square contains 4 right angles.
So, the answer is option C.

Question 5.
To make dough, Reba needs 2 \(\frac{1}{2}\) cups of flour. How much flour does she need to make 5 batches of dough?
Options:
a. 14 \(\frac{1}{2}\) cups
b. 12 \(\frac{1}{2}\) cups
c. 11 \(\frac{1}{2}\) cups
d. 10 \(\frac{1}{2}\) cups

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

Explanation:

To make dough, Reba needs 2 \(\frac{1}{2}\) cups of flour.
5 × 2 \(\frac{1}{2}\)
= 12 \(\frac{1}{2}\) cups
She need 12 \(\frac{1}{2}\) cups of flour to make dough.
So, the correct answer is option B.

Question 6.
Judi’s father is 6 feet tall. The minimum height to ride a rollercoaster is given in inches. How many inches tall is Judi’s father?
Options:
a. 60 inches
b. 66 inches
c. 72 inches
d. 216 inches

Answer: 72 inches

Explanation:

Judi’s father is 6 feet tall. The minimum height to ride a rollercoaster is given in inches.
1 feet = 12 inches
6 feet = 6 × 12 inches = 72 inches
Thus the correct answer is option C.

Page No. 661

Question 1.
Compare the size of a quart to the size of a pint.
Use a model to help.


1 quart is ____ times as much as _____ pint.

Answer: 1 quart is 2 times as much as 1 pint.

Complete.

Question 2.
2 pints = _____ cups

Answer: 4 cups

Explanation:

1 pint = 2 cups
2 pints = 2 × 2 cups = 4 cups
2 pints = 4 cups

Question 3.
3 gallons = _____ quarts

Answer: 12 quarts

Explanation:

1 gallon = 4 quarts
3 gallons = 3 × 4 quarts = 12 quarts
3 gallons = 12 quarts

Question 4.
6 quarts = _____ cups

Answer: 24 cups

Explanation:

1 quart = 4 cups
6 quarts = 6 × 4 cups = 24 cups
6 quarts = 24 cups

Use a model or Tools to complete.

Question 5.
4 gallons = _____ pints

Answer: 32 pints

Explanation:

1 gallon = 8 pints
4 gallons = 4 × 8 pints = 32 pints
4 gallons = 32 pints

Question 6.
5 cups = _____ fluid ounces

Answer:

1 cup = 8 fluid ounces
5 cups = 5 × 8 fluid ounces = 40 fluid ounces
5 cups = 40 fluid ounces

Use Symbols Algebra Compare using >, <, or =.

Question 7.
2 gallons _____ 32 cups

Answer: 2 gallons = 32 cups

Explanation:

1 gallon = 16 cups
2 gallons = 2 × 16 cups = 32 cups
2 gallons = 32 cups

Question 8.
4 pints _____ 6 cups

Answer: 4 pints > 6 cups

Explanation:

1 pint = 2 cups
4 pints = 4 × 2 cups = 8 cups
So, 4 pints > 6 cups

Question 9.
5 quarts _____ 11 pints

Answer: 5 quarts < 11 pints

Explanation:

1 quart = 2 pints
5 quarts = 5 × 2 pints = 10 pints
10 is less than 11 pints
So, 5 quarts < 11 pints

Question 10.
A soccer team has 25 players. The team’s thermos holds 4 gallons of water. If the thermos is full, is there enough water for each player to have 2 cups? Explain. Make a table to help.

________

Answer: Enough water

Page No. 662

Question 11.
Verify the Reasoning of Others Whose statement makes sense? Whose statement is nonsense? Explain your reasoning.

_______ ’s statement makes sense.

Answer: Angela’s Statement is true. A gallon is 8 times as much as a pint, so 1 pint is 1/8 of a gallon.
Zach’s statement is nonsense. There are 8 pints in a gallon, not 4, so a pint cannot be 1/4 of a gallon.

Question 12.
Peter’s glasses each hold 8 fluid ounces. How many glasses of juice can Peter pour from a bottle that holds 2 quarts?
_____ glasses

Answer: 8 glasses

Explanation:

Peter’s glasses each hold 8 fluid ounces.
There is 32oz per quart. 8 goes into 32 a total of four times. So since there are two quarts, Peter can pour 8 glasses.

Question 13.
A pitcher contains 5 quarts of water. Josy says the pitcher contains 10 cups of water. Explain Josy’s error. Then find the correct number of cups the pitcher contains.
Type below:
________

Answer: 20 cups

Explanation:

Josy multiplied the number of quarts by 2.
There are 4 cups in each quart.
She should have multiplied the number of quarts by 4
5 × 4 = 20
Therefore there are 20 cups in the pitcher.

Common Core – New – Page No. 663

Customary Units of Liquid Volume

Complete.

Question 1.
6 gallons = 24 quarts
Think: 1 gallon = 4 quarts,
so 6 gallons = 6 × 4 quarts, or 24 quarts

Question 2.
12 quarts = _____ pints

Answer: 24 pints

Explanation:

1 quart = 2 pints
12 quarts = 12 × 2 pints
12 pints = 24 pints

Question 3.
6 cups = _____ fluid ounces

Answer: 48 fluid ounces

Explanation:

1 cup = 8 fluid ounces
6 cups = 6 × 8 fluid ounces = 48 fluid ounces
So, 6 cups = 48 fluid ounces

Question 4.
9 pints = _____ cups

Answer: 18 cups

Explanation:

1 pint = 2 cups
9 pints = 9 × 2 cups = 18 cups
9 pints = 18 cups

Question 5.
10 quarts = _____ cups

Answer: 40 cups

Explanation:

1 quart = 4 cups
10 quarts = 10 × 4 cups = 40 cups
10 quarts = 40 cups

Question 6.
5 gallons = _____ pints

Answer: 40 pints

Explanation:

1 gallon = 8 pints
5 gallons = 5 × 8 pints = 40 pints
5 gallons = 40 pints

Question 7.
3 gallons = _____ cups

Answer: 48 cups

Explanation:

1 gallon = 16 cups
3 gallons = 3 × 16 cups = 48 cups
Therefore 3 gallons = 48 cups

Compare using <, >, or =.

Question 8.
6 pints _____ 60 fluid ounces

Answer: 6 pints > 60 fluid ounces

Explanation:

1 pint = 16 fluid ounces
6 pints = 6 × 16 fluid ounces = 96 fluid ounces
96 fluid ounces is greater than 60 fluid ounces
So, 6 pints > 60 fluid ounces

Question 9.
3 gallons _____ 30 quarts

Answer: 3 gallons < 30 quarts

Explanation:

1 gallon = 4 quarts
3 gallons = 3 × 4 quarts = 12 quarts
12 is less than 30
So, 3 gallons < 30 quarts

Question 10.
5 quarts _____ 20 cups

Answer: 5 quarts = 20 cups

Explanation:

1 quart = 4 cups
5 quarts = 5 × 4 cups = 20 cups
5 quarts = 20 cups

Question 11.
6 cups _____ 12 pints

Answer: 6 cups < 12 pints

Explanation:

1 cup = \(\frac{1}{2}\) pint
6 cups = 6 × \(\frac{1}{2}\) pint = 3 pints
3 is less than 12.
So, 6 cups < 12 pints

Question 12.
8 quarts _____ 16 pints

Answer: 8 quarts = 16 pints

Explanation:

1 quart = 2 pints
8 quarts = 8 × 2 pints = 16 pints
8 quarts = 16 pints

Question 13.
6 gallons _____ 96 pints

Answer: 6 gallons < 96 pints

Explanation:

1 gallon = 8 pints
6 gallons = 6 × 8 pints = 48 pints
48 is less than 96 pints
So, 6 gallons < 96 pints

Problem Solving

Question 14.
A chef makes 1 \(\frac{1}{2}\) gallons of soup in a large pot. How many 1-cup servings can the chef get from this large pot of soup?
_____ 1-cup servings

Answer: 24 1-cup servings

Explanation:

A chef makes 1 \(\frac{1}{2}\) gallons of soup in a large pot.
1 gallon = 16 cups
We have to convert a mixed fraction into a proper fraction.
1 \(\frac{1}{2}\) = \(\frac{3}{2}\)
\(\frac{3}{2}\) × 16 cups = 24 cups
Thus the chef get 24 1-cup servings from this large pot of soup.

Question 15.
Kendra’s water bottle contains 2 quarts of water. She wants to add a drink mix to it, but the directions for the drink mix give the amount of water in fluid ounces. How many fluid ounces are in her bottle?
_____ fluid ounces

Answer: 64 fluid ounces

Explanation:

Kendra’s water bottle contains 2 quarts of water.
She wants to add a drink mix to it, but the directions for the drink mix give the amount of water in fluid ounces.
1 quart = 4 cups
1 cup = 8 fluid ounces
4 cups = 4 × 8 fluid ounces = 32 fluid ounces
2 quarts = 2 × 32 fluid ounces = 64 fluid ounces
Thus 64 fluid ounces are in her bottle.

Common Core – New – Page No. 664

Lesson Check

Question 1.
Joshua drinks 8 cups of water a day. The recommended daily amount is given in fluid ounces. How many fluid ounces of water does he drink each day?
Options:
a. 16 fluid ounces
b. 32 fluid ounces
c. 64 fluid ounces
d. 128 fluid ounces

Answer: 64 fluid ounces

Explanation:

1 cup = 8 fluid ounces
8 cups = 8 × 8 fluid ounces = 64 fluid ounces
8 cups = 64 fluid ounces
Thus the correct answer is option C.

Question 2.
A cafeteria used 5 gallons of milk in preparing lunch. How many 1-quart containers of milk did the cafeteria use?
Options:
a. 10
b. 20
c. 40
d. 80

Answer: 20

Explanation:

A cafeteria used 5 gallons of milk in preparing lunch.
1 gallon = 4 quarts
5 gallons = 5 × 4 quarts = 20 quarts
5 gallons = 20 quarts
So, the correct answer is option B.

Spiral Review

Question 3.
Roy uses \(\frac{1}{4}\) cup of batter for each muffin. Which list shows the amounts of batter he will use depending on the number of muffins he makes?
Options:
a. \(\frac{1}{4}, \frac{1}{5}, \frac{1}{6}, \frac{1}{7}, \frac{1}{8}\)
b. \(\frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{4}{4}, \frac{5}{4}\)
c. \(\frac{1}{4}, \frac{2}{8}, \frac{3}{12}, \frac{4}{16}, \frac{5}{20}\)
d. \(\frac{1}{4}, \frac{2}{8}, \frac{4}{16}, \frac{6}{24}, \frac{8}{32}\)

Answer: \(\frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{4}{4}, \frac{5}{4}\)

Explanation:

Given that, Roy uses \(\frac{1}{4}\) cup of batter for each muffin.
The amounts of batter he will use depending on the number of muffins he makes is \(\frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{4}{4}, \frac{5}{4}\)
The correct answer is option B.

Question 4.
Beth has \(\frac{7}{100}\) of a dollar. Which shows the amount of money Beth has?
Options:
a. $7.00
b. $0.70
c. $0.07
d. $0.007

Answer: $0.07

Explanation:

Beth has \(\frac{7}{100}\) of a dollar.
The decimal of \(\frac{7}{100}\) = 0.07
The amount of money Beth has is $0.07
So, the answer is option C.

Question 5.
Name the figure that Enrico drew below.

Options:
a. a ray
b. a line
c. a line segment
d. an octagon

Answer: a ray

Explanation:

A part of a line with a start point but no endpoint is called a ray.
The above figure has no endpoint.
So, the answer is option A.

Question 6.
A hippopotamus weighs 4 tons. Feeding instructions are given for weights in pounds. How many pounds does the hippopotamus weigh?
Options:
a. 4,000 pounds
b. 6,000 pounds
c. 8,000 pounds
d. 12,000 pounds

Answer: 8,000 pounds

Explanation:

A hippopotamus weighs 4 tons. Feeding instructions are given for weights in pounds.
We know that 1 ton = 2000 pounds
4 tons = 4 × 2000 pounds = 8000 pounds
Thus the answer is option C.

Page No. 667

Question 1.
A food critic collected data on the lengths of time customers waited for their food. Order the data from least to greatest time. Make a tally table and a line plot to show the data.



Type below:
________

Answer:

Tally Table:

Line plot:

Use your line plot for 2 and 3.

Question 2.
On how many customers did the food critic collect data?
________

Answer: 7

Explanation:

Number of customers waited for half an hour = 2
Number of customers waited for an hour = 1
Number of customers waited for \(\frac{3}{4}\) of an hour = 1
Number of customers waited for \(\frac{1}{4}\) of an hour = 3
Total number of customers = 2 + 1 + 1 + 3 = 7
The food critic collects data from 7 customers.

Question 3.
What is the difference between the longest time and the shortest time that customers waited?
\(\frac{□}{□}\)

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

The longest time is 1 hour
And the shortest time is \(\frac{1}{4}\)
1 – \(\frac{1}{4}\) = \(\frac{3}{4}\)

Question 4.
Use Models The data show the lengths of the ribbons Mia used to wrap packages. Make a tally table and a line plot to show the data.



Type below:
________

Answer:

Line plot:

Question 5.
What is the difference in length between the longest ribbon and the shortest ribbon Mia used?
\(\frac{□}{□}\) yard

Answer: \(\frac{5}{6}\) yard

Explanation:

The longest ribbon is \(\frac{6}{6}\) yard
The shortest ribbon is \(\frac{1}{6}\) yard
To find the difference of both the ribbons we have to subtract the shortest ribbon from the longest ribbon
\(\frac{6}{6}\) – \(\frac{1}{6}\) = \(\frac{5}{6}\)

Page No. 668

Question 6.
The line plot shows the distances the students in Mr. Boren’s class ran at the track in miles. Altogether, did the students run more or less than 5 miles?

a. What are you asked to find?
Type below:
________

Answer: If the students ran more or less than 5 miles together.

Question 6.
b. What information do you need to use?
Type below:
________

Answer: I need the information about the distance each student ran.

Question 6.
c. How will the line plot help you solve the problem?
Type below:
________

Answer: With the help of the line plot I can know how far each student ran.

Question 6.
d. What operation will you use to solve the problem?
Type below:
________

Answer: I use addition to solve the problem.

Question 6.
e. Show the steps to solve the problem.
Type below:
________

Answer: \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{2}{5}\) + \(\frac{2}{5}\) + \(\frac{3}{5}\) + \(\frac{4}{5}\) + \(\frac{4}{5}\) + \(\frac{5}{5}\) = \(\frac{22}{5}\)
The mixed fraction of \(\frac{22}{5}\) is 4 \(\frac{2}{5}\).

Question 6.
Complete the sentences.
The students ran a total of ____ miles.
The distance is ____ than 5 miles. Altogether the students ran ____ than 5 miles.
Type below:
________

Answer: he students ran a total of 4 \(\frac{2}{5}\) miles.
The distance is less than 5 miles. Altogether the students ran less than 5 miles.

Question 7.
Lena collects antique spoons. The line plot shows the lengths of the spoons in her collection. If she lines up all of her spoons in order of size, what is the size of the middle spoon? Explain.

\(\frac{□}{□}\) feet spoon

Answer: \(\frac{4}{4}\) feet
I ordered the data from the least to the greatest value and found the middle value.

Question 8.
A hiking group recorded the distances they hiked. Complete the line plot to show the data.


Type below:
________

Answer:

Common Core – New – Page No. 669

Line Plots

Question 1.
Some students compared the time they spend riding the school bus. Complete the tally table and line plot to show the data.

Answer:

Use your line plot for 2 and 3.

Question 2.
How many students compared times?
______ students

Answer: 8

Explanation:

Number of students spent \(\frac{1}{6}\) of an hour on school bus = 2
Number of students spent \(\frac{2}{6}\) of an hour on school bus = 1
Number of students spent \(\frac{3}{6}\) of an hour on school bus = 4
Number of students spent \(\frac{4}{6}\) of an hour on school bus = 1
Total number of students = 2 + 1 + 4 + 1 = 8 students

Question 3.
What is the difference between the longest time and shortest time students spent riding the bus?
\(\frac{□}{□}\) hour

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

Explanation:

Longest time is \(\frac{4}{6}\) and shortest time is \(\frac{1}{6}\)
\(\frac{4}{6}\) – \(\frac{1}{6}\) = \(\frac{3}{6}\)
Thus the difference between the longest time and shortest time students spent riding the bus is \(\frac{3}{6}\)

Problem Solving

For 4–5, make a tally table on a separate sheet of paper.
Make a line plot in the space below the problem.

Question 4.

Answer:

Question 5.

Answer:

Common Core – New – Page No. 670

Lesson Check

Use the line plot for 1 and 2.

Question 1.
How many students were reading during study time?

Options:
a. 5
b. 6
c. 7
d. 8

Answer: 8

Explanation:

By seeing the above line plot we can say that the number of students was reading during study time is 8.
So, the correct answer is option D.

Question 2.
What is the difference between the longest time and shortest time spent reading?
Options:
a. \(\frac{4}{8}\) hour
b. \(\frac{3}{8}\) hour
c. \(\frac{2}{8}\) hour
d. \(\frac{1}{8}\) hour

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

Explanation:

The line plot shows that the shortest time is \(\frac{1}{8}\) hour and the longest time is \(\frac{4}{8}\) hour.
The difference of between the longest time and shortest time spent reading is \(\frac{4}{8}\) – \(\frac{1}{8}\) = \(\frac{3}{8}\) hour
So, the correct answer is option B.

Spiral Review

Question 3.
Bridget is allowed to play on-line games for \(\frac{75}{100}\) of an hour each day. Which shows that fraction as a decimal?
Options:
a. 75.0
b. 7.50
c. 0.75
d. 0.075

Answer: 0.75

Explanation:

The decimal form of the fraction \(\frac{75}{100}\) is 0.75.
So, the answer is option C.

Question 4.
Bobby’s collection of sports cards has \(\frac{3}{10}\) baseball cards and \(\frac{39}{100}\) football cards. The rest are soccer cards. What fraction of Bobby’s sports cards are baseball or football cards?
Options:
a. \(\frac{9}{100}\)
b. \(\frac{42}{100}\)
c. \(\frac{52}{100}\)
d. \(\frac{69}{100}\)

Answer: \(\frac{69}{100}\)

Explanation:

The way the question is written, there are other possibilities, but it seems to me the simplest possibility is that Bobby has 100 sports cards. If 3/10 are baseball, that’s 30. He has 39 football cards. So for baseball and football together it’s 69 cards.
So, the fraction is of Bobby’s sports cards are baseball or football cards is \(\frac{69}{100}\)
Thus the correct answer is option D.

Question 5.
Jeremy gives his horse 12 gallons of water each day. How many 1-quart pails of water is that?
Options:
a. 24
b. 48
c. 72
d. 96

Answer: 48

Explanation:

Jeremy gives his horse 12 gallons of water each day.
For 1 quart he needs 12 × 4 = 48 gallons of water
So, the answer is option B.

Question 6.
An iguana at a pet store is 5 feet long. Measurements for iguana cages are given in inches. How many inches long is the iguana?
Options:
a. 45 inches
b. 50 inches
c. 60 inches
d. 72 inches

Answer: 60 inches

Explanation:

An iguana at a pet store is 5 feet long. Measurements for iguana cages are given in inches.
1 feet = 12 inches
5 feet = 5 × 12 inches = 60 inches
Thus the answer is option C.

Page No. 671

Question 1.
A _______ is a customary unit used to measure weight.
_______

Answer: Pound

Question 2.
The cup and the _____ are both customary units for measuring liquid volume.
_______

Answer: Pint

Complete the sentence. Write more or less.

Question 3.
A cat weighs _______ than one ounce
____

Answer: more

Explanation:
Pound, unit of avoirdupois weight, equal to 16 ounces
The weigh of the cat is measured in pounds. So, the cat weighs more than one ounce

Question 4.
Serena’s shoe is ______ than one yard long.
____

Answer: Less

The length of the shoe is less when compared to the yard.
So, Serena’s shoe is less than one yard long.

Complete.

Question 5.
5 feet = ____ inches

Answer: 60 inches

Explanation:

1 feet = 12 inches
5 feets = 5 × 12 inches = 60 inches
5 feets = 60 inches

Question 6.
4 tons = ____ pounds

Answer: 8000 pounds

Explanation:

1 ton = 2000 pounds
4 tons = 4 × 2000 pounds = 8000 pounds
The answer is 4 tons = 8000 pounds

Question 7.
4 cups = ____ pints

Answer: 2 pints

Explanation:

1 pint = 2 cups
4 cups = 4 × 1/2 pint = 2 pints
Thus 4 cups = 2 pints

Question 8.
Mrs. Byrne’s class went raspberry picking. The data show the weights of the cartons of raspberries the students picked. Make a tally table and a line plot to show the data.



Type below:
_________

Line plot:

Tally Marks:

Use your line plot for 9 and 10.

Question 9.
What is the difference in weight between the heaviest carton and the lightest carton of raspberries?
\(\frac{□}{□}\) pound

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

Explanation:

The heaviest carton of raspberries is \(\frac{4}{4}\)
The lightest carton of raspberries is \(\frac{1}{4}\)
The difference in weight between the heaviest carton and a lightest carton of raspberries = \(\frac{4}{4}\) – \(\frac{1}{4}\) = \(\frac{3}{4}\) pounds.

Question 10.
How many pounds of raspberries did Mrs. Byrne’s class pick in all?
______ pounds

Answer: 5 pounds

Explanation:

Add total weight of carton of raspberries picked
= \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{2}{4}\) + \(\frac{2}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{4}{4}\) = 5
Therefore Mrs. Byrne’s class picked 5 pounds of raspberries in all.

Page No. 672

Question 11.
A jug contains 2 gallons of water. How many quarts of water does the jug contain?
______ quarts

Answer: 8 quarts

Explanation:

A jug contains 2 gallons of water
Now we have to gallons into quarts.
We know that 1 gallon = 4 quarts
2 gallons = 2 × 4 quarts = 8 quarts
Thus the jug contain 8 quarts of water.

Question 12.
Serena bought 4 pounds of dough to make pizzas. The recipe gives the amount of dough needed for a pizza in ounces. How many ounces of dough did she buy?
______ ounces

Answer: 64 ounces

Explanation:

Serena bought 4 pounds of dough to make pizzas.
The recipe gives the amount of dough needed for a pizza in ounces.
We know that,
1 pound = 16 ounces
4 pounds = 4 × 16 ounces = 64 ounces
Thus Serena bought 64 ounces of dough.

Question 13.
Vicki has a 50 inch roll of ribbon. She used 3 feet of the ribbon to wrap a gift. How many inches of ribbon does she have left?
______ inches

Answer: 14 inches

Explanation:

Vicki has a 50 inch roll of ribbon. She used 3 feet of the ribbon to wrap a gift.
1 feet = 12 inches
3 feet = 3 × 12 inches = 36 inches
Now subtract 36 inches from 50 inches
50 inches – 36 inches = 14 inches
Therefore 14 inches of ribbon is left.

Question 14.
The watering can that Carlos uses in his vegetable garden holds 5 of a certain unit of liquid volume. When full, how much water is in the watering can?

5 ______ of water

Answer: 5 gallons of water
The unit to measure the liquid volume is the gallon. So, the watering can holds 5 gallons of water.

Page No. 675

Complete.

Question 1.
2 meters = _____ centimeters

Answer: 200 centimeters

Explanation:

Convert meters into centimeters
1 meter = 100 centimeters
2 meters = 2 × 100 centimeters = 200 centimeters

Question 2.
3 centimeters = _____ millimeters

Answer: 30 millimeters

Explanation:

Convert the centimeters into millimeters
1 centimeter = 10 millimeters
3 centimeters = 3 × 10 millimeters = 30 millimeters
3 centimeters = 30 millimeters

Question 3.
5 decimeters = _____ centimeters

Answer: 50 centimeters

Explanation:

1 decimeter = 10 centimeters
5 decimeters = 5 × 10 centimeters = 50 centimeters
5 decimeters = 50 centimeters

Use Symbols Algebra Compare using <, >, or =.

Question 4.
4 meters _____ 40 decimeters

Answer: 4 meters = 40 decimeters

Explanation:

1 meter = 10 decimeters
4 meters = 4 × 10 decimeters = 40 decimeters
4 meters = 40 decimeters

Question 5.
5 centimeters _____ 5 millimeters

Answer: 5 centimeters > 5 millimeters

Explanation:

1 centimeter = 10 millimeters
5 centimeters = 50 millimeters
50 millimeters is greater than 5 millimeters
Thus 5 centimeters > 5 millimeters

Question 6.
6 decimeters _____ 65 centimeters

Answer: 6 decimeters < 65 centimeters

Explanation:

1 decimeter = 10 centimeters
6 decimeters = 6 × 10 centimeters = 60 centimeters
60 is less than 65 centimeters
6 decimeters < 65 centimeters

Question 7.
7 meters _____ 700 millimeters

Answer: 7 meters > 700 millimeters

Explanation:

1 meter = 1000 millimeters
7 meters = 7 × 1000 millimeters = 7000 millimeters
7000 is greater than 700
So, 7 meters > 700 millimeters

Describe the length in meters. Write your answer as a fraction and as a decimal.

Question 8.
65 centimeters = ______ or ______ meter
Type below:
_________

Answer: \(\frac{65}{100}\) or 0.65 meter

Explanation:

The fraction for 65 centimeters is \(\frac{65}{100}\) and the decimal form of the fraction is 0.65 meter

Question 9.
47 centimeters = ______ or ______ meter
Type below:
_________

Answer: \(\frac{47}{100}\) or 0.47 meter

Explanation:

The fraction for 47 centimeters is \(\frac{47}{100}\) and the decimal is 0.47 meter.

Question 10.
9 decimeters = ______ or ______ meter
Type below:
_________

Answer: \(\frac{9}{10}\) or 0.9 meter

Explanation:

The fraction for 9 decimeters is \(\frac{9}{10}\) and the decimal for the fraction is 0.9 meter.

Question 11.
2 decimeters = ______ or ______ meter
Type below:
_________

Answer: \(\frac{2}{10}\) or 0.2 meter

Explanation:

The fraction for 2 decimeters is \(\frac{2}{10}\) and the decimal for the fraction is 0.2 meter.

Question 12.
A new building is 25 meters tall. How many decimeters tall is the building?
______ decimeters

Answer: 250 decimeters

Explanation:

A new building is 25 meters tall.
Now we have to convert the meters into decimeters
1 meter = 10 decimeters
25 meters = 25 × 10 decimeters = 250 decimeters
The height of the building is 250 decimeters.

Question 13.
Alexis is knitting a blanket 2 meters long. Every 2 decimeters, she changes the color of the yarn to make stripes. How many stripes will the blanket have? Explain.
______ stripes

Answer: 10 stripes

Explanation:

Given that, Alexis is knitting a blanket 2 meters long. Every 2 decimeters, she changes the color of the yarn to make stripes.
First of all, convert the meters into the decimeters
1 meter = 10 decimeters
2 meters = 20 decimeters
If she changes the color of the yarn for every 2 decimeters then the blanket will have 10 stripes.

Page No. 676

Question 14.
Julianne’s desk is 75 centimeters long. She says her desk is 7.5 meters long. Describe her error.
Type below:
_________

Answer: \(\frac{75}{100}\) or 0.75 meter

The fraction form of 75 centimeters is \(\frac{75}{100}\). The decimation for the fraction is 0.75 meter

Question 15.
Write the equivalent measurements in each column.

Type below:
_________

Answer:

Question 16.
Aruna was writing a report on pecan trees. She made the table of information to the right. Write a problem that can be solved by using the data.

Type below:
_________

Answer: The height of the tree is 21m to 30m. How many centimeters is the height of the tree?

Question 16.
Describe how you could change the problem by changing a unit in the problem. Then solve the problem.
Type below:
_________

Answer:

Convert meters into centimeters.
Given that the height of the height is 21 to 30m
1 meter = 100 centimeters
21 meters = 2100 centimeters, 30 meters = 3000 centimeters
So, the height of the tree in centimeters is 2100 to 3000 centimeters.

Common Core – New – Page No. 677

Metric Units of Length

Complete.

Question 1.
4 meters = 400 centimeters
Think: 1 meter = 100 centimeters,
so 4 meters = 4 × 100 centimeters, or 400 centimeters

Question 2.
8 centimeters = ______ millimeters

Answer: 80 millimeters

Explanation:

1 centimeter = 10 millimeters
8 centimeters = 8 × 10 millimeters = 80 millimeters
8 centimeters = 80 millimeters

Question 3.
5 meters = ______ decimeters

Answer: 50 decimeters

Explanation:

We have to convert meters into decimeters
1 meter = 10 decimeters
5 meters = 5 × 10 decimeters = 50 decimeters
5 meters = 50 decimeters

Question 4.
9 meters = ______ millimeters

Answer: 9000 millimeters

Explanation:

You need to convert meters into millimeters
1 meter = 1000 millimeters
9 meters = 9 × 1000 millimeters = 9000 millimeters
9 meters = 9000 millimeters

Question 5.
7 meters = ______ centimeters

Answer: 700 centimeters

Explanation:

Convert meters into centimeters
1 meter = 100 centimeters
7 meters = 7 × 100 centimeters = 700 centimeters
7 meters = 700 centimeters

Compare using <, >, or =.

Question 6.
8 meters ______ 80 centimeters

Answer: 8 meters > 80 centimeters

Explanation:

1 meter = 100 centimeters
8 meters = 800 centimeters
800 centimeters is greater than 80 centimeters
8 meters > 80 centimeters

Question 7.
3 decimeters ______ 30 centimeters

Answer: 3 decimeters = 30 centimeters

Explanation:

1 decimeter = 10 centimeters
3 decimeters = 3 × 10 centimeters = 30 centimeters
So, 3 decimeters = 30 centimeters

Question 8.
4 meters ______ 450 centimeters

Answer: 4 meters < 450 centimeters

Explanation:

1 meter = 100 centimeters
4 meters = 400 centimeters
400 centimeters < 450 centimeters
So, 4 meters < 450 centimeters

Question 9.
90 centimeters ______ 9 millimeters

Answer: 90 centimeters > 9 millimeters

Explanation:

1 millimeter = 1/10 centimeters
9 millimeters = 1/90 centimeters
So, 90 centimeters > 9 millimeters

Describe the length in meters. Write your answer as a fraction and as a decimal.

Question 10.
43 centimeters =
Type below:
________

Answer: \(\frac{43}{100}\), 0.43

Explanation:

The fraction of 43 centimeters is \(\frac{43}{100}\). the decimal form of \(\frac{43}{100}\) is 0.43

Question 11.
6 decimeters =
Type below:
________

Answer: \(\frac{6}{10}\), 0.6

Explanation:

The fraction form of 6 decimeters is \(\frac{6}{10}\) and the decimal for the fraction is 0.6

Question 12.
8 centimeters =
Type below:
________

Answer: \(\frac{8}{100}\), 0.08

Explanation:

The fraction form of 8 centimeters is \(\frac{8}{100}\). The decimal for the fraction of \(\frac{8}{100}\) is 0.08

Question 13.
3 decimeters =
Type below:
________

Answer: \(\frac{3}{10}\), 0.3

Explanation:

The fraction of 3 decimeters is \(\frac{3}{10}\) and the decimal for the 3 decimeters is 0.3

Problem Solving

Question 14.
A flagpole is 4 meters tall. How many centimeters tall is the flagpole?
_____ centimeters

Answer: 400 centimeters

Explanation:

A flagpole is 4 meters tall.
Now we have to convert the meters into centimeters.
We know that
1 meter = 100 centimeters
4 meters = 4 × 100 centimeters = 400 centimeters
Thus the height of the flagpole is 400 centimeters

Question 15.
A new building is 25 meters tall. How many decimeters tall is the building?
_____ decimeters

Answer: 250 decimeters

Explanation:

A new building is 25 meters tall.
We know that 1 meter = 10 decimeters
25 meters = 25 × 10 decimeters = 250 decimeters
The height of the building is 250 decimeters.

Common Core – New – Page No. 678

Lesson Check

Question 1.
A pencil is 15 centimeters long. How many millimeters long is that pencil?
Options:
a. 1.5 millimeters
b. 15 millimeters
c. 150 millimeters
d. 1,500 millimeters

Answer: 150 millimeters

Explanation:

A pencil is 15 centimeters long
1 centimeter = 10 millimeters
15 centimeters = 15 × 10 millimeters = 150 millimeters
15 centimeters = 150 millimeters
So, the correct answer is option C.

Question 2.
John’s father is 2 meters tall. How many centimeters tall is John’s father?
Options:
a. 2,000 centimeters
b. 200 centimeters
c. 20 centimeters
d. 2 centimeters

Answer: 200 centimeters

Explanation:

John’s father is 2 meters tall.
Convert meters to centimeters.
1 meter = 100 centimeters
2 meters = 2 × 100 centimeters = 200 centimeters
The correct answer is option B.

Spiral Review

Question 3.
Bruce reads for \(\frac{3}{4}\) hour each night. How long will he read in 4 nights?
Options:
a. \(\frac{3}{16}\)hours
b. \(\frac{7}{4}\) hours
c. \(\frac{9}{4}\) hours
d. \(\frac{12}{4}\) hours

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

Explanation:

Bruce reads for \(\frac{3}{4}\) hour each night.
Multiply latex]\frac{3}{4}[/latex] hour with 4 = latex]\frac{3}{4}[/latex] × 4 = \(\frac{12}{4}\) hours
Thus the correct answer is option D.

Question 4.
Mark jogged 0.6 mile. Caroline jogged 0.49 mile. Which inequality correctly compares the distances they jogged?
Options:
a. 0.6 = 0.49
b. 0.6 > 0.49
c. 0.6 < 0.49
d. 0.6 + 0.49 = 1.09

Answer: 0.6 > 0.49

Explanation:

Mark jogged 0.6 mile. Caroline jogged 0.49 mile.
0.49 miles is less than 0.6 miles
So, the correct answer is option B.

Use the line plot for 5 and 6.

Question 5.
How many lawns were mowed?
Options:
a. 8
b. 9
c. 10
d. 11

Answer: 11

Explanation:

The line plot shows that the total number lawns = 11
The correct answer is option D.

Question 6.
What is the difference between the greatest amount and the least amount of gasoline used to mow lawns?
Options:
a. \(\frac{6}{8}\) gallon
b. \(\frac{5}{8}\) gallon
c. \(\frac{4}{8}\) gallon
d. \(\frac{3}{8}\) gallon

Answer: \(\frac{4}{8}\) gallon

Explanation:

The greatest amount of gasoline used to mow lawns = \(\frac{5}{8}\)
The least amount of gasoline used to mow lawns = \(\frac{1}{8}\)
\(\frac{5}{8}\) – \(\frac{1}{8}\) = \(\frac{4}{8}\) gallon
The correct answer is option C.

Page No. 680

Question 1.
There are 3 liters of water in a pitcher. How many milliliters of water are in the pitcher?
There are _____ milliliters in 1 liter. Since I am changing from a larger unit to a smaller unit, I can _____ 3 by 1,000 to find the number of milliliters in 3 liters.
So, there are _____ milliliters of water in the pitcher.

Answer: There are 1000 milliliters in 1 liter. Since I am changing from a larger unit to a smaller unit, I can multiply 3 by 1,000 to find the number of milliliters in 3 liters.
So, there are 3000 milliliters of water in the pitcher.

Complete.

Question 2.
4 liters = _____ milliliters

Answer: 4000 milliliters

Explanation:

1 liter = 1000 milliliters
4 liters = 4 × 1000 milliliters = 4000 milliliters
4 liters = 4000 milliliters

Question 3.
6 kilograms = _____ grams

Answer: 6000 grams

Explanation:

1 kilogram = 1000 grams
6 kilograms = 6 × 1000 grams = 6000 grams
6 kilograms = 6000 grams

Complete.

Question 4.
8 kilograms = _____ grams

Answer: 8000 grams

Explanation:

1 kilogram = 1000 grams
8 kilograms = 8 × 1000 grams = 8000 grams
8 kilograms = 8000 grams

Question 5.
7 liters = _____ milliliters

Answer: 7000 milliliters

Explanation:

1 liter = 1000 milliliters
7 liters = 7 × 1000 milliliters = 7000 milliliters
7 liters = 7000 milliliters

Use Symbols Algebra Compare using <, >, or =.

Question 6.
1 kilogram _____ 900 grams

Answer: 1 kilogram < 900 grams

Explanation:

1 kilogram = 1000 grams
1000 grams is less than 900 grams
1 kilogram < 900 grams

Question 7.
2 liters _____ 2,000 milliliters

Answer: 2 liters = 2,000 milliliters

Explanation:

1 liter = 1000 milliliters
2 liters = 2 × 1000 milliliters = 2000 liters
2 liters = 2,000 milliliters

Look for a Pattern Algebra Complete.

Question 8.

Type below:
_________

Answer:

Question 9.

Type below:
_________

Answer:

Page No. 681

Question 10.
Frank wants to fill a fish tank with 8 liters of water. How many milliliters is that?

_____ milliliters

Answer: 8000 milliliters

Explanation:

Frank wants to fill a fish tank with 8 liters of water.
Convert liters into milliliters.
1 liter = 1000 milliliters
8 liters = 8 × 1000 milliliters = 8000 milliliters

Question 11.
Kim has 3 water bottles. She fills each bottle with 1 liter of water. How many milliliters of water does she have?
_____ milliliters

Answer: 3000 milliliters

Explanation:

Kim has 3 water bottles. She fills each bottle with 1 liter of water.
Convert liters into milliliters.
1 liter = 1000 milliliters
3 liters = 3 × 1000 milliliters = 3,000 milliliters
She has 3000 milliliters of water.

Question 12.
Jared’s empty backpack has a mass of 3 kilograms. He doesn’t want to carry more than 7 kilograms on a trip. How many grams of equipment can Jared pack?
_____ grams

Answer: 4000 grams

Explanation:

Jared’s empty backpack has a mass of 3 kilograms.
He doesn’t want to carry more than 7 kilograms on a trip.
7 kilograms – 3 kilograms = 4 kilograms
Convert kilogram into grams
1 kilogram = 1000 grams
4 kilograms = 4 × 1000 grams = 4000 grams.
Jared can pack 4000 grams of equipment.

Question 13.
A large cooler contains 20 liters of iced tea and a small cooler contains 5 liters of iced tea. How many more milliliters of iced tea does the large cooler contain than the small cooler?
_____ milliliters

Answer: 15000 milliliters

Explanation:

A large cooler contains 20 liters of iced tea and a small cooler contains 5 liters of iced tea.
20 liters – 5 liters = 15 liters
1 liter = 1000 milliliters
15 liters = 15 × 1000 milliliters = 15,000 milliliters
The large cooler contain 15,000 milliliters than the small cooler.

Question 14.
A 500-gram bag of granola costs $4, and a 2-kilogram bag of granola costs $15. What is the least expensive way to buy 2,000 grams of granola? Explain.
Type below:
_________

Answer:
A 500-gram bag of granola costs $4, and a 2-kilogram bag of granola costs $15.
500-gram bag of granola costs $4
2000 grams = 4 × $4 = $16
2-kilogram bag of granola costs $15.
The Least expensive way to buy 2,000 grams of granola is $15.

Question 15.
Verify the Reasoning of Others The world’s largest apple had a mass of 1,849 grams. Sue said the mass was greater than 2 kilograms. Does Sue’s statement make sense? Explain.
Type below:
_________

Answer:

The world’s largest apple had a mass of 1,849 grams.
Sue said the mass was greater than 2 kilograms.
The statement of Sue doesn’t make sense. Because 1,849 grams is less than 2 kilograms.

Page No. 682

Question 16.
Lori bought 600 grams of cayenne pepper and 2 kilograms of black pepper. How many grams of pepper did she buy in all?

a. What are you asked to find?
Type below:
_________

Answer: I am asked to find How many grams of pepper did Lori buy in all.

Question 16.
b. What information will you use?
Type below:
_________

Answer: Number of grams of black pepper and cayenne pepper.

Question 16.
c. Tell how you might solve the problem.
Type below:
_________

Answer: I will solve by adding the weight of both the peppers.

Question 16.
d. Show how you solved the problem.
Type below:
_________

Answer: I solved the problem by converting the kilograms into grams and then add the weight of both the peppers.

Question 16.
e. Complete the sentences.
Lori bought ______ grams of cayenne pepper.
She bought ______ grams of black pepper.
______ + ______ = ______ grams
So, Lori bought ______ grams of pepper in all.
Type below:
_________

Answer:

Lori bought 600 grams of cayenne pepper.
She bought 2000 grams of black pepper.
600 + 2000 = 2600
So, Lori bought 2600 grams of the pepper in all.

Question 17.
Jill has two rocks. One has a mass of 20 grams and the other has a mass of 20 kilograms. Which rock has the greater mass? Explain.
Type below:
_________

Answer:

Jill has two rocks. One has a mass of 20 grams and the other has a mass of 20 kilograms.
To find the greater mass of both the rocks. We have to compare the mass of two rocks.
20 grams is less than 20 kilograms.
The rock of 20 kilograms is having the greater mass.

Question 18.
For numbers 18a–18c, choose Yes or No to tell whether the measurements are equivalent.
a. 5,000 grams and 5 kilograms
i. yes
ii. no

Answer: Yes

Explanation:

1 kilogram = 1000 grams
5 kilograms = 5 × 1000 grams = 5000 grams
So, the above statement is true.

Question 18.
b. 300 milliliters and 3 liters
i. yes
ii. no

Answer: No

Explanation:

1 liter = 1000 milliliters
3 liters = 3000 milliliters
So, the above statement is false.

Question 18.
c. 8 grams and 8,000 kilograms
i. yes
ii. no

Answer: Yes

Explanation:

1 kilogram = 1000 grams
8 kilograms = 8 × 1000 grams = 8000 grams
So, the above statement is true.

Common Core – New – Page No. 683

Metric Units of Mass and Liquid Volume

Complete.

Question 1.
5 liters = 5,000 milliliters
Think: 1 liter 5 1,000 milliliters,
so 5 liters 5 5 × 1,000 milliliters, or 5,000 milliliters

Question 2.
3 kilograms = _____ grams

Answer: 3000 grams

Explanation:

Convert kilograms into grams
1 kilogram = 1000 grams
3 kilograms = 3 × 1000 grams = 3000 grams
3 kilograms = 3000 grams

Question 3.
8 liters = _____ milliliters

Answer: 8000 milliliters

Explanation:

Convert liters to milliliters
1 liter = 1000 milliliters
8 liters = 8 × 1000 milliliters = 8000 milliliters
8 liters = 8000 milliliters

Question 4.
7 kilograms = _____ grams

Answer: 7000 grams

Explanation:

Convert kilograms into grams
1 kilogram = 1000 grams
7 kilograms = 7 × 1000 grams = 7000 grams
7 kilograms = 7000 grams

Question 5.
9 liters = _____ milliliters

Answer: 9000 milliliters

Explanation:

Convert liters to milliliters
1 liter = 1000 milliliters
9 liters = 9 × 1000 milliliters = 9000 milliliters
9 liters = 9000 milliliters

Question 6.
2 liters = _____ milliliters

Answer: 2000 milliliters

Explanation:

Convert liters to milliliters
1 liter = 1000 milliliters
2 liters = 2 × 1000 milliliters = 2000 milliliters
2 liters = 2000 milliliters

Question 7.
6 kilograms = _____ grams

Answer: 6000 grams

Explanation:

Convert kilograms into grams
1 kilogram = 1000 grams
6 kilograms = 6 × 1000 grams = 6000 grams
6 kilograms = 6000 grams

Compare using <, >, or =.

Question 8.
8 kilograms _____ 850 grams

Answer: 8 kilograms > 850 grams

Explanation:

1 kilogram = 1000 grams
8 kilograms = 8 × 1000 grams = 8000 grams
8000 grams is greater than 850 grams
So, 8 kilograms > 850 grams

Question 9.
3 liters _____ 3,500 milliliters

Answer: 3 liters < 3,500 milliliters

Explanation:

Convert liters to milliliters
1 liter = 1000 milliliters
3 liters = 3 × 1000 milliliters = 3000 milliliters
3000 milliliters is less than 3,500 milliliters
Thus, 3 liters < 3,500 milliliters

Question 10.
1 kilogram _____ 1,000 grams

Answer: 1 kilogram = 1,000 grams

Explanation:

1 kilogram = 1000 grams
The symbol the above statement is 1 kilogram = 1,000 grams

Question 11.
5 liters _____ 520 milliliters

Answer: 5 liters > 520 milliliters

Explanation:

Convert liters to milliliters
1 liter = 1000 milliliters
5 liters = 5 × 1000 milliliters = 5000 milliliters
5000 milliliters is greater than 520 milliliters
5 liters > 520 milliliters

Problem Solving

Question 12.
Kenny buys four 1-liter bottles of water. How many milliliters of water does Kenny buy?
_____ milliliters

Answer: 4000 milliliters

Explanation:

Kenny buys four 1-liter bottles of water.
4 × 1-liter = 4 liters
Kenny buys 4-liter bottles
Now convert liters into milliliters
1 liter = 1000 milliliters
4 liters = 4 × 1000 milliliters = 4000 milliliters
Kenny bought 4000 milliliters of water.

Question 13.
Mrs. Jones bought three 2-kilogram packages of flour. How many grams of flour did she buy?
_____ grams

Answer: 6000 grams

Explanation:

Mrs. Jones bought three 2-kilogram packages of flour.
That means she buys 6 kilograms of flour.
1 kilogram = 1000 grams
6 kilograms = 6 × 1000 grams = 6000 grams
Mrs. Jones bought 6000 grams of flour.

Question 14.
Colleen bought 8 kilograms of apples and 2.5 kilograms of pears. How many more grams of apples than pears did she buy?
_____ grams

Answer: 5500 grams

Explanation:

Colleen bought 8 kilograms of apples and 2.5 kilograms of pears.
1 kilogram = 1000 grams
8 kilograms = 8 × 1000 grams = 8000 grams
2.5 kilograms = 2.5 × 1000 grams = 2500 grams
8000 grams – 2500 grams = 5500 grams
That means Collen bought 5500 grams of apples than pears.

Question 15.
Dave uses 500 milliliters of juice for a punch recipe. He mixes it with 2 liters of ginger ale. How many milliliters of punch does he make?
_____ milliliters

Answer: 2500 milliliters

Explanation:

Dave uses 500 milliliters of juice for a punch recipe. He mixes it with 2 liters of ginger ale.
1 liter = 1000 milliliters
2 liters = 2 × 1000 milliliters = 2000 milliliters
Add 2000 milliliters from 500 milliliters
2000 milliliters + 500 milliliters = 2500 milliliters
Dave made 2500 milliliters of punch.

Common Core – New – Page No. 684

Lesson Check

Question 1.
During his hike, Milt drank 1 liter of water and 1 liter of sports drink. How many milliliters of liquid did he drink in all?
Options:
a. 20 milliliters
b. 200 milliliters
c. 2,000 milliliters
d. 20,000 milliliters

Answer: 2,000 milliliters

Explanation:

Given,
During his hike, Milt drank 1 liter of water and 1 liter of sports drink.
we have to convert liters into milliliters.
1 liter = 1000 milliliters
2 liters = 2 × 1000 milliliters = 2000 milliliters.
Thus the correct answer is option C.

Question 2.
Larinda cooked a 4-kilogram roast. The roast left over after the meal weighed 3 kilograms. How many grams of roast were eaten during that meal?
Options:
a. 7,000 grams
b. 1,000 grams
c. 700 grams
d. 100 grams

Answer: 1,000 grams

Explanation:

Given that,
Larinda cooked a 4-kilogram roast.
The roast leftover after the meal weighed 3 kilograms.
4 kilogram – 3 kilogram = 1kilogram
Convert kilograms into grams.
1 kilogram = 1000 grams
So, the correct answer is option B.

Spiral Review

Question 3.
Use a protractor to find the angle measure.

Options:
a. 15°
b. 35°
c. 135°
d. 145°

Answer: 145°

Explanation:

By using the protractor we can measure the unknown angle for the above figure.
The angle for the above figure is 145°
The correct answer is option D.

Question 4.
Which of the following shows parallel lines?
Options:
a.
b.
c.
d.

Answer:

Non-intersecting lines are known as parallel lines. From the above figures, we can that option c has non intersecting lines.
So, the correct answer is option C.

Question 5.
Carly bought 3 pounds of birdseed. How many ounces of birdseed did she buy?
Options:
a. 30 ounces
b. 36 ounces
c. 42 ounces
d. 48 ounces

Answer: 48 ounces

Explanation:

Carly bought 3 pounds of birdseed.
Convert the pounds into ounces.
1 pound = 16 ounces
3 pounds = 3 × 16 ounces = 48 ounces.
Thus Carly bought 48 ounces of birdseed.
The correct answer is option D.

Question 6.
A door is 8 decimeters wide. How wide is the door in centimeters?
Options:
a. 8 centimeters
b. 80 centimeters
c. 800 centimeters
d. 8,000 centimeters

Answer: 80 centimeters

Explanation:

A door is 8 decimeters wide.
1 decimeter = 10 centimeters
8 decimeters = 8 × 10 centimeters = 80 centimeters
The door is 80 centimeters wide.
Thus the correct answer is option B.

Page No. 687

Question 1.
Compare the length of a year to the length of a month.
Use a model to help.


1 year is _____ times as long as _____ month.
Type below:
_______

Answer: 1 year is 12 times as long as 1 month.

Complete.

Question 2.
2 minutes = _____ seconds

Answer: 120 seconds

Explanation:

Convert minutes to seconds.
1 minute = 60 seconds
2 minutes = 2 × 60 seconds = 120 seconds
2 minutes = 120 seconds

Question 3.
4 years = _____ months

Answer: 48 months

Explanation:

Convert year to months
1 year = 12 months
4 years = 4 × 12 months = 48 months
So, 4 years = 48 months

Complete.

Question 4.
3 minutes = _____ seconds

Answer: 180 seconds

Explanation:

Convert minutes to seconds.
1 minute = 60 seconds
3 minutes = 3 × 60 seconds = 180 seconds
So, 3 minutes = 180 seconds

Question 5.
4 hours = _____ minutes

Answer: 240 minutes

Explanation:

Convert hours to minutes
1 hour = 60 minutes
4 hours = 4 × 60 minutes = 240 minutes
4 hours = 240 minutes

Use Symbols Algebra Compare using >, <, or =.

Question 6.
3 years _____ 35 months

Answer: 3 years > 35 months

Explanation:

First of all, you need to convert years to minutes
1 year = 12 months
3 years = 3 × 12 months = 36 months
36 months is greater than 35 months
Thus 3 years > 35 months

Question 7.
2 days _____ 40 hours

Answer: 2 days > 40 hours

Explanation:

Convert days to hours
1 day = 24 hours
2 days = 2 × 24 hours = 48 hours
48 is greater than 40.
So, 2 days > 40 hours

Question 8.
Damien has lived in the apartment building for 5 years. Ken has lived there for 250 weeks. Who has lived in the building longer? Explain. Make a table to help.

_____

Answer:

Given that, Damien has lived in the apartment building for 5 years. Ken has lived there for 250 weeks.

Damien has lived in the building longer.

Question 9.
How many hours are in a week? Explain.
_____ hours

Answer: 168 hours

Explanation:

Convert week to hours
1 day = 24 hours
1 week = 7 days
7 days = 7 × 24 hours = 168 hours
Therefore there are 168 hours in a week.

Page No. 688

Question 10.
Communicate Explain how you know that 9 minutes is less than 600 seconds.
Type below:
________

Answer:

First, convert minutes to seconds
We know that,
1 minute = 60 seconds
9 minutes = 9 × 60 seconds = 540 seconds.
540 is less than 600 seconds.
Therefore 9 minutes is less than 600 seconds.

Question 11.
Draw lines to match equivalent time intervals. Some intervals might not have a match.

Type below:
________

Answer:

One day is the length of time it takes Earth to make one complete rotation. One year is the time it takes Earth to revolve around the sun. To make the calendar match Earth’s orbit time, there are leap years. Leap years add one extra day to the year. A leap day, February 29, is added to the calendar every four years.

Question 12.
How many days are there in 4 years, if the fourth year is a leap year? Explain. Make a table to help.

_____ days

Answer:

Question 13.
Parker was born on February 29, 2008. The second time he is able to celebrate on his actual birthday is in 2016. How many days old will Parker be on February 29, 2016?
_____ days

Answer: 2922 days

Explanation:

Parker was born on February 29, 2008.
The second time he is able to celebrate on his actual birthday is in 2016.
Parker was 8 years old.
There are 2 leap years out of 8 years. There are 366 days in a leap year = 366 × 2 = 732
And multiply 6 years with 365 = 365 × 6 = 2190
2190+ 732 = 2920 days.
Parker will be 2920 days old on February 29, 2016.

Common Core – New – Page No. 689

Units of Time

Complete.

Question 1.
6 minutes = 360 seconds
Think: 1 minute = 60 seconds,
so 6 minutes = 6 × 60 seconds, or 360 seconds

Question 2.
5 weeks = ____ days

Answer: 35 days

Explanation:

1 week = 7 days
5 weeks = 5 × 7 days = 35 days
5 weeks = 35 days

Question 3.
3 years = ____ weeks

Answer: 156 weeks

Explanation:

Convert years to weeks.
1 year = 52 weeks
3 years = 3 × 52 weeks = 156 weeks
3 years = 156 weeks.

Question 4.
9 hours = ____ minutes

Answer: 540 minutes

Explanation:

Convert hours into minutes.
1 hour = 60 minutes
9 hours = 9 × 60 minutes = 540 minutes
9 hours = 540 minutes

Question 5.
9 minutes = ____ seconds

Answer: 540 seconds

Explanation:

Convert minutes to seconds.
1 minute = 60 seconds
9 minutes = 9 × 60 seconds = 540 seconds
9 minutes = 540 seconds

Question 6.
5 years = ____ months

Answer: 60 months

Explanation:

Convert years to months
1 year = 12 months
5 years = 5 × 12 months = 60 months
5 years = 60 months

Question 7.
7 days = ____ hours

Answer: 168 hours

Explanation:

Convert days to hours.
1 day = 24 hours
7 days = 7 × 24 hours = 168 hours
7 days = 168 hours

Compare using <, >, or =.

Question 8.
2 years ____ 14 months

Answer: 2 years > 14 months

Explanation:

Convert years to months
1 year = 12 months
2 years = 2 × 12 months = 24 months
24 months is greater than 14 months.
So, 2 years > 14 months

Question 9.
3 hours ____ 300 minutes

Answer: 3 hours < 300 minutes

Explanation:

1 hour = 60 minutes
3 hours = 3 × 60 minutes = 180 minutes.
180 is less than 300 minutes.
So, 3 hours < 300 minutes

Question 10.
2 days ____ 48 hours

Answer: 2 days = 48 hours

Explanation:

Convert days to hours
1 day = 24 hours
2 days = 2 × 24 hours = 48 hours
So, 2 days = 48 hours

Question 11.
6 years ____ 300 weeks

Answer: 6 years > 300 weeks

Explanation:

Convert years to weeks.
1 year = 52 weeks
6 years = 6 × 52 weeks = 312 weeks
312 weeks is greater than 300 weeks.
So, 6 years > 300 weeks.

Question 12.
4 hours ____ 400 minutes

Answer: 4 hours < 400 minutes

Explanation:

Convert hours to minutes
1 hour = 60 minutes
4 hours = 4 × 60 minutes = 240 minutes
240 minutes is less than 400 minutes
4 hours < 400 minutes

Question 13.
5 minutes ____ 300 seconds

Answer: 5 minutes = 300 seconds

Explanation:

Convert minutes to seconds.
1 minute = 60 seconds
5 minutes = 5 × 60 seconds = 300 seconds
5 minutes = 300 seconds

Problem Solving

Question 14.
Jody practiced a piano piece for 500 seconds. Bill practiced a piano piece for 8 minutes. Who practiced longer?
_________

Answer: Jody

Explanation:

Jody practiced a piano piece for 500 seconds.
Bill practiced a piano piece for 8 minutes.
First, convert minutes to seconds.
8 × 60 seconds = 480 seconds
480 seconds is less than 500 seconds.
So, Jody practiced for a longer time.

Question 15.
Yvette’s younger brother just turned 3 years old. Fred’s brother is now 30 months old. Whose brother is older?
_________ ‘s brother

Answer: Yvette’s

Explanation:

Yvette’s younger brother just turned 3 years old.
Fred’s brother is now 30 months old.
Convert years to months.
1 year = 12 months
3 years = 3 × 12 months = 36 months
36 months is more than 30 months.
So, Yvette’s brother is older than Fred’s brother.

Common Core – New – Page No. 690

Lesson Check

Question 1.
Glen rode his bike for 2 hours. For how many minutes did Glen ride his bike?
Options:
a. 60 minutes
b. 100 minutes
c. 120 minutes
d. 150 minutes

Answer: 120 minutes

Explanation:

Glen rode his bike for 2 hours.
Convert hours to minutes.
1 hour = 60 minutes
2 hours = 2 × 60 minutes = 120 minutes.
Thus the correct answer is option C.

Question 2.
Tina says that vacation starts in exactly 4 weeks. In how many days does vacation start?
Options:
a. 28 days
b. 35 days
c. 42 days
d. 48 days

Answer: 28 days

Explanation:

Tina says that vacation starts in exactly 4 weeks.
Convert weeks to days.
1 week = 7 days
4 weeks = 4 × 7 days = 28 days
So, the correct answer is option A.

Spiral Review

Question 3.
Kayla bought \(\frac{9}{4}\) pounds of apples. What is that weight as a mixed number?
Options:
a. 1 \(\frac{1}{4}\) pounds
b. 1 \(\frac{4}{9}\) pounds
c. 2 \(\frac{1}{4}\) pounds
d. 2 \(\frac{3}{4}\) pounds

Answer: 2 \(\frac{1}{4}\) pounds

Explanation:

Kayla bought \(\frac{9}{4}\) pounds of apples.
The mixed fraction of \(\frac{9}{4}\) is 2 \(\frac{1}{4}\) pounds.
Thus the correct answer is option C.

Question 4.
Judy, Jeff, and Jim each earned $5.40 raking leaves. How much did they earn in all?
Options:
a. $1.60
b. $10.80
c. $15.20
d. $16.20

Answer: $16.20

Explanation:

Judy, Jeff, and Jim each earned $5.40 raking leaves.
= 3 × $5.40 = $16.20
They earned $16.20 in all.
The correct answer is option D.

Question 5.
Melinda rode her bike \(\frac{54}{100}\) mile to the library. Then she rode \(\frac{4}{10}\) mile to the store. How far did Melinda ride her bike in all?
Options:
a. 0.14 mile
b. 0.58 mile
c. 0.94 mile
d. 1.04 miles

Answer: 0.94 mile

Explanation:

Melinda rode her bike \(\frac{54}{100}\) mile to the library.
Then she rode \(\frac{4}{10}\)mile to the store.
The decimal form of \(\frac{54}{100}\) is 0.54 mile
The decimal form of \(\frac{4}{10}\) is 0.40 mile
0.54 + 0.40 = 0.94 mile
Thus the answer is option C.

Question 6.
One day, the students drank 60 quarts of milk at lunch. How many pints of milk did the students drink?
Options:
a. 30 pints
b. 120 pints
c. 240 pints
d. 480 pints

Answer: 120 pints

Explanation:

One day, the students drank 60 quarts of milk at lunch.
1 quart = 2 pints
60 quarts = 60 × 2 pints = 120 pints
The correct answer is option B.

Page No. 693

Question 1.
Evelyn has dance class every Saturday. It lasts 1 hour and 15 minutes and is over at 12:45 p.m. At what time does Evelyn’s dance class begin?

First, write the problem you need to solve.
Type below:
________

Answer: I need to find when Evelyn’s dance class begins.

Question 1.
Next, draw a time line to show the end time and the elapsed time.

Type below:
________

Answer:

Question 1.
Finally, find the start time.
Evelyn’s dance class begins at _________ .
______ A.M.

Answer: 11:30 A.M.

Explanation:

Evelyn has dance class every Saturday. It lasts 1 hour and 15 minutes and is over at 12:45 p.m.
12 hr 45 minutes
-1 hr 15 minutes
11 hr 30 minutes

Thus Evelyn dance class starts at 11:30 A.M.

Question 2.
What if Evelyn’s dance class started at 11:00 a.m. and lasted 1 hour and 25 minutes? At what time would her class end? Describe how this problem is different from Problem 1.
Type below:
________

Answer: 12:25 P.M.

Explanation:

If Evelyn’s dance class started at 11:00 a.m. and lasted 1 hour and 25 minutes.
Then the class ends at 12:25 P.M.
11 hours 0 minutes
+1 hour 25 minutes
12 hour 25 minutes

Question 3.
Beth got on the bus at 8:06 a.m. Thirty-five minutes later, she arrived at school. At what time did Beth arrive at school?
______ a.m.

Answer: 8:41 A.M.

Explanation:

Beth got on the bus at 8:06 a.m.
Thirty-five minutes later, she arrived at school.
8 hour 06 minutes
+ 0 hour 35 minutes
8 hour 41 minutes

Beth arrived to school at 8:41 A.M.

Question 4.
Lyle went fishing for 1 hour and 30 minutes until he ran out of bait at 6:40 p.m. At what time did Lyle start fishing?
______ p.m.

Answer: 5:10 P.M.

Explanation:

Lyle went fishing for 1 hour and 30 minutes until he ran out of bait at 6:40 p.m.
Subtract 1 hour and 30 minutes from 6:40 p.m.
6 hour 40 minutes
-1 hour 30 minutes
5 hour 10 minutes

Lyle starts fishing at 5:10 P.M.

Page No. 694

Question 5.
Mike and Jed went skiing at 10:30 a.m. They skied for 1 hour and 55 minutes before stopping for lunch. At what time did Mike and Jed stop for lunch?
______ p.m

Answer: 12:25 P.M.

Explanation:

Mike and Jed went skiing at 10:30 a.m.
They skied for 1 hour and 55 minutes before stopping for lunch.
Add 1 hour and 55 minutes to 10:30 a.m
10 hour 30 minutes
+1 hour 55 minutes
12 hour 25 minutes
= 12:25 P.M.
Mike and Jed stop for lunch at 12:25 P.M.

Question 6.
Mike can run a mile in 12 minutes. He starts his run at 11:30 am. and runs 4 miles. What time does Mike finish his run?
_____ : _____  _____

Answer: 12:18 P.M

Explanation:

Mike can run a mile in 12 minutes. He starts his run at 11:30 am. and runs 4 miles.
1 mile = 12 minutes
4 miles = 4 × 12 minutes = 48 minutes
Add 48 minutes to 11:30 A.M.
11 hour 30 minutes
0 hour 48 minutes
12 hour 18 minutes

Mike finish his run at 12:18 P.M.

Question 7.
Communicate Explain how you can use a diagram to determine the start time when the end time is 9:00 a.m. and the elapsed time is 26 minutes. What is the start time?
______ a.m.

Answer: 8:34 A.M.

Explanation:

End time = 9:00 A.M.
Elapsed time = 26 minutes
Subtract 26 minutes from 9 hours.
9 hour 00 minutes
-0 hour 26 minutes
8 hour 34 minutes
So, the start time is 8:34 A.M.

Question 8.
Bethany finished her math homework at 4:20 p.m. She did 25 multiplication problems in all. If each problem took her 3 minutes to do, at what time did Bethany start her math homework?
______ p.m.

Answer: 3:05 P.M.

Explanation:

Bethany finished her math homework at 4:20 p.m. She did 25 multiplication problems in all.
If she took 3 minutes to solve each problem then multiply 25 with 3
25 × 3 = 75 minutes = 1 hour 15 minutes
Subtract 1 hour 15 minutes from 4:20 P.M.
4 hour 20 minutes
-1 hour 15 minutes
3 hour 05 minutes

Therefore Bethany started her math homework at 3:05 P.M.

Question 9.
Vincent began his weekly chores on Saturday morning at 11:20 a.m. He finished 1 hour and 10 minutes later. Draw a time line to show the end time.

Vincent finished his chores at _______ p.m.
______ p.m.

Answer: 12:30 P.M.

Explanation:

Vincent began his weekly chores on Saturday morning at 11:20 a.m. He finished 1 hour and 10 minutes later.
Add 1 hour 10 minutes to 11:20 A.M.
11 hour 20 minutes
+1 hour 10 minutes
12 hour 30 minutes
Thus the Endtime is 12:30 P.M.

Common Core – New – Page No. 695

Problem Solving Elapsed Time

Read each problem and solve.

Question 1.
Molly started her piano lesson at 3:45 P.M. The lesson lasted 20 minutes. What time did the piano lesson end?
Think: What do I need to find?
How can I draw a diagram to help?
4:05 P.M.

Question 2.
Brendan spent 24 minutes playing a computer game. He stopped playing at 3:55 P.M and went outside to ride his bike. What time did he start playing the computer game?
______ P.M.

Answer: 3:31 P.M

Explanation:

Brendan spent 24 minutes playing a computer game.
He stopped playing at 3:55 P.M and went outside to ride his bike.
You need to subtract 24 minutes from 3:55 P.M. = 3:31 P.M.

Question 3.
Aimee’s karate class lasts 1 hour and 15 minutes and is over at 5:00 P.M. What time does Aimee’s karate class start?
______ P.M.

Answer: 3:45 P.M

Explanation:

Aimee’s karate class lasts 1 hour and 15 minutes and is over at 5:00 P.M.
You need to subtract 1 hour 15 minutes from 5:00 P.M = 5:00 – 1:15 = 3:45 P.M.
Aimee’s karate class started at 3:45 P.M.

Question 4.
Mr. Giarmo left for work at 7:15 A.M. Twenty-five minutes later, he arrived at his work. What time did Mr. Giarmo arrive at his work?
______ A.M.

Answer: 7:40 A.M.

Explanation:

Mr. Giarmo left for work at 7:15 A.M.
Twenty-five minutes later, he arrived at his work.
Add 25 minutes to 7:15 A.M. = 7:40 A.M.
Mr. Giarmo arrived at his work at 7:40 A.M.

Question 5.
Ms. Brown’s flight left at 9:20 A.M. Her plane landed 1 hour and 23 minutes later. What time did her plane land?
______ A.M.

Answer: 10:43 A.M.

Explanation:

Ms. Brown’s flight left at 9:20 A.M.
Her plane landed 1 hour and 23 minutes later.
Add 1 hour and 23 minutes to 9:20 A.M = 10:43 A.M.
Her plane landed at 10:43 A.M.

Common Core – New – Page No. 696

Lesson Check

Question 1.
Bobbie went snowboarding with friends at 10:10 A.M. They snowboarded for 1 hour and 43 minutes, and then stopped to eat lunch. What time did they stop for lunch?
Options:
a. 8:27 A.M.
b. 10:53 A.M.
c. 11:53 A.M.
d. 12:53 A.M.

Answer: 11:53 A.M.

Explanation:

Bobbie went snowboarding with friends at 10:10 A.M.
They snowboarded for 1 hour and 43 minutes and then stopped to eat lunch.
Add 1 hour and 43 minutes to 10:10 A.M. = 11:53 A.M.
Thus the correct answer is option C.

Question 2.
The Cain family drove for 1 hour and 15 minutes and arrived at their camping spot at 3:44 P.M. What time did the Cain family start driving?
Options:
a. 4:59 P.M.
b. 2:44 P.M.
c. 2:39 P.M.
d. 2:29 P.M.

Answer: 2:29 P.M.

Explanation:

The Cain family drove for 1 hour and 15 minutes and arrived at their camping spot at 3:44 P.M.
Subtract 1 hour and 15 minutes from 3:44 P.M
3:44 P.M. – 1:15 = 2:29 P.M.
The correct answer is option D.

Spiral Review

Question 3.
A praying mantis can grow up to 15 centimeters long. How long is this in millimeters?
Options:
a. 15 millimeters
b. 150 millimeters
c. 1,500 millimeters
d. 15,000 millimeters

Answer: 150 millimeters

Explanation:

A praying mantis can grow up to 15 centimeters long.
Convert centimeters to millimeters
1 centimeter = 10 millimeters
15 centimeters = 15 × 10 millimeters = 150 millimeters
The correct answer is option B.

Question 4.
Thom’s minestrone soup recipe makes 3 liters of soup. How many milliliters of soup is this?
Options:
a. 30 milliliters
b. 300 milliliters
c. 3,000 milliliters
d. 30,000 milliliters

Answer: 3,000 milliliters

Explanation:

Thom’s minestrone soup recipe makes 3 liters of soup.
Convert liters to milliliters.
1 liter = 1000 milliliters
3 liters = 3 × 1000 milliliters = 3,000 milliliters
Thus the correct answer is option C.

Question 5.
Stewart walks \(\frac{2}{3}\) mile each day. Which is a multiple of \(\frac{2}{3}\) ?
Options:
a. \(\frac{4}{3}\)
b. \(\frac{4}{6}\)
c. \(\frac{8}{10}\)
d. \(\frac{2}{12}\)

Answer: \(\frac{4}{6}\)

Explanation:

Stewart walks \(\frac{2}{3}\) mile each day.
\(\frac{2}{3}\) × \(\frac{2}{3}\) = \(\frac{4}{6}\)
The correct answer is option B.

Question 6.
Angelica colored in 0.60 of the squares on her grid. Which of the following expresses 0.60 as tenths in fraction form?
Options:
a. \(\frac{60}{100}\)
b. \(\frac{60}{10}\)
c. \(\frac{6}{100}\)
d. \(\frac{6}{10}\)

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

Explanation:

Angelica colored in 0.60 of the squares on her grid.
The fraction of 0.60 is \(\frac{6}{10}\)
The correct answer is option D.

Page No. 699

Question 1.
A truck is carrying 2 tons 500 pounds of steel. How many pounds of steel is the truck carrying?
Think of 2 tons 500 pounds as 2 tons + 500 pounds.
Write tons as pounds.

So, the truck is carrying _____ pounds of steel.
______ pounds

Answer: 4,500 pounds

Explanation:

A truck is carrying 2 tons 500 pounds of steel.
Before you add convert tons to pounds.
1 ton = 2000 pounds
2 tons = 2 × 2000 pounds = 4000 pounds
4000 pounds
+500 pounds
4500 pounds
So, the truck is carrying 4500 pounds of steel.

Rewrite each measure in the given unit.

Question 2.
1 yard 2 feet
______ feet

Answer: 5 feet

Explanation:

Convert yard to feet
1 yard = 3 feet
3 feet + 2 feet = 5 feet

Question 3.
3 pints 1 cup
______ cups

Answer: 7 cups

Explanation:

1 pint = 2 cups
3 pints = 3 × 2 cups = 6 cups
6 cups + 1 cup = 7 cups

Question 4.
3 weeks 1 day
______ days

Answer: 22 days

Explanation:

Convert weeks to days.
1 week = 7 days
3 weeks = 21 days
21 days + 1 day = 22 days.

Add or subtract.

Question 5.
2 lb 4 oz
+ 1 lb 6 oz
————–
_____ lb _____ oz

Answer: 3 lb 10 oz

Explanation:

Add 2 lb 4 oz and 1 lb 6 oz

2 lb 4 oz
+ 1 lb 6 oz
3 lb 10 oz

Question 6.
3 gal 2 qt
− 1 gal 3 qt
————–
_____ gal _____ qt

Answer: 1 gal 3 qt

Explanation:

Subtract 1 gal 3 qt from 3 gal 2 qt
Convert gallon to a quart and then borrow to 2 quarts = 6 quarts

3 gal 2 qt
− 1 gal 3 qt
1 gal 3 qt

Question 7.
5 hr 20 min
− 3 hr 15 min
—————–
_____ hr _____ min

Answer: 2 hr 5 min

Explanation:

Subtract 3 hr 15 min from 5 hr 20 min

5 hr 20 min
− 3 hr 15 min
2 hr 5 min

Rewrite each measure in the given unit.

Question 8.
1 hour 15 minutes
_____ minutes

Answer: 75 minutes

Explanation:

Convert hours to minutes.
1 hour = 60 minutes
60 minutes + 15 minutes = 75 minutes

Question 9.
4 quarts 2 pints
_____ pints

Answer: 10 pints

Explanation:

Convert quart to pints
1 quart = 2 pints
4 quarts = 8 pints
8 pints + 2 pints = 10 pints

Question 10.
10 feet 10 inches
_____ inches

Answer: 130 inches

Explanation:

Convert feet to inches
1 feet = 12 inches
10 feet = 10 × 12 inches = 120 inches
120 inches + 10 inches = 130 inches

Add or subtract.

Question 11.
2 tons 300 lb
– 1 ton 300 lb
—————–
_____ ton(s) _____ lb

Answer: 1ton

Explanation:

Subtract 1 ton 300 lb from 2 tons 300 lb

2 tons 300 lb
– 1 ton 300 lb
1ton 0 lb

Question 12.
10 gal 8 c
+ 8 gal 9 c
—————–
_____ gal _____ c

Answer: 19 gal 1 c

Explanation:

Add 10 gal 8 c and 8 gal 9 c
Convert cups to gallon
17 cups = 1 gal 1 cup

10 gal 8 c
+ 8 gal 9 c
18 gal 17 c = 19 gal 1 c

Question 13.
7 lb 6 oz
− 2 lb 12 oz
—————–
_____ lb _____ oz

Answer: 4 lb 10 oz

Explanation:

Subtract 2 lb 12 oz from 7 lb 6 oz
1 lb = 16 oz
Borrow 16 oz to ones place.
7 lb 6 oz

6 lb 22 oz
− 2 lb 12 oz
4 lb 10 oz

Question 14.
Apply Ahmed fills 6 pitchers with juice. Each pitcher contains 2 quarts 1 pint. How many pints of juice does he have in all?
_____ pints of juice

Answer: 30 pints of juice

Explanation:

Apply Ahmed fills 6 pitchers with juice. Each pitcher contains 2 quarts 1 pint.
Convert quarts to pints.
1 quart = 2 pint
2 quarts = 2 × 2 pint = 4 pints
2 quarts 1 pint = 4 pints + 1 pint = 5 pints
5 pints × 6 pitchers = 30 pints of juice.

Question 15.
Sense or Nonsense? Sam and Dave each solve the problem at the right. Sam says the sum is 4 feet 18 inches. Dave says the sum is 5 feet 6 inches. Whose answer makes sense? Whose answer is nonsense? Explain.
2 ft 10 in.
+ 2 ft 8 in.
—————-
Type below:
_________

Answer: The answer of Dave and Sam makes sense. Because 4 feet 18 inches and 5 feet 6 inches are the same.
Convert feet to inches
1 feet = 12 inches
4 feet 18 inches = 5 feet 6 inches.

Question 16.
Jackson has a rope 1 foot 8 inches long. He cuts it into 4 equal pieces. How many inches long is each piece?
______ inches

Answer: 5 inches

Explanation:

Jackson has a rope 1 foot 8 inches long. He cuts it into 4 equal pieces.
Convert feet to inches
1 feet = 12 inches
12 inches + 8 inches = 20 inches
20 ÷ 4 = 5 inches.
Therefore there are 5 inches in each piece.

Page No. 700

Question 17.
Theo is practicing for a 5-kilometer race. He runs 5 kilometers every day and records his time. His normal time is 25 minutes 15 seconds. Yesterday it took him only 23 minutes 49 seconds. How much faster was his time yesterday than his normal time?

a. What are you asked to find?
Type below:
_________

Answer: I am asked to find how much faster was his time yesterday than his normal time.

Question 17.
b. What information do you know?
Type below:
_________

Answer: I know the information about his normal time and the time he took to run yesterday.

Question 17.
c. How will you solve the problem?
Type below:
_________

Answer: I will solve this problem by subtracting the time taken by him yesterday from normal time.
25 minutes 15 seconds
-23 minutes 49 seconds

Question 17.
d. Solve the problem.
Type below:
_________

Answer:

25 minutes 15 seconds
-23 minutes 49 seconds
1 minute 26 seconds     

Question 17.
e. Fill in the sentence.
Yesterday, Theo ran 5 kilometers in a time that was ______ faster than his normal time.
_____ min _____ sec

Answer: 1 min 26 sec

Question 18.
Don has 5 pieces of pipe. Each piece is 3 feet 6 inches long. If Don joins the pieces end to end to make one long pipe, how long will the new pipe be?
_____ ft _____ in

Answer: 17 ft 6 in.

Explanation:

Don has 5 pieces of pipe. Each piece is 3 feet 6 inches long.
5 pieces = 5 × 3 feet 6 inches
= 15 feet 30 inches
1 feet = 12 inches
30 inches = 2 feet 6 inches
15 feet 30 inches = 17 feet 6 inches
The new pipe will be 17 feet 6 inches long.

Question 19.
Ana mixes 2 quarts 1 pint of apple juice and 1 quart 3 cups of cranberry juice. Will her mixture be able to fit in a 1 gallon pitcher? Explain.
Type below:
_________

Answer: Yes

Ana mixes 2 quarts 1 pint of apple juice and 1 quart 3 cups of cranberry juice.
We should convert it into gallons.
Before that convert pint to cups.
1 pint = 2 cups
2 quarts 1 pint = 2 quarts 2 cups

2 quarts 2 cups
1 quart 3 cups
3 quart 5 cups

1 quart = 4 cups
5 cups = 1 quart 1 cup
3 quart 5 cups = 4 quart 1 cup
Now we can convert 4 quarts 1 cup into gallons.
1 gallon = 4 quarts
1 gallon 1 cup.

Common Core – New – Page No. 701

Mixed Measures

Complete.

Question 1.
8 pounds 4 ounces = 132 ounces
Think: 8 pounds = 8 × 16 ounces, or 128 ounces.
128 ounces + 4 ounces = 132 ounces

Question 2.
5 weeks 3 days = _____ days

Answer: 38 days

Explanation:

Convert weeks to days
1 week = 7 days
5 weeks = 5 × 7 days = 35 days
35 days + 3 days = 38 days

Question 3.
4 minutes 45 seconds = _____ seconds

Answer: 285 seconds

Explanation:

Convert minutes to seconds
1 minute = 60 seconds
4 minutes = 4 × 60 seconds = 240 seconds
240 seconds + 45 seconds = 285 seconds

Question 4.
4 hours 30 minutes = _____ minutes

Answer: 270 minutes

Explanation:

Convert hours to minutes
1 hour = 60 minutes
4 hours = 4 × 60 minutes = 240 minutes
240 minutes + 30 minutes = 270 minutes

Question 5.
3 tons 600 pounds = _____ pounds

Answer: 6600 pounds

Explanation:

Convert tons to pounds
1 ton = 2,000 pounds
3 tons = 3 × 2000 pounds = 6,000 pounds
6,000 pounds + 600 pounds = 6,600 pounds

Question 6.
6 pints 1 cup = _____ cups

Answer: 13 cups

Explanation:

Convert pints to cups.
1 pint = 2 cups
6 pints = 6 × 2 cups = 12 cups
12 cups + 1 cup = 13 cups

Question 7.
7 pounds 12 ounces = _____ ounces

Answer: 124 ounces

Explanation:

Convert pounds to ounces
1 pound = 16 ounces
7 pounds = 7 × 16 ounces = 112 ounces
112 ounces + 12 ounces = 124 ounces

Add or subtract.

Question 8.
9 gal 1 qt
+ 6 gal 1 qt
—————
______ gal ______ qt

Answer: 15 gal 2 qt

Explanation:

9 gal + 6 gal = 15 gal
1 qt + 1 qt = 2qt

9 gal 1 qt
+ 6 gal 1 qt
15 gal 2 qt

Question 9.
12 lb 5 oz
– 7 lb 10 oz
—————
______ lb ______ oz

Answer: 4 lb 11 oz

Explanation:

21 oz – 10 oz = 11 oz
11 lb – 7 lb = 4 lb

12 lb 5 oz
– 7 lb 10 oz
4 lb 11 oz

Question 10.
8 hr 3 min
+ 4 hr 12 min
—————
______ hr ______ min

Answer: 12 hr 15 min

Explanation:

8 hr + 4 hr = 12 hr
3 min + 12 min = 15 min

8 hr 3 min
+ 4 hr 12 min
12 hr 15 min

Problem Solving

Question 11.
Michael’s basketball team practiced for 2 hours 40 minutes yesterday and 3 hours 15 minutes today. How much longer did the team practice today than yesterday?
______ minutes

Answer: 35 minutes

Explanation:

Michael’s basketball team practiced for 2 hours 40 minutes yesterday and 3 hours 15 minutes today.
3 hours 15 minutes
– 2 hours 40 minutes
0 hours 35 minutes

Question 12.
Rhonda had a piece of ribbon that was 5 feet 3 inches long. She removed a 5-inch piece to use in her art project. What is the length of the piece of ribbon now?
______ feet ______ inches

Answer: 4 feet 10 inches

Explanation:

Rhonda had a piece of ribbon that was 5 feet 3 inches long. She removed a 5-inch piece to use in her art project.
5 feet 3 inches
– 0 feet 5-inch

1 feet = 12 inches
12 inches – 5 inches = 7 inches
5 feet 3 inches
– 0 feet 5-inch
4 feet 10 inches

Common Core – New – Page No. 702

Lesson Check

Question 1.
Marsha bought 1 pound 11 ounces of roast beef and 2 pounds 5 ounces of corned beef. How much more corned beef did she buy than roast beef?
Options:
a. 16 ounces
b. 10 ounces
c. 7 ounces
d. 6 ounces

Answer: 10 ounces

Explanation:

Marsha bought 1 pound 11 ounces of roast beef and 2 pounds 5 ounces of corned beef.
Subtract 1 pound 11 ounces of roast beef from 2 pounds 5 ounces of corned beef.
2 pounds 5 ounces
1 pound 11 ounces
0 pound 10 ounces
Thus the correct answer is option B.

Question 2.
Theodore says there are 2 weeks 5 days left in the year. How many days are left in the year?
Options:
a. 14 days
b. 15 days
c. 19 days
d. 25 days

Answer: 19 days

Explanation:

Theodore says there are 2 weeks 5 days left in the year.
Convert weeks to days.
1 week = 7 days
2 weeks = 14 days
14 days + 5 days = 19 days.
So, the correct answer is option C.

Spiral Review

Question 3.
On one grid, 0.5 of the squares are shaded. On another grid, 0.05 of the squares are shaded. Which statement is true?
Options:
a. 0.05 > 0.5
b. 0.05 = 0.5
c. 0.05 < 0.5
d. 0.05 + 0.5 = 1.0

Answer: 0.05 < 0.5

Explanation:

Given,
On one grid, 0.5 of the squares are shaded.
On another grid, 0.05 of the squares are shaded.
0.5 is greater than 0.05
So, the answer is option C.

Question 4.
Classify the triangle shown below.

Options:
a. right
b. acute
c. equilateral
d. obtuse

Answer: right

Explanation:

The above figure is the right angle triangle.
So, the correct answer is option A.

Question 5.
Sahil’s brother is 3 years old. How many weeks old is his brother?
Options:
a. 30 weeks
b. 36 weeks
c. 90 weeks
d. 156 weeks

Answer: 156 weeks

Explanation:

Sahil’s brother is 3 years old.
Convert years to weeks.
1 year = 52 weeks
3 years = 3 × 52 = 156 weeks.
Therefore the correct answer is option D.

Question 6.
Sierra’s swimming lessons last 1 hour 20 minutes. She finished her lesson at 10:50 A.M. At what time did her lesson start?
Options:
a. 9:30 A.M.
b. 9:50 A.M.
c. 10:30 A.M.
d. 12:10 A.M.

Answer: 9:30 A.M.

Explanation:

Sierra’s swimming lessons last 1 hour 20 minutes. She finished her lesson at 10:50 A.M.
10 hour 50 minutes
– 1 hour 20 minutes
9 hours 30 minutes
9:30 A.M.
So, the correct answer is option A.

Page No. 705

Question 1.
The table shows a pattern for two units of time. Label the columns of the table with the units of time.
Think: What unit of time is 24 times as great as another unit?

Type below:
________

Answer: Days, Hours
The conversion of the day to hours is
1 day = 24 hours.

Each table shows a pattern for two customary units. Label the columns of the table.

Question 2.

Type below:
________

Answer: Pint, Cups
1 pint = 2 Cups
So, the label for the above table is:

Question 3.

Type below:
________

Answer: Pound, Ounces
Conversion of pounds to ounces is 1 pound = 16 ounces

Each table shows a pattern for two customary units. Label the columns of the table.

Question 4.

Type below:
________

Answer: Yard, Inches
1 yard = 36 inches

Question 5.

Type below:
________

Answer: Feet, Inches
1 Feet = 12 inches

Each table shows a pattern for two metric units of length. Label the columns of the table.

Question 6.

Type below:
________

Answer: Decimeter, Centimeter, and Centimeter, Millimeter

1 decimeter = 10 centimeters
1 centimeter = 10 millimeters

Label for Decimeter and Centimeter:

Label for Centimeter and Millimeter:

Question 7.

Type below:
________

Answer: Meter, Centimeter

1 meter = 100 centimeters,

Label for Meter and Centimeter is:

Question 8.
List the number pairs for the table in Exercise 6. Describe the relationship between the numbers in each pair.

Answer: There are 8 pairs for the table.
The relationship for the first pair is Day, Hour.
The relationship for the second pair is Pound, Ounces.
The relationship for the third pair is Yard, Inches.
The relationship for the fourth pair is Feet, inches.
The relationship for the fifth pair is Decimeter, Centimeter.
The relationship for the sixth pair is Centimeter, Millimeter.
The relationship for the seventh pair is Meter, Centimeter.

Page No. 706

Question 9.
What’s the Error? Maria wrote Weeks as the label for the first column of the table and Years as the label for the second column. Describe her error.

Type below:
________

Answer: The error of Maria is she didn’t write the name for the pair of table.

Question 10.
Verify the Reasoning of Others The table shows a pattern for two metric units. Lou labels the columns Meters and Millimeters. Zayna labels them Liters and Milliliters. Whose answer makes sense? Whose answer is nonsense? Explain.

Type below:
________

Answer: Both Lou and Zayna labels are correct but they didn’t name the pair of units.

Question 11.
Look at the following number pairs: 1 and 365, 2 and 730, 3 and 1,095. The number pairs describe the relationship between which two units of time? Explain.
____ ____

Answer:

Question 12.
The tables show patterns for some units of measurement. Write the correct labels in each table.

Type below:
________

Answer:

The suitable units the first table is

The suitable units the second table is

The suitable units the third table is

Common Core – New – Page No. 707

Patterns in Measurement Units

Each table shows a pattern for two customary units of time or volume. Label the columns of the table.

Question 1.

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Problem Solving

Use the table for 5 and 6.

Question 5.
Marguerite made the table to compare two metric measures of length. Name a pair of units Marguerite could be comparing.
1 _________
= 10 _________

Answer: The pair of units for the above table is Centimeters, Millimeters.

Question 6.
Name another pair of metric units of length that have the same relationship.
1 _________
= 10 _________

Answer: Another pair of metric units of length are Meters, Decimeters.

Common Core – New – Page No. 708

Lesson Check

Question 1.
Joanne made a table to relate two units of measure. The number pairs in her table are 1 and 16, 2 and 32, 3 and 48, 4 and 64. Which are the best labels for
Joanne’s table?
Options:
a. Cups, Fluid Ounces
b. Gallons, Quarts
c. Pounds, Ounces
d. Yards, Inches

Answer: Pounds, Ounces

Explanation:

Joanne made a table to relate two units of measure. The number pairs in her table are 1 and 16, 2 and 32, 3 and 48, 4 and 64.
The label for Joanna’s table is pounds and ounces.
Thus the correct answer is option C.

Question 2.
Cade made a table to relate two units of time. The number pairs in his table are 1 and 24, 2 and 48, 3 and 72, 4 and 96. Which are the best labels for Cade’s table?
Options:
a. Days, Hours
b. Days, Weeks
c. Years, Months
d. Years, Weeks

Answer: Days, Hours

Explanation:

Cade made a table to relate two units of time. The number pairs in his table are 1 and 24, 2 and 48, 3 and 72, 4 and 96.
The label for Joanna’s table is Days and Hours.
The correct answer is option B.

Spiral Review

Question 3.
Anita has 2 quarters, 1 nickel, and 4 pennies. Write Anita’s total amount as a fraction of a dollar
Options:
a. \(\frac{39}{100}\)
b. \(\frac{54}{100}\)
c. \(\frac{59}{100}\)
d. \(\frac{84}{100}\)

Answer: \(\frac{59}{100}\)

Question 4.
The minute hand of a clock moves from 12 to 6. Which describes the turn the minute hand makes?
Options:
a. \(\frac{1}{4}\) turn
b. \(\frac{1}{2}\) turn
c. \(\frac{3}{4}\) turn
d. 1 full turn

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

Explanation:

The minute hand of a clock moves from 12 to 6.
If the minute hand move from 12 to 6 then the fraction of the turn is \(\frac{1}{2}\)
Thus the correct answer is option B.

Question 5.
Roderick has a dog that has a mass of 9 kilograms. What is the mass of the dog in grams?
Options:
a. 9 grams
b. 900 grams
c. 9,000 grams
d. 90,000 grams

Answer: 9,000 grams

Explanation:

Roderick has a dog that has a mass of 9 kilograms.
Convert kilograms to grams.
1 kilogram = 1000 grams
9 kilograms = 9 × 1000 grams = 9000 grams
Therefore the correct answer is option C.

Question 6.
Kari mixed 3 gallons 2 quarts of lemon lime drink with 2 gallons 3 quarts of pink lemonade to make punch. How much more lemon-lime drink did Kari use than pink lemonade?
Options:
a. 3 quarts
b. 4 quarts
c. 1 gallon 1 quart
d. 1 gallon 2 quarts

Answer: 3 quarts

Explanation:

Kari mixed 3 gallons 2 quarts of lemon-lime drink with 2 gallons 3 quarts of pink lemonade to make punch.
Kari used 3 quarts of pink lemonade more to make punch.
The correct answer is option A.

Common Core – New – Page No. 709

Question 1.
Mrs. Miller wants to estimate the width of the steps in front of her house. Select the best benchmark for her to use.
Options:
a. her fingertip
b. the thickness of a dime
c. the width of a license plate
d. how far she can walk in 20 minutes

Answer: the thickness of a dime

Question 2.
Franco played computer chess for 3 hours. Lian played computer chess for 150 minutes. Compare the times spent playing computer chess. Complete the sentence.
_____ played for _____ minutes longer than _____.

Answer: Franco played for 30 minutes longer than Lian.

Question 3.
Select the measures that are equal. Mark all that apply.
Options:
a. 6 feet
b. 15 yards
c. 45 feet
d. 600 inches
e. 12 feet
f. 540 inches

Answer: B, F; C, F

The measure of 15 yards = 45 feet = 540 inches

Question 4.
Jackie made 6 quarts of lemonade. Jackie says she made 3 pints of lemonade. Explain Jackie’s error. Then find the correct number of pints of lemonade.
Type below:
_________

Answer: The error of Jackie is that she made 12 pints of lemonade but she noted 3 pints of lemonade.
1 quart = 2 pints
6 quarts = 6 × 2 pints = 12 pints

Page No. 710

Question 5.
Josh practices gymnastics each day after school. The data shows the lengths of time Josh practiced gymnastics for 2 weeks.

Part A
Make a tally table and line plot to show the data.

Type below:
_________

Answer:

Line Plot:

Question 5.
Part B
Explain how you used the tally table to label the numbers and plot the Xs.
Type below:
_________

Answer: By using the tally marks table I have plotted the X’s on the line plot. Based on the tally of each fraction I have plotted X on the point.

Question 5.
Part C
What is the difference between the longest time and shortest time Josh spent practicing gymnastics?
\(\frac{□}{□}\) hour

Answer:

The longest time is 1
The shortest time is \(\frac{1}{4}\)
1 – \(\frac{1}{4}\) = \(\frac{3}{4}\)
Thus the difference between the longest time and shortest time Josh spent practicing gymnastics is \(\frac{3}{4}\)

Question 6.
Select the correct word to complete the sentence.
Juan brings a water bottle with him to soccer practice.
A full water bottle holds of water.
_________

Answer: A full water bottle holds 1 liter of water

Page No. 711

Question 7.
Write the symbol that compares the weights correctly.

128 ounces ____ 8 pounds
8,000 pounds ____ 3 tons

Answer:

i. 128 ounces ____ 8 pounds

1 pound = 16ounces
8 pounds = 8 × 16 ounces = 128 ounces
Thus 128 ounces = 8 pounds

ii. 8,000 pounds ____ 3 tons

1 ton = 2000 pounds
4 tons = 4 × 2000 pounds = 8000 pounds
8000 pounds is greater than 6000 pounds
So, 8,000 pounds > 3 tons

Question 8.
Dwayne bought 5 yards of wrapping paper. How many inches of wrapping paper did he buy?
____ inches

Answer: 180 inches

Convert yards to inches
1 yard = 36 inches
5 yards = 5 × 36 inches = 180 inches
Therefore he bought 180 inches of wrapping paper.

Question 9.
A sack of potatoes weighs 14 pounds 9 ounces. After Wendy makes potato salad for a picnic, the sack weighs 9 pounds 14 ounces. What is the weight of the potatoes Wendy used for the potato salad? Write the numbers to show the correct subtraction.


____ pounds ____ ounces

Answer: 4 pounds 11 ounces

14 pounds 9 ounces
-9 pounds 14 ounces
Borrow 1 pound to ones place to subtract 11 ounces
1 pound = 16 ounces
16 + 9 = 25 ounces

13 pounds 25 ounces
-9 pounds 14 ounces
4 pounds 11 ounces

Question 10.
Sabita made this table to relate two customary units of liquid volume.

Part A
List the number pairs for the table. Then describe the relationship between the numbers in each pair.
Type below:
________

Answer: The relationship between the numbers in each pair is Pint, Cups.

Question 10.
Part B
Label the columns of the table. Explain your answer.
Type below:
________

Answer:

Page No. 712

Question 11.
The table shows the distances some students swam in miles. Complete the line plot to show the data.

Answer:

What is the difference between the longest distance and the shortest distance the students swam?
\(\frac{□}{□}\) mile

Answer: \(\frac{4}{8}\) mile

Explanation:

The longest distance = \(\frac{5}{8}\) mile
The shortest distance = \(\frac{1}{8}\) mile
\(\frac{5}{8}\) – \(\frac{1}{8}\) = \(\frac{4}{8}\) mile
The difference between the longest distance and the shortest distance the students swam is \(\frac{4}{8}\) mile.

Question 12.
An elephant living in a wildlife park weighs 4 tons. How many pounds does the elephant weigh?
______ pounds

Answer: 8000 pounds

Explanation:

An elephant living in a wildlife park weighs 4 tons.
1 ton = 2000 pounds
4 tons = 4 × 2000 pounds = 8000 pounds
The elephant weighs 8000 pounds.

Question 13.
Katia bought two melons. She says the difference in mass between the melons is 5,000 grams. Which two melons that did Katia buy?
Options:
a. watermelon: 8 kilograms
b. cantaloupe: 5 kilograms
c. honeydew: 3 kilograms
d. casaba melon: 2 kilograms
e. crenshaw melon: 1 kilogram

Answer: cantaloupe: 5 kilograms

Katia bought two melons. She says the difference in mass between the melons is 5,000 grams.
She bought cantaloupe: 5 kilograms.
The correct answer is option B.

Question 14.
Write the equivalent measurements in each column.

Type below:
________

Answer:

Page No. 713

Question 15.
Cheryl is making a mixed fruit drink for a party. She mixes 7 pints each of apple juice and cranberry juice. How many fluid ounces of mixed fruit drink does Cheryl make?
______ fluid ounces

Answer: 224 fluid ounces

Explanation:

Cheryl is making a mixed fruit drink for a party. She mixes 7 pints each of apple juice and cranberry juice.
We need to convert pints into fluid ounces
We know that, 1 pint = 32 fluid ounces
7 pints = 7 × 32 fluid ounces = 224 fluid ounces.
Therefore Cheryl makes 224 fluid ounces of mixed fruit drink.

Question 16.
Hamid’s soccer game will start at 11:00 a.m., but the players must arrive at the field three-quarters of an hour early to warm up. The game must end by 1:15 p.m.
Part A
Hamid says he has to be at the field at 9:45 a.m. is Hamid correct? Explain your answer.
______

Answer: No

Explanation:

The statement of Hamid is wrong. Because Hamid’s soccer game starts at 10:15 A.M.

Question 16.
Part B
The park closes at 6:30 p.m. There is a 15-minute break between each game played at the park, and each game takes the same amount of time as Hamid’s soccer game. How many more games can be played before the park closes? Explain your answer.
______ more games

Answer: 2 more games

Explanation:

Given that,
The park closes at 6:30 p.m.
There is a 15-minute break between each game played at the park, and each game takes the same amount of time as Hamid’s soccer game.
The game starts at 11:00 A.M and ends at 1:15 P.M.
After completion of the game, they will take a break for 15 minutes.
So, game starts at 1:30 P.M or 2:00 P.M. and ends at 4:15 P.M.
By this, we can say that 2 more games can be played before the park closes.

Question 17.
For numbers 17a–17e, select Yes or No to tell whether the measurements are equivalent.
a. 7,000 grams and 7 kilograms
i. yes
ii. no

Answer: Yes

Explanation:

1 kilogram = 1000 grams
7 kilograms = 7 × 1000 grams = 7000 grams.
Thus the above statement is true.

Question 17.
b. 200 milliliters and 2 liters
i. yes
ii. no

Answer: No

Explanation:

1 liter = 1000 milliliters
2 liters = 2000 milliliters
So, the above statement is not correct.

Question 17.
c. 6 grams and 6,000 kilograms
i. yes
ii. no

Answer: No

Explanation:

1 kilogram = 1000 grams
6 kilograms = 6 × 1000 grams = 6000 grams.
Thus the above statement is true.

Question 17.
d. 5 liters and 5,000 milliliters
i. yes
ii. no

Answer: Yes

Explanation:

1 liter = 1000 milliliters
5 liters = 5000 milliliters
Thus the above statement is true.

Question 17.
e. 2 milliliters and 2,000 liters
i. yes
ii. no

Answer: No

Explanation:

1 liter = 1000 milliliters
2 liters = 2000 milliliters
the above statement is false.

Page No. 714

Question 18.
Draw lines to match equivalent time intervals.

Answer:

Question 19.
Anya arrived at the library on Saturday morning at 11:10 a.m. She left the library 1 hour 20 minutes later. Draw a time line to show the end time.

Anya left the library at _____ P. M.

Question 20.
The tables show patterns for some units of measurement. Write the correct labels in each table.

Answer: Yard, Feet; Week, days; Quart, Cups.

The label for the first table is:

The label for the second table is:

The label for the third table is:

Question 21.
An Olympic swimming pool is 25 meters wide. How many decimeters wide is an Olympic swimming pool?
_____ decimeters wide

Answer: 250 decimeter

Explanation:

An Olympic swimming pool is 25 meters wide.
Convert meters to decimeters.
1 meter = 10 decimeter
25 meters = 25 × 10 decimeter = 250 decimeters
Thus the Olympic swimming pool is 250 decimeters wide.

Question 22.
Frankie is practicing for a 5-kilometer race. His normal time is 31 minutes 21 seconds. Yesterday it took him only 29 minutes 38 seconds.
How much faster was Frankie yesterday than his normal time?
Type below:
________

Answer: 1 minute 43 seconds

Explanation:

Frankie is practicing for a 5-kilometer race.
His normal time is 31 minutes 21 seconds. Yesterday it took him only 29 minutes 38 seconds.
Subtract 29 minutes 38 seconds from 31 minutes 21 seconds
31 minutes 21 seconds
29 minutes 38 seconds
1 minute 43 seconds

Page No. 719

Question 1.
Find the perimeter of the rectangle.

The perimeter is _______ feet.
_____ ft

Answer: 24 ft.

Explanation:

The length of the rectangle = 8 ft.
The width of the rectangle = 4 ft.
The formula for the perimeter of the rectangle is 2 (l + w)
= 2 (8 ft. + 4 ft.) = 2(12 ft.) = 24 ft.
The perimeter of the rectangle = 24 ft.

Find the perimeter of the rectangle or square.

Question 2.

P = _____ yards

Answer: 40 yards

Explanation:

The length of the rectangle = 16 yards
The width of the rectangle = 4 yards
The formula for the perimeter of the rectangle is 2 (l + w)
= 2 (16 yards + 4 yards) = 2(20 yards) = 40 yards
The perimeter of the rectangle is 40 yards.

Question 3.

P = _____ meters

Answer: 304 meters

Explanation:

The length of the rectangle = 110 m
The width of the rectangle = 42 m
The formula for the perimeter of the rectangle is 2 (l + w)
= 2 (110 m + 42 m) = 2(152 m)
= 304 meters
Therefore the perimeter of the rectangle is 304 meters.

Question 4.

P = _____ meters

Answer: 16 meters

Explanation:

The side of the square is 4 meters
The perimeter of the square = 4a
= 4 × 4 = 16 meters.
Therefore the perimeter of the square is 16 meters.

Find the perimeter of the rectangle or square.

Question 5.

P = _____ inches

Answer: 108 in.

Explanation:
Length = 34 in.
Width = 20 in.
The formula for the perimeter of the rectangle is 2 (l + w)
= 2 (34 in. + 20 in.)
= 108 in.

Question 6.

P = _____ feet

Answer: 464 feet

Explanation:

The side of the square is 116 feet
The perimeter of the square = 4a
= 4 × 116 feet = 464 feet.
Thus the perimeter of the square is 464 feet.

Question 7.

P = _____ meters

Answer: 126 meters

Explanation:

The length of the rectangle = 42 meters
The width of the rectangle = 21 meters
The formula for the perimeter of the rectangle is 2 (l + w)
= 2 (42 m + 21 m) = 2 (63 m) = 126 meters
Therefore the perimeter of the above rectangle is 126 meters.

Question 8.
Robert wants to put lights around the edge of his yard. The yard is 40 feet long and 23 feet wide. How many yards of lights does he need?
_____ feet

Answer: 126 feet

Explanation:

Given that, Robert wants to put lights around the edge of his yard. The yard is 40 feet long and 23 feet wide.
The length = 40 ft.
The width = 23 ft.
The formula for the perimeter of the rectangle is 2 (l + w)
= 2 (40 ft. + 23 ft.) = 2 (63 feet) = 126 feets
Thus Robert need 126 feet to put lights.

Question 9.
Analyze What is the side length of a square with a perimeter of 60 meters?
l = _____ meters

Answer: 15 meters

Explanation:

The perimeter of the square = 60 meters
We know that, the perimeter of the square = 4a
4a = 60 meters
a = 60/4 = 15 meters
Thus the length of a square is 15 meters.

Page No. 720

Question 10.
Alejandra plans to sew fringe on a scarf. The scarf is shaped like a rectangle. The length of the scarf is 48 inches. The width is one half the length. How much fringe does Alejandra need?

a. Draw a picture of the scarf, and label the given measurements on your drawing.
Type below:
________

Answer:

Question 10.
b. What do you need to find?
Type below:
___9 _____

Answer: I need to find how much fringe does Alejandra need?

Question 10.
c. What formula will you use?
Type below:
________

Answer: I will use the perimeter of the rectangle formula = 2 (l + w).

Question 10.

d. Show the steps you use to solve the problem.
Type below:
________

Answer:

First I will calculate the width of the rectangle.
After that, I will use the formula of perimeter of the rectangle.
I will substitute the value of the length and width of the rectangle.

Question 10.
e. Complete.
The length of the scarf is ____ inches.
The width is one half the length, or
____ ÷ 2 = ____ inches.
So, the perimeter is
(____ × ____) + (____ × ____) = ____ inches.
Type below:
________

Answer:

The length of the scarf is 48 inches.

The width is one half the length, or 48 ÷ 2 = 24 inches.

So, the perimeter is

(2 × 24) + (2 × 48) = 144 inches

Question 10.
f. Alejandra needs _____ of fringe.
____ inches of fringe

Answer: 144 inches of fringe

Question 11.
Marcia will make a frame for her picture. The picture frame will be three times as long as it is wide. The width of the frame will be 5 inches. How much wood does Marcia need for the frame?
____ inches

Answer: 40 inches

Explanation:

Given that, Marcia will make a frame for her picture.
The picture frame will be three times as long as it is wide.
The width of the frame will be 5 inches.
Length = 3 × 5 inches = 15 inches
Perimeter of the rectangle = 2 (l + w)
= 2 (15 + 5) = 2 × 20 = 40 inches
Marcia needs 40 inches of wood for the frame.

Question 12.
Maya is building a sandbox that is 36 inches wide. The length is four times the width. What is the perimeter of the sandbox? Show your work. Explain.
____ inches

Answer: 360 inches

Explanation:

Maya is building a sandbox that is 36 inches wide. The length is four times the width.
Width = 36 inches
length = 4 × 36 inches = 144 inches
The perimeter of the rectangle = 2 (l + w)
= 2 (144 in. + 36 in.) = 2 × 180 inches = 360 inches
Therefore, the perimeter of the sandbox is 360 inches.

Conclusion:

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Go Math Grade 6 Answer Key Chapter 8 Solutions of Equations

Enhance your performance in practice tests or assignments with the help of HMH Go Math 6th Grade Answer Key Chapter 8 Solutions of Equations. Get the solutions of Review Test and Mid Chapter Checkpoint in Go Math 6th Grade Chapter 8 Solutions of Equations. Scroll down this page to know the topics covered in this chapter. Make use of the links and Download Grade 6 Go Math Answer Key Chapter 8 Solutions of Equations.

Lesson 1: Solutions of Equations

• Share and Show – Page No. 423
• Problem Solving + Applications – Page No. 424
• Solutions of Equations – Page No. 425
• Lesson Check – Page No. 426

Lesson 2: Write Equations

• Share and Show – Page No. 429
• Problem Solving + Applications – Page No. 430
• Write Equations – Page No. 431
• Lesson Check – Page No. 432

Lesson 3: Investigate • Model and Solve Addition Equations

• Share and Show – Page No. 435
• Problem Solving + Applications – Page No. 436
• Model and Solve Addition Equations – Page No. 437
• Lesson Check – Page No. 438

Lesson 4: Solve Addition and Subtraction Equations

• Share and Show – Page No. 441
• Unlock the Problem – Page No. 442
• Solve Addition and Subtraction Equations – Page No. 443
• Lesson Check – Page No. 444

Lesson 5: Investigate • Model and Solve Multiplication Equations

• Share and Show – Page No. 447
• Page No. 448
• Model and Solve Multiplication Equations – Page No. 449
• Lesson Check – Page No. 450

Lesson 6: Solve Multiplication and Division Equations

• Share and Show – Page No. 453
• Problem Solving + Applications – Page No. 454
• Solve Multiplication and Division Equations – Page No. 455
• Lesson Check – Page No. 456

Lesson 7: Problem Solving • Equations with Fractions

• Share and Show – Page No. 459
• On Your Own – Page No. 460
• Problem Solving Equations with Fractions – Page No. 461
• Lesson Check – Page No. 462

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Vocabulary – Page No. 463
• Mid-Chapter Checkpoint – Page No. 464

Lesson 8: Solutions of Inequalities

• Share and Show – Page No. 467
• Problem Solving + Applications – Page No. 468
• Solutions of Inequalities – Page No. 469
• Lesson Check – Page No. 470

Lesson 9: Write Inequalities

• Share and Show – Page No. 473
• Make Generalizations – Page No. 474
• Write Inequalities – Page No. 475
• Lesson Check – Page No. 476

Lesson 10: Graph Inequalities

• Share and Show – Page No. 479
• Problem Solving + Applications – Page No. 480
• Graph Inequalities – Page No. 481
• Lesson Check – Page No. 482

Chapter 8 Review/Test

• Chapter 8 Review/Test – Page No. 483
• Chapter 8 Review/Test – Page No. 484
• Chapter 8 Review/Test Page No. 485
• Chapter 8 Review/Test – Page No. 486
• Chapter 8 Review/Test Page No. 487
• Chapter 8 Review/Test Page No. 488

Share and Show – Page No. 423

Determine whether the given value of the variable is a solution of the equation.

Question 1.
x + 12 = 29; x = 7
The variable is __________

Answer: not a solution

Explanation:
Substitute the value in the given equation
x + 12 = 29
If x = 7
7 + 12 = 29
19 ≠ 29
Thus the variable is not a solution.

Question 2.
n − 13 = 2; n = 15
The variable is __________

Answer: a solution

Explanation:
Substitute the value in the given equation
n = 15
n − 13 = 2
15 – 13 = 2
The variable is a solution.

Question 3.
\(\frac{1}{2}\)c = 14; c = 28
The variable is __________

Answer: a solution

Explanation:
Substitute the value in the given equation
c = 28
\(\frac{1}{2}\)c = 14
\(\frac{1}{2}\) × 28 = 14
14 = 14
Thus the variable is a solution.

Question 4.
m + 2.5 = 4.6; m = 2.9
The variable is __________

Answer: not a solution

Explanation:
Substitute the value in the given equation
m + 2.5 = 4.6
m = 2.9
2.9 + 2.5 = 4.6
5.4 ≠ 4.6
Thus the variable is not a solution.

Question 5.
d − 8.7 = 6; d = 14.7
The variable is __________

Answer: a solution

Explanation:
Substitute the value in the given equation
d = 14.7
d − 8.7 = 6
14.7 – 8.7 = 6
6 = 6
Thus the variable is a solution.

Question 6.
k − \(\frac{3}{5}\) = \(\frac{1}{10}\); k = \(\frac{7}{10}\)
The variable is __________

Answer: a solution

Explanation:
Substitute the value in the given equation
k = \(\frac{7}{10}\)
k − \(\frac{3}{5}\) = \(\frac{1}{10}\)
\(\frac{7}{10}\) – \(\frac{3}{5}\) = \(\frac{1}{10}\)
\(\frac{7}{10}\) – \(\frac{6}{10}\) = \(\frac{1}{10}\)
\(\frac{1}{10}\) = \(\frac{1}{10}\)
Thus the variable is a solution.

On Your Own

Determine whether the given value of the variable is a solution of the equation.

Question 7.
17.9 + v = 35.8; v = 17.9
The variable is __________

Answer: a solution

Explanation:
Substitute the value in the given equation
17.9 + v = 35.8
v = 17.9
17.9 + 17.9 = 35.8
35.8 = 35.8
Thus the variable is a solution.

Question 8.
c + 35 = 57; c = 32
The variable is __________

Answer: not a solution

Explanation:
Substitute the value in the given equation
c + 35 = 57
c = 32
32 + 35 = 57
67 ≠ 57
Thus the variable is not a solution.

Question 9.
18 = \(\frac{2}{3}\)h; h= 12
The variable is __________

Answer: not a solution

Explanation:
Substitute the value in the given equation
18 = \(\frac{2}{3}\)h
h = 12
\(\frac{2}{3}\) × 12 = 8
18 ≠ 8
Thus the variable is not a solution.

Question 10.
In the equation t + 2.5 = 7, determine whether t = 4.5, t = 5, or t = 5.5 is a solution of the equation.
The solution is ________.

Answer: t = 4.5

Explanation:
Substitute the value in the given equation
t = 4.5
t + 2.5 = 7
4.5 + 2.5 = 7
7 = 7
t = 5
t + 2.5 = 7
5 + 2.5 = 7
7.5 ≠ 7
Not a solution
t = 5.5
t + 2.5 = 7
5.5 + 2.5 = 7
8 ≠ 7
Not a solution

Question 11.
Antonio ran a total of 9 miles in two days. The first day he ran 5 \(\frac{1}{4}\) miles. The equation 9 – d = 5 \(\frac{1}{4}\) can be used to find the distance d in miles Antonio ran the second day. Determine whether d = 4 \(\frac{3}{4}\), d = 4, or d = 3 \(\frac{3}{4}\) is a solution of the equation, and tell what the solution means.
The solution is ________ \(\frac{□}{□}\)

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

Explanation:
9 – d = 5 \(\frac{1}{4}\)
Substitute d = 4 \(\frac{3}{4}\) in the above equation
9 – 4 \(\frac{3}{4}\) = 5 \(\frac{1}{4}\)
4 \(\frac{1}{4}\) ≠ 5 \(\frac{1}{4}\)
Not a solution
Substitute d = 4
9 – 4 = 5 \(\frac{1}{4}\)
5 ≠ 5 \(\frac{1}{4}\)
Not a solution
Substitute d = 3 \(\frac{3}{4}\)
9 – 3 \(\frac{3}{4}\) = 5 \(\frac{1}{4}\)
5 \(\frac{1}{4}\) = 5 \(\frac{1}{4}\)
9 – d = 5 \(\frac{1}{4}\); d = 3 \(\frac{3}{4}\) is a solution.

Problem Solving + Applications – Page No. 424

Use the table for 12–14.

Question 12.
Connect Symbols and Words The length of a day on Saturn is 14 hours less than a day on Mars. The equation 24.7 − s = 14 can be used to find the length in hours s of a day on Saturn. Determine whether s = 9.3 or s = 10.7 is a solution of the equation, and tell what the solution means.
Type below:
_____________

Answer: s = 10.7

Explanation:
The length of a day on Saturn is 14 hours less than a day on Mars.
The equation 24.7 − s = 14 can be used to find the length in hours s of a day on Saturn.
24.7 − s = 14
Substitute s = 9.3 in the equation
24.7 – 9.3 = 14
15.4 ≠ 14
Not a solution
Substitute s = 10.7 in the equation
24.7 – 10.7 = 14
14 = 14
Therefore s = 10.7 is a solution to the equation.

Question 13.
A storm on one of the planets listed in the table lasted for 60 hours, or 2.5 of the planet’s days. The equation 2.5h = 60 can be used to find the length in hours h of a day on the planet. Is the planet Earth, Mars, or Jupiter? Explain.
Type below:
_____________

Answer: Earth

Explanation:
A storm on one of the planets listed in the table lasted for 60 hours, or 2.5 of the planet’s days.
2.5h = 60
h = 60/2.5
h = 24 hours
By seeing the above table we can say that Earth is the answer.

Question 14.
A day on Pluto is 143.4 hours longer than a day on one of the planets listed in the table. The equation 153.3 − p = 143.4 can be used to find the length in hours p of a day on the planet. What is the length of a storm that lasts \(\frac{1}{3}\) of a day on this planet?
________ hours

Answer: 3.3 hours

Explanation:
A day on Pluto is 143.4 hours longer than a day on one of the planets listed in the table.
153.3 − p = 143.4
153.3 – 143.4 = p
p = 153.3 – 143.4
p = 9.9
Now p with \(\frac{1}{3}\) to find the length of a storm that lasts of a day on this planet
9.9 × \(\frac{1}{3}\) = 3.3 hours

Question 15.
What’s the Error? Jason said that the solution of the equation 2m = 4 is m = 8. Describe Jason’s error, and give the correct solution.
Type below:
_____________

Answer: m = 2

Explanation:
Jason said that the solution of the equation 2m = 4 is m = 8.
2m = 4
m = 4/2 = 2
The error of Jason is he multiplied 2 and 4 but he should divide 4 by 2.

Question 16.
The marking period is 45 school days long. Today is the twenty-first day of the marking period. The equation x + 21 = 45 can be used to find the number of days x left in the marking period. Using substitution, Rachel determines there are _____ days left in the marking period.
Rachel determines there are _____________ days left.

Answer: 24

Explanation:
The marking period is 45 school days long. Today is the twenty-first day of the marking period.
The equation x + 21 = 45
x = 45 – 21 = 24 days
Using substitution, Rachel determines there are 24 days left in the marking period.
Thus Rachel determines there are 24 days left.

Solutions of Equations – Page No. 425

Determine whether the given value of the variable is a solution of the equation.

Question 1.
x − 7 = 15; x = 8
The variable is __________

Answer: not a solution

Explanation:
Substitute the value in the given equation.
x = 8
8 – 7 = 15
1 ≠ 15
Therefore the variable is not a solution.

Question 2.
c + 11 = 20; c = 9
The variable is __________

Answer: a solution

Explanation:
Substitute the value in the given equation.
c = 9
9 + 11 = 20
20 = 20
Therefore the variable is a solution.

Question 3.
\(\frac{1}{3}\)h = 6; h = 2
The variable is __________

Answer: not a solution

Explanation:
Substitute the value in the given equation.
\(\frac{1}{3}\)h = 6
h = 2
\(\frac{1}{3}\) × 2 = 6
\(\frac{2}{3}\) ≠ 6
Therefore the variable is not a solution.

Question 4.
16.1 + d = 22; d = 6.1
The variable is __________

Answer: not a solution

Explanation:
Substitute the value in the given equation.
16.1 + d = 22
d = 6.1
16.1 + 6.1 = 22
22.2 ≠ 22
Therefore the variable is not a solution.

Question 5.
9 = \(\frac{3}{4}\)e; e = 12
The variable is __________

Answer: a solution

Explanation:
Substitute the value in the given equation.
9 = \(\frac{3}{4}\)e
e = 12
9 = \(\frac{3}{4}\)(12)
9 = 3 × 3
9 = 9
Therefore the variable is a solution.

Question 6.
15.5 – y = 7.9; y = 8.4
The variable is __________

Answer: not a solution

Explanation:
Substitute the value in the given equation.
15.5 – y = 7.9
y = 8.4
15.5 – 8.4 = 7.9
7.1 ≠ 7.9
Therefore the variable is not a solution.

Problem Solving

Question 7.
Terrance needs to score 25 points to win a game. He has already scored 18 points. The equation 18 + p = 25 can be used to find the number of points p that Terrance still needs to score. Determine whether p = 7 or p = 13 is a solution of the equation, and tell what the solution means.
Type below:
_____________

Answer: p = 7

Explanation:
Terrance needs to score 25 points to win a game. He has already scored 18 points.
The equation is 18 + p = 25
Substitute p = 7 in the above equation.
18 + 7 = 25
25 = 25
The variable is a solution.
Substitute p = 13
18 + p = 25
18 + 13 = 25
31 ≠ 25
The variable is not a solution.
Therefore p = 7 is a solution for the equation.

Question 8.
Madeline has used 50 sheets of a roll of paper towels, which is \(\frac{5}{8}\) of the entire roll. The equation \(\frac{5}{8}\)s = 50 can be used to find the number of sheets s in a full roll. Determine whether s = 32 or s = 80 is a solution of the equation, and tell what the solution means.
Type below:
_____________

Answer:
Madeline has used 50 sheets of a roll of paper towels, which is \(\frac{5}{8}\) of the entire roll.
\(\frac{5}{8}\)s = 50
s = 50 × \(\frac{8}{5}\)
s = 80 because 80 × 5 = 400
400 ÷ 8 = 50

Question 9.
Use mental math to find the solution to 4x = 36. Then use substitution to check your answer.
Type below:
_____________

Answer: x = 9

Explanation:
4x = 36
x = 36/4
x = 9

Lesson Check – Page No. 426

Question 1.
Sheena received a gift card for $50. She has already used it to buy a lamp for $39.99. The equation 39.99 + x = 50 can be used to find the amount x that is left on the gift card. What is the solution of the equation?
_____

Answer: 10.01

Explanation:
Given:
Sheena received a gift card for $50. She has already used it to buy a lamp for $39.99.
The equation 39.99 + x = 50
39.99 + x = 50
x = 50 – 39.99
x = 50.00 – 39.99
x = 10.01
Thus $10.01 is left on the gift card.

Question 2.
When Pete had a fever, his temperature was 101.4°F. After taking some medicine, his temperature was 99.2°F. The equation 101.4 – d = 99.2 can be used to find the number of degrees d that Pete’s temperature decreased. What is the solution of the equation?
_____

Answer: 2.2

Explanation:
Given,
When Pete had a fever, his temperature was 101.4°F.
After taking some medicine, his temperature was 99.2°F.
The equation 101.4 – d = 99.2
104.4 – 99.2 = d
d = 104.4 – 99.2
d = 2.2

Spiral Review

Question 3.
Melanie has saved $60 so far to buy a lawn mower. This is 20% of the price of the lawn mower. What is the full price of the lawn mower that she wants to buy?
$ _____

Answer: 300

Explanation:
Melanie has saved $60 so far to buy a lawn mower. This is 20% of the price of the lawn mower.
60 ÷ 20%
60 ÷ 20/100
60 × 100/20 = 6000/20 = 300
She wants to buy a $300 price of the lawn mower.

Question 4.
A team of scientists is digging for fossils. The amount of soil in cubic feet that they remove is equal to 6³. How many cubic feet of soil do the scientists remove?
_____ cubic feet

Answer: 216

Explanation:
A team of scientists is digging for fossils. The amount of soil in cubic feet that they remove is equal to 6³.
6 × 6 × 6 = 216
Thus the scientists remove 216 cubic feet of soil.

Question 5.
Andrew made p picture frames. He sold 2 of them at a craft fair. Write an expression that could be used to find the number of picture frames Andrew has left.
Type below:
_____________

Answer: p – 2

Explanation:
Andrew made p picture frames. He sold 2 of them at a craft fair.
The expression is the difference of 9 and 2
The equation is p – 2

Question 6.
Write an expression that is equivalent to 4 + 3(5 + x).
Type below:
_____________

Answer: 4 + 15 + 3x

Explanation:
4 + 3(5 + x) = 4 + 15 + 3x
3x + 19
Thus the expression 4 + 3(5 + x) is equivalent to 4 + 15 + 3x or 3x + 19

Share and Show – Page No. 429

Question 1.
Write an equation for the word sentence “25 is 13 more than a number.”
Type below:
_____________

Answer:
Let n represents the unknown number. The phrase ‘more than’ indicates addition operation.
Thus the equation is 25 = 13 + n.

Write an equation for the word sentence.

Question 2.
The difference of a number and 2 is 3 \(\frac{1}{3}\).
Type below:
_____________

Answer:
Let n represents the unknown number.
The phrase “difference” indicates the subtraction operation.
The equation is n – 2 = 3 \(\frac{1}{3}\)

Question 3.
Ten times the number of balloons is 120.
Type below:
_____________

Answer:
Let n represents the unknown number.
The phrase “times” indicates multiplication operation.
The equation is 10 × n = 120

Write a word sentence for the equation.

Question 4.
x − 0.3 = 1.7
Type below:
_____________

Answer: The difference of x and 0.3 is 1.7

Question 5.
25 = \(\frac{1}{4}\)n
Type below:
_____________

Answer: 25 is n times \(\frac{1}{4}\)

Write an equation for the word sentence.

Question 6.
The quotient of a number and 20.7 is 9.
Type below:
_____________

Answer:
Let n represents the unknown number.
The phrase “quotient” indicates the division operation.
Thus the equation is n ÷ 20.7 = 9.

Question 7.
24 less than the number of snakes is 35.
Type below:
_____________

Answer:
Let n represents the unknown number.
The phrase “less than” indicates subtraction operation.
Thus the equation is n – 24 = 35

Question 8.
75 is 18 \(\frac{1}{2}\) more than a number.
Type below:
_____________

Answer:
Let n represents the unknown number.
The phrase “more than” indicates addition operation.
75 = 18 \(\frac{1}{2}\) + n

Question 9.
d degrees warmer than 50 degrees is 78 degrees.
Type below:
_____________

Answer:
Let n represents the unknown number.
The phrase “warmer than” indicates addition operation.
The equation is d + 50 = 78 degrees

Write a word sentence for the equation.

Question 10.
15g = 135
Type below:
_____________

Answer: g times 15 is 135

Question 11.
w ÷ 3.3 = 0.6
Type below:
_____________

Answer: The quotient of w and 3.3 is 0.6

Problem Solving + Applications – Page No. 430

To find out how far a car can travel on a certain amount of gas, multiply the car’s fuel efficiency in miles per gallon by the gas used in gallons. Use this information and the table for 12–13.

Question 12.
Write an equation that could be used to find how many miles a hybrid SUV can travel in the city on 20 gallons of gas.
Type below:
_____________

Answer:
From table 36 miles per gallon in the city.
A hybrid SUV uses 36 miles per gallon in the city.
So, no. of miles = y
x = no. of gallons
So, y = 36 × x
x = 20 gallons
Thus y = 36 × 20

Question 13.
A sedan traveled 504 miles on the highway on a full tank of gas. Write an equation that could be used to find the number of gallons the tank holds.
Type below:
_____________

Answer:
A sedan uses 28 miles per gallon on the highway.
The equation that could be used to find the number of gallons the tank holds is
504 = 28g

Question 14.
Connect Symbols to Words Sonya was born in 1998. Carmen was born 11 years after Sonya. If you wrote an equation to find the year in which Carmen was born, what operation would you use in your equation?
Type below:
_____________

Answer: In this equation, I would use addition or subtraction operation.

Question 15.
A magazine has 110 pages. There are 23 full-page ads and 14 half-page ads. The rest of the magazine consists of articles. Write an equation that can be used to find the number of pages of articles in the magazine.
Type below:
_____________

Answer:
The equation that can be used to find the number of pages of articles in the magazine is
23 + 14/2 + a = 110
where a represents the number of articles.

Question 16.
What’s the Error? Tony is traveling 560 miles to visit his cousins. He travels 313 miles the first day. He says that he can use the equation m − 313 = 560 to find the number of miles m he has left on his trip. Describe and correct Tony’s error.
Type below:
_____________

Answer:
Tony subtracted the number of miles traveled from the number of miles left.
Tony should have written m + 313 = 560

Question 17.
Jamie is making cookies for a bake sale. She triples the recipe in order to have enough cookies to sell. Jamie uses 12 cups of flour to make the triple batch. Write an equation that can be used to find out how much flour f is needed for one batch of cookies.
Type below:
_____________

Answer:
The equation that can be used to find out how much flour f is needed for one batch of cookies is 3f = 12

Write Equations – Page No. 431

Write an equation for the word sentence.

Question 1.
18 is 4.5 times a number.
Type below:
_____________

Answer:
Let n represents the unknown number.
The phrase “times” indicates the multiplication operation.
The equation is 18 = 4.5n

Question 2.
Eight more than the number of children is 24.
Type below:
_____________

Answer:
Let c represents the number of children.
The phrase “more than” indicates addition operation.
Thus the equation is 8 + c = 24.

Question 3.
The difference of a number and \(\frac{2}{3}\) is \(\frac{3}{8}\).
Type below:
_____________

Answer:
Let n represents the unknown number.
The phrase “difference” indicates a subtraction operation.
The equation is n – \(\frac{2}{3}\) = \(\frac{3}{8}\)

Question 4.
A number divided by 0.5 is 29.
Type below:
_____________

Answer:
Let n represents the unknown number.
The phrase divided by indicates division operation.
The equation is n ÷ 0.5 = 29

Write a word sentence for the equation.

Question 5.
x − 14 = 52
Type below:
_____________

Answer:
14 less than x is 52
the difference of x and 14 is 52
14 fewer than a number is 52.

Question 6.
2.3m = 0.46
Type below:
_____________

Answer:
The product of 2.3 and m is 0.46
2.3 times m is .46
2.3 of m is 0.46

Question 7.
25 = k ÷ 5
Type below:
_____________

Answer: 25 is the quotient of k and 5.

Question 8.
\(4 \frac{1}{3}+q=5 \frac{1}{6}\)
Type below:
_____________

Answer:
The sum of \(4 \frac{1}{3}\) and q is [/latex]5 \frac{1}{6}[/latex]
q is more than \(4 \frac{1}{3}\) and [/latex]5 \frac{1}{6}[/latex]
\(4 \frac{1}{3}\) increased by a number is [/latex]5 \frac{1}{6}[/latex]

Question 9.
An ostrich egg weighs 2.9 pounds. The difference between the weight of this egg and the weight of an emu egg is 1.6 pounds. Write an equation that could be used to find the weight w, in pounds, of the emu egg.
Type below:
_____________

Answer: 2.9 – w = 1.6

Explanation:
An ostrich egg weighs 2.9 pounds.
The difference between the weight of this egg and the weight of an emu egg is 1.6 pounds.
The phrase “difference” indicates the subtraction operation.
The equation will be 2.9 – w = 1.6

Question 10.
In one week, the number of bowls a potter made was 6 times the number of plates. He made 90 bowls during the week. Write an equation that could be used to find the number of plates p that the potter made.
Type below:
_____________

Answer: 6p = 90

Explanation:
Given,
In one week, the number of bowls a potter made was 6 times the number of plates.
He made 90 bowls during the week.
The phrase “times” indicates the multiplication operation.
The equation to find the number of plates p that the potter made will be 6p = 90

Question 11.
When writing a word sentence as an equation, explain when to use a variable.
Type below:
_____________

Answer:
In a word sentence, a variable represents “a number.”
The sum of a number and three = n + 3
The difference of five times a number and four = 5n – 4

Lesson Check – Page No. 432

Question 1.
Three friends are sharing the cost of a bucket of popcorn. The total cost of the popcorn is $5.70. Write an equation that could be used to find the amount a in dollars that each friend should pay.
Type below:
_____________

Answer: 3a = 5.70

Explanation:
Three friends are sharing the cost of a bucket of popcorn.
The total cost of the popcorn is $5.70.
The expression will be “5.70 is the product of 3 and a.
The equation is 3a = 5.70

Question 2.
Salimah had 42 photos on her phone. After she deleted some of them, she had 23 photos left. What equation could be used to find the number of photos p that Salimah deleted?
Type below:
_____________

Answer: p + 23 = 42

Explanation:
Salimah had 42 photos on her phone. After she deleted some of them, she had 23 photos left.
The expression is the sum of p and 23 is 42.
Thus the equation is p + 23 = 42

Question 3.
A rope is 72 feet long. What is the length of the rope in yards?
______ yards

Answer: 24 yard

Explanation:
A rope is 72 feet long.
Convert from feet to yards.
1 yard = 3 feet
1 foot = 1/3 yards
72 feet = 72 × 1/3 = 24 yards
Thus the length of the rope is 24 yards.

Question 4.
Julia evaluated the expression 3³ + 20 ÷ 2². What value should she get as her answer?
______

Answer: 32

Explanation:
The equation is 3³ + 20 ÷ 2².
3³ = 3 × 3 × 3 = 27
2² = 2 × 2 = 4
27 + (20 ÷ 4)
27 + 5 = 32
The answer for the above equation is 32.

Question 5.
The sides of a triangle have lengths s, s + 4, and 3s. Write an expression in the simplest form that represents the perimeter of the triangle.
Type below:
_____________

Answer: 5s + 4

Explanation:
The perimeter of the triangle is a + b + c
P = a + b + c
P = s + s + 4 + 3s
P = 5s + 4
Thus the perimeter of the triangle is 5s + 4

Question 6.
Gary knows that p = 2 \(\frac{1}{2}\) is a solution to one of the following equations. Which one has p = 2 \(\frac{1}{2}\) as its solution?
\(p+2 \frac{1}{2}=5\)        \(p-2 \frac{1}{2}=5\)
\(2+p=2 \frac{1}{2}\)       4 – p = 2 \(\frac{1}{2}\)
Type below:
_____________

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

Explanation:
\(p+2 \frac{1}{2}=5\)
p + 2 \(\frac{1}{2}\) = 5
p = 5 – 2 \(\frac{1}{2}\)
p = 2 \(\frac{1}{2}\)
\(p-2 \frac{1}{2}=5\)
p – 2 \(\frac{1}{2}\) = 5
p = 5 + 2 \(\frac{1}{2}\)
p = 7 \(\frac{1}{2}\)
\(2+p=2 \frac{1}{2}\)
2 + p = 2 \(\frac{1}{2}\)
p = 2 \(\frac{1}{2}\) – 2
p = \(\frac{1}{2}\)
4 – p = 2 \(\frac{1}{2}\)
p = 4 – 2 \(\frac{1}{2}\)
p = 1 \(\frac{1}{2}\)

Share and Show – Page No. 435

Model and solve the equation by using algebra tiles or iTools.

Question 1.
x + 5 = 7
x = ______

Answer: 2

Explanation:

• Draw 2 rectangles on your MathBoard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model x + 5 in the left rectangle, and model 7 in the right rectangle.
• To solve the equation, get the x tile by itself on one side. If you remove a tile from one side, you can keep the two sides equal by removing the same type of tile from the other side.
• Remove five 1 tiles on the left side and five 1 tiles on the right side.
• The remaining titles will be two 1 tiles on the right sides.

Question 2.
8 = x + 1
x = ______

Answer: 7

Explanation:

• Draw 2 rectangles on your MathBoard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model x + 1 in the left rectangle, and model 8 in the right rectangle.
• To solve the equation, get the x tile by itself on one side. If you remove a tile from one side, you can keep the two sides equal by removing the same type of tile from the other side.
• Remove one 1 tiles on the left side and one 1 tiles on the right side.
• The remaining titles will be seven 1 tiles on the right sides.

Question 3.
x + 2 = 5
x = ______

Answer: 3

Explanation:

• Draw 2 rectangles on your MathBoard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model x + 2 in the left rectangle, and model 5 in the right rectangle.
• To solve the equation, get the x tile by itself on one side. If you remove a tile from one side, you can keep the two sides equal by removing the same type of tile from the other side.
• Remove two 1 tiles on the left side and five 1 tiles on the right side.
• The remaining titles will be three 1 tiles on the right sides.

Question 4.
x + 6 = 8
x = ______

Answer: 2

Explanation:

• Draw 2 rectangles on your MathBoard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model x + 6 in the left rectangle, and model 8 in the right rectangle.
• To solve the equation, get the x tile by itself on one side. If you remove a tile from one side, you can keep the two sides equal by removing the same type of tile from the other side.
• Remove six 1 tiles on the left side and six 1 tiles on the right side.
• The remaining titles will be two 1 tiles on the right sides.

Question 5.
5 + x = 9
x = ______

Answer: 4

Explanation:

• Draw 2 rectangles on your MathBoard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model x + 5 in the left rectangle, and model 9 in the right rectangle.
• To solve the equation, get the x tile by itself on one side. If you remove a tile from one side, you can keep the two sides equal by removing the same type of tile from the other side.
• Remove five 1 tiles on the left side and five 1 tiles on the right side.
• The remaining titles will be four 1 tiles on the right sides.

Question 6.
5 = 4 + x
x = ______

Answer: 1

Explanation:

• Draw 2 rectangles on your MathBoard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model x + 4 in the left rectangle, and model 5 in the right rectangle.
• To solve the equation, get the x tile by itself on one side. If you remove a tile from one side, you can keep the two sides equal by removing the same type of tile from the other side.
• Remove four 1 tiles on the left side and four 1 tiles on the right side.
• The remaining titles will be one 1 tiles on the right sides.

Solve the equation by drawing a model.

Question 7.
x + 1 = 5
x = ______

Answer: 4

Explanation:

• Draw 2 rectangles on your MathBoard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model x + 1 in the left rectangle, and model 5 in the right rectangle.
• To solve the equation, get the x tile by itself on one side. If you remove a tile from one side, you can keep the two sides equal by removing the same type of tile from the other side.
• Remove one 1 tiles on the left side and one 1 tiles on the right side.
• The remaining titles will be four 1 tiles on the right sides.

Question 8.
3 + x = 4
x = ______

Answer: 1

Explanation:

• Draw 2 rectangles on your MathBoard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model x + 3 in the left rectangle, and model 4 in the right rectangle.
• To solve the equation, get the x tile by itself on one side. If you remove a tile from one side, you can keep the two sides equal by removing the same type of tile from the other side.
• Remove three 1 tiles on the left side and three 1 tiles on the right side.
• The remaining titles will be one 1 tiles on the right sides.

Question 9.
6 = x + 4
x = ______

Answer: 2

Explanation:

• Draw 2 rectangles on your MathBoard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model x + 4 in the left rectangle, and model 6 in the right rectangle.
• To solve the equation, get the x tile by itself on one side. If you remove a tile from one side, you can keep the two sides equal by removing the same type of tile from the other side.
• Remove four 1 tiles on the left side and four 1 tiles on the right side.
• The remaining titles will be two 1 tiles on the right sides.

Question 10.
8 = 2 + x
x = ______

Answer: 6

Explanation:

• Draw 2 rectangles on your MathBoard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model x + 2 in the left rectangle, and model 8 in the right rectangle.
• To solve the equation, get the x tile by itself on one side. If you remove a tile from one side, you can keep the two sides equal by removing the same type of tile from the other side.
• Remove two 1 tiles on the left side and two 1 tiles on the right side.
• The remaining titles will be six 1 tiles on the right sides.

Question 11.
Describe a Method Describe how you would draw a model to solve the equation x + 5 = 10.
Type below:
_____________

Answer: x = 5

Explanation:

• Draw 2 rectangles on your MathBoard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model x + 5 in the left rectangle, and model 10 in the right rectangle.
• To solve the equation, get the x tile by itself on one side. If you remove a tile from one side, you can keep the two sides equal by removing the same type of tile from the other side.
• Remove five 1 tiles on the left side and five 1 tiles on the right side.
• The remaining titles will be five 1 tiles on the right sides.

Problem Solving + Applications – Page No. 436

Question 12.
Interpret a Result The table shows how long several animals have lived at a zoo. The giraffe has lived at the zoo 4 years longer than the mountain lion. The equation 5 = 4 + y can be used to find the number of years y the mountain lion has lived at the zoo. Solve the equation. Then tell what the solution means.
Type below:
_____________

Answer:
The table shows how long several animals have lived in a zoo.
The giraffe has lived at the zoo 4 years longer than the mountain lion.
5 = 4 + y
y = 5 – 4
y = 1
The solution is y = 1
The solution means that the mountain lion has lived at the zoo for 1 year.

Question 13.
Carlos walked 2 miles on Monday and 5 miles on Saturday. The number of miles he walked on those two days is 3 miles more than the number of miles he walked on Friday. Write and solve an addition equation to find the number of miles Carlos walked on Friday
Type below:
_____________

Answer:
Given that,
Carlos walked 2 miles on Monday and 5 miles on Saturday.
The number of miles he walked on those two days is 3 miles more than the number of miles he walked on Friday.
The equation is f + 3 = 2 + 5
f + 3 = 7
f = 7 – 3
f = 4
The solution is f = 4
The solution means that Carlos walked 4 miles on Friday.

Question 14.
Sense or Nonsense? Gabriela is solving the equation x + 1 = 6. She says that the solution must be less than 6. Is Gabriela’s statement sense or nonsense? Explain.
Type below:
_____________

Answer: Gabriela’s statement makes sense.
x + 1 = 6
x = 6 – 1
x = 5
Thus the solution is less than 6.

Question 15.
The Hawks beat the Tigers by 5 points in a football game. The Hawks scored a total of 12 points.
Use numbers and words to explain how this model can be used to solve the equation x + 5 = 12.

Type below:
_____________

Answer:
Remove 5 squares from each side. The rectangle is by itself on the left and 7 squares are on the right side.
So, the solution is x = 7

Model and Solve Addition Equations – Page No. 437

Model and solve the equation by using algebra tiles.

Question 1.
x + 6 = 9
x = ________

Answer: 3

Explanation:

• Draw 2 rectangles on your MathBoard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model x + 6 in the left rectangle, and model 9 in the right rectangle.
• To solve the equation, get the x tile by itself on one side. If you remove a tile from one side, you can keep the two sides equal by removing the same type of tile from the other side.
• Remove six 1 tiles on the left side and six 1 tiles on the right side.
• The remaining titles will be three 1 tiles on the right sides.

Thus x = 3

Question 2.
8 + x = 10
x = ________

Answer: 2

Explanation:

• Draw 2 rectangles on your MathBoard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model x + 8 in the left rectangle, and model 10 in the right rectangle.
• To solve the equation, get the x tile by itself on one side. If you remove a tile from one side, you can keep the two sides equal by removing the same type of tile from the other side.
• Remove eight 1 tiles on the left side and eight 1 tiles on the right side.
• The remaining titles will be two 1 tiles on the right sides.

8 + x = 10
x = 10 – 8 = 2
x = 2

Question 3.
9 = x + 1
x = ________

Answer: 8

Explanation:

• Draw 2 rectangles on your MathBoard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model x + 1 in the left rectangle, and model 9 in the right rectangle.
• To solve the equation, get the x tile by itself on one side. If you remove a tile from one side, you can keep the two sides equal by removing the same type of tile from the other side.
• Remove 1 tile on the left side and 1 tile on the right side.
• The remaining titles will be eight 1 tiles on the right sides.

Thus x = 8

Solve the equation by drawing a model.

Question 4.
x + 4 = 7
x = ________

Answer: 3

Question 5.
x + 6 = 10
x = ________

Answer: 4

Problem Solving

Question 6.
The temperature at 10:00 was 10°F. This is 3°F warmer than the temperature at 8:00. Model and solve the equation x + 3 = 10 to find the temperature x in degrees Fahrenheit at 8:00.
Type below:
_____________

Answer: x = 7

Explanation:
The temperature at 10:00 was 10°F. This is 3°F warmer than the temperature at 8:00.
The equation is x + 3 = 10
x = 10 – 3 = 7

Question 7.
Jaspar has 7 more checkers left than Karen does. Jaspar has 9 checkers left. Write and solve an addition equation to find out how many checkers Karen has left.
Type below:
_____________

Answer: c = 2

Explanation:
Jaspar has 7 more checkers left than Karen does. Jaspar has 9 checkers left.
The expression is c + 7 = 9
The equation to find out how many checkers Karen has left is c + 7 = 9.

Question 8.
Explain how to use a drawing to solve an addition equation such as x + 8 = 40.
Type below:
_____________

Answer: 32

Explanation:

• Draw 2 rectangles on your MathBoard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model x + 8 in the left rectangle, and model 40 in the right rectangle.
• To solve the equation, get the x tile by itself on one side. If you remove a tile from one side, you can keep the two sides equal by removing the same type of tile from the other side.
• Remove eight 1 tile on the left side and eight 1 tile on the right side.
• The remaining titles will be 32 1 tiles on the right side.

x + 8 = 40
x = 40 – 8
x = 32

Lesson Check – Page No. 438

Question 1.
What is the solution of the equation that is modeled by the algebra tiles?

x = ________

Answer: 1

The equation is x + 6 = 7
x = 7 – 6
x = 1

Question 2.
Alice has played soccer for 8 more years than Sanjay has. Alice has played for 12 years. The equation y + 8 = 12 can be used to find the number of years y Sanjay has played. How long has Sanjay played soccer?
________ years

Answer: 4 years

Explanation:
Alice has played soccer for 8 more years than Sanjay has. Alice has played for 12 years.
the equation is y + 8 = 12
y = 12 – 8
y = 4 years
Sanjay played soccer games for 4 years.

Spiral Review

Question 3.
A car’s gas tank has a capacity of 16 gallons. What is the capacity of the tank in pints?
________ pints

Answer: 128 pints

Explanation:
A car’s gas tank has a capacity of 16 gallons.
Convert from gallons to pints.
1 gallon = 8 pints
16 gallons = 16 × 8 = 128 pints
Thus the capacity of the tank is 128 pints.

Question 4.
Craig scored p points in a game. Marla scored twice as many points as Craig but 5 fewer than Nelson scored. How many points did Nelson score?
Type below:
_____________

Answer: 2p + 5

Explanation:
Craig scored p points in a game.
Marla scored twice as many points as Craig but 5 fewer than Nelson score.
The equation will be 2p + 5.

Question 5.
Simplify 3x + 2(4y + x).
Type below:
_____________

Answer: 5x + 8y

Explanation:
The expression is 3x + 2(4y + x)
3x + 2 × 4y + 2 × x
3x + 8y + 2x
Combine the like terms.
5x + 8y
3x + 2(4y + x) = 5x + 8y

Question 6.
The Empire State Building in New York City is 443.2 meters tall. This is 119.2 meters taller than the Eiffel Tower in Paris. Write an equation that can be used to find the height h in meters of the Eiffel Tower.
Type below:
_____________

Answer: 119.2 + h = 443.2

Explanation:
The Empire State Building in New York City is 443.2 meters tall.
This is 119.2 meters taller than the Eiffel Tower in Paris.
Here we have to use the addition operation.
The equation is 119.2 + h = 443.2

Share and Show – Page No. 441

Question 1.
Solve the equation n + 35 = 80.
n = ________

Answer: 45

Explanation:
The given equation is
n + 35 = 80
n = 80 – 35
n = 45

Solve the equation, and check the solution.

Question 2.
16 + x = 42
x = ________

Answer: 26

Explanation:
Given the equation 16 + x = 42
x + 16 = 42
x = 42 – 16
x = 26

Question 3.
y + 6.2 = 9.1
y = ________

Answer: 2.9

Explanation:
The given equation is
y + 6.2 = 9.1
y = 9.1 – 6.2
y = 2.9

Question 4.
m + \(\frac{3}{10}=\frac{7}{10}\)
m = \(\frac{□}{□}\)

Answer: \(\frac{4}{10}\)

Explanation:
The given equation is
m + \(\frac{3}{10}=\frac{7}{10}\)
m = \(\frac{7}{10}\) – \(\frac{3}{10}\)
The denominators are common so subtract the numerators
m = \(\frac{4}{10}\)

Question 5.
z – \(\frac{1}{3}=1 \frac{2}{3}\)
z = ________

Answer: 2

Explanation:
The given equation is
z – \(\frac{1}{3}=1 \frac{2}{3}\)
z = \(\frac{1}{3}\) + 1 \(\frac{2}{3}\)
z = 1 + \(\frac{1}{3}\) + \(\frac{2}{3}\)
z = 1 + \(\frac{3}{3}\)
z = 1 + 1 = 2
Thus the value of z is 2.

Question 6.
12 = x − 24
x = ________

Answer: 36

Explanation:
The given equation is
12 = x − 24
x – 24 = 12
x = 12 + 24
x = 36
Thus the value of x is 36.

Question 7.
25.3 = w − 14.9
w = ________

Answer: 40.2

Explanation:
The given equation is
25.3 = w − 14.9
w – 14.9 = 25.3
w = 25.3 + 14.9
w = 40.2
The value of w is 40.2

On Your Own

Practice: Copy and Solve Solve the equation, and check the solution.

Question 8.
y − \(\frac{3}{4}=\frac{1}{2}\)
y = _______ \(\frac{□}{□}\)

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

Explanation:
The given equation is
y − \(\frac{3}{4}=\frac{1}{2}\)
y = \(\frac{1}{2}\) + \(\frac{3}{4}\)
y = 1 \(\frac{1}{4}\)
Therefore the value of y is 1 \(\frac{1}{4}\).

Question 9.
75 = n + 12
n = ________

Answer: 63

Explanation:
The given equation is
75 = n + 12
n + 12 = 75
n = 75 – 12
n = 63
The value of n is 63.

Question 10.
m + 16.8 = 40
m = ________

Answer: 23.2

Explanation:
The given equation is
m + 16.8 = 40
m = 40 – 16.8
m = 23.2
The value of m is 23.2

Question 11.
w − 36 = 56
w = ________

Answer: 92

Explanation:
The given equation is
w − 36 = 56
w = 56 + 36
w = 92
The value of  is 92.

Question 12.
8 \(\frac{2}{5}\) = d + 2\(\frac{2}{5}\)
d = ________

Answer: 6

Explanation:
The given equation is
8 \(\frac{2}{5}\) = d + 2\(\frac{2}{5}\)
d + 2\(\frac{2}{5}\) = 8 \(\frac{2}{5}\)
d = 8 \(\frac{2}{5}\) – 2\(\frac{2}{5}\)
d = 8 + \(\frac{2}{5}\) – 2 – \(\frac{2}{5}\)
d = 8 – 2 = 6
Thus the value of d is 6.

Question 13.
8.7 = r − 1.4
r = ________

Answer: 10.1

Explanation:
The given equation is
8.7 = r − 1.4
r − 1.4 = 8.7
r = 8.7 + 1.4
r = 10.1
The value of r is 10.1

Question 14.
The temperature dropped 8 degrees between 6:00 p.m. and midnight. The temperature at midnight was 26ºF. Write and solve an equation to find the temperature at 6:00 p.m.
________ ºF

Answer: 34ºF

Explanation:
The temperature dropped 8 degrees between 6:00 p.m. and midnight.
The temperature at midnight was 26ºF.
26ºF + 8ºF = 34ºF
The equation to find the temperature at 6:00 p.m is 34ºF

Question 15.
Reason Abstractly Write an addition equation that has the solution x = 9.
Type below:
_____________

Answer: x + 4 = 13

Explanation:
Let the equation be x + 4 = 13
x = 13 – 4
x = 9

Unlock the Problem – Page No. 442

Question 16.
In July, Kimberly made two deposits into her bank account. She made no withdrawals. At the end of July, her account balance was $120.62. Write and solve an equation to find Kimberly’s balance at the beginning of July.

a. What do you need to find?
Type below:
_____________

Answer: We need to find Kimberly’s balance at the beginning of July.

Question 16.
b. What information do you need from the bank statement?
Type below:
_____________

Answer: We need the information about the deposit on July 12 and July 25 from the bank statement.

Question 16.
c. Write an equation you can use to solve the problem. Explain what the variable represents.
Type below:
_____________

Answer:
x = bank account balance
y = deposit 1
z = deposit 2
x = y + z

Question 16.
d. Solve the equation. Show your work and describe each step.
Type below:
_____________

Answer: 120.62 = y + z
Where y is the deposit 1 and z represents the deposit 2.
y = $45.50, z = $43.24
45.50 + 43.24 = 88.74
x + 88.74 = 120.62

Question 16.
e. Write Kimberly’s balance at the beginning of July.
$ _______

Answer: 31.88

Explanation:
x + 88.74 = 120.62
x = 120.62 – 88.74
x = $31.88
Kimberly’s balance at the beginning of July is $31.88

Question 17.
If x + 6 = 35, what is the value of x + 4? Explain how to find the value without solving the equation.
Type below:
_____________

Answer:
x + 6 = 35
x + 4 + 2 = 35
x  + 4 = 35 – 2
x + 4 = 33
Thus the value of x + 4 = 33

Question 18.
Select the equations that have the solution n = 23. Mark all that apply.
Options:
a. 16 + n = 39
b. n – 4 = 19
c. 25 = n – 2
d. 12 = n – 11

Answer: A, B, D

Explanation:
a. 16 + n = 39
n = 23
16 + 23 = 39
39 = 39
The variable is a solution.
b. n – 4 = 19
n = 23
23 – 4 = 19
19 = 19
The variable is a solution.
c. 25 = n – 2
25 = 23 – 2
25 ≠ 21
The variable is not a solution.
d. 12 = n – 11
n = 23
12 = 23 – 11
12 = 12
The variable is a solution.
Thus the correct answers are options A, B, D.

Solve Addition and Subtraction Equations – Page No. 443

Solve the equation, and check the solution.

Question 1.
y − 14 = 23
y = _______

Answer: 37

Explanation:
y − 14 = 23
y = 23 + 14
y = 37
Thus the solution is 37.

Question 2.
x + 3 = 15
x = _______

Answer: 12

Explanation:
The equation is x + 3 = 15
x = 15 – 3
x = 12
The solution is 12.

Question 3.
n + \(\frac{2}{5}=\frac{4}{5}\)
n = _______ \(\frac{□}{□}\)

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

Explanation:
The equation is n + \(\frac{2}{5}=\frac{4}{5}\)
n + \(\frac{2}{5}\) = \(\frac{4}{5}\)
n = \(\frac{4}{5}\) – \(\frac{2}{5}\)
n = (4 – 2)/5
n = \(\frac{2}{5}\)
Thus the solution is \(\frac{2}{5}\)

Question 4.
16 = m − 14
m = _______

Answer: 30

Explanation:
The equation is 16 = m − 14
m – 14 = 16
m = 16 + 14
m = 30
The solution is m = 30

Question 5.
w − 13.7 = 22.8
w = _______

Answer: 36.5

Explanation:
The equation is w − 13.7 = 22.8
w = 22.8 + 13.7
w = 36.5
The solution is w = 36.5

Question 6.
s + 55 = 55
s = _______

Answer: 0

Explanation:
The equation is s + 55 = 55
s = 55 – 55
s = 0
The solution is s = 0

Question 7.
23 = x − 12
x = _______

Answer: 35

Explanation:
The given equation is 23 = x – 12
x – 12 = 23
x = 23 + 12
x = 35
The solution is x = 35.

Question 8.
p − 14 = 14
p = _______

Answer: 28

Explanation:
The given equation is p − 14 = 14
p = 14 + 14
p = 28
The solution is p = 28.

Question 9.
m − \(2 \frac{3}{4}=6 \frac{1}{2}\)
m = _______ \(\frac{□}{□}\)

Answer: 9 \(\frac{1}{4}\)

Explanation:
The given equation is m − \(2 \frac{3}{4}=6 \frac{1}{2}\)
m – 2 \(\frac{3}{4}\) = 6 \(\frac{1}{2}\)
m = 6 \(\frac{1}{2}\) + 2 \(\frac{3}{4}\)
m = 6 + 2 + \(\frac{1}{2}\) + \(\frac{3}{4}\)
m = 8 + 1 \(\frac{1}{4}\)
m = 9 \(\frac{1}{4}\)

Problem Solving

Question 10.
A recipe calls for 5 \(\frac{1}{2}\) cups of flour. Lorenzo only has 3 \(\frac{3}{4}\) cups of flour. Write and solve an equation to find the additional amount of flour Lorenzo needs to make the recipe.
Type below:
_____________

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

Explanation:
A recipe calls for 5 \(\frac{1}{2}\) cups of flour.
Lorenzo only has 3 \(\frac{3}{4}\) cups of flour.
x + 3 \(\frac{3}{4}\) = 5 \(\frac{1}{2}\)
x = 5 \(\frac{1}{2}\) – 3 \(\frac{3}{4}\)
x =  1 \(\frac{3}{4}\)

Question 11.
Jan used 22.5 gallons of water in the shower. This amount is 7.5 gallons less than the amount she used for washing clothes. Write and solve an equation to find the amount of water Jan used to wash clothes.
Type below:
_____________

Answer: 30

Explanation:
Jan used 22.5 gallons of water in the shower.
This amount is 7.5 gallons less than the amount she used for washing clothes.
Let the amount of water Jan used to wash clothes be x
x – 7.5 = 22.5
x = 22.5 + 7.5
x = 30
Therefore the amount of water Jan used to wash clothes is 30 gallons.

Question 12.
Explain how to check if your solution to an equation is correct.
Type below:
_____________

Answer:
i. Evaluate the left-hand side expression at the given value to get a number.
ii. Evaluate the right-hand side expression at the given value to get a number.
iii. See if the numbers match.

Lesson Check – Page No. 444

Question 1.
The price tag on a shirt says $21.50. The final cost of the shirt, including sales tax, is $23.22. The equation 21.50 + t = 23.22 can be used to find the amount of sales tax t in dollars. What is the sales tax?
$ _______

Answer: 1.72

Explanation:
The price tag on a shirt says $21.50.
The final cost of the shirt, including sales tax, is $23.22.
The equation is 21.50 + t = 23.22
t = 23.22 – 21.50
t = 1.72
Therefore the sales tax is $1.72 dollars.

Question 2.
The equation l – 12.5 = 48.6 can be used to find the original length l in centimeters of a wire before it was cut. What was the original length of the wire?
_______ centimeters

Answer: 61.1 centimeters

Explanation:
The equation l – 12.5 = 48.6 can be used to find the original length l in centimeters of a wire before it was cut.
l – 12.5 = 48.6
l = 48.6 + 12.5
l = 61.1 centimeters
Thus the original length of the wire is 61.1 centimeters.

Spiral Review

Question 3.
How would you convert a mass in centigrams to a mass in milligrams?
Type below:
_____________

Answer: The conversion factor is 10; so 1 centigram = 10 milligrams. In other words, the value in cg multiplies by 10 to get a value in mg.

Question 4.
In the expression 4 + 3x + 5y, what is the coefficient of x?
The coefficient is _______

Answer:
A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
Thus the coefficient of 3x is 3.

Question 5.
Write an expression that is equivalent to 10c.
Type below:
_____________

Answer:
-2(-5c) expand the brackets
-2 × -5c
= 10c

Question 6.
Miranda bought a $7-movie ticket and popcorn for a total of $10. The equation 7 + x = 10 can be used to find the cost x in dollars of the popcorn. How much did the popcorn cost?
$ _______

Answer: 3

Explanation:
Miranda bought a $7-movie ticket and popcorn for a total of $10.
The equation is 7 + x = 10
x = 10 – 7
x = 3
Therefore the cost of the popcorn is $3.

Share and Show – Page No. 447

Model and solve the equation by using algebra tiles.

Question 1.
4x = 16
x = _______

Answer: 4

Explanation:

• Draw 2 rectangles on your Mathboard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model 4x in the left rectangle, and model 16 in the right rectangle.
• There are four x tiles on the left side of your model. To solve the equation by using the model, you need to find the value of one x tile.
• To do this, divide each side of your model into 4 equal groups.

Question 2.
3x = 12
x = _______

Answer: 4

Explanation:

• Draw 2 rectangles on your Mathboard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model 3x in the left rectangle, and model 12 in the right rectangle.
• There are three x tiles on the left side of your model. To solve the equation by using the model, you need to find the value of one x tile.
• To do this, divide each side of your model into 3 equal groups.

Question 3.
4 = 4x
x = _______

Answer: 1

Explanation:

• Draw 2 rectangles on your Mathboard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model 4x in the left rectangle, and model 4 in the right rectangle.
• There are four x tiles on the left side of your model. To solve the equation by using the model, you need to find the value of one x tile.
• To do this, divide each side of your model into 4 equal groups.

Question 4.
3x = 9
x = _______

Answer: 3

Explanation:

• Draw 2 rectangles on your Mathboard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model 3x in the left rectangle, and model 9 in the right rectangle.
• There are three x tiles on the left side of your model. To solve the equation by using the model, you need to find the value of one x tile.
• To do this, divide each side of your model into 3 equal groups.

Question 5.
2x = 10
x = _______

Answer: 5

Explanation:

• Draw 2 rectangles on your Mathboard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model 2x in the left rectangle, and model 10 in the right rectangle.
• There are two x tiles on the left side of your model. To solve the equation by using the model, you need to find the value of one x tile.
• To do this, divide each side of your model into two equal groups.

Question 6.
15 = 5x
x = _______

Answer: 3

Explanation:

• Draw 2 rectangles on your Mathboard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model 5x in the left rectangle, and model 15 in the right rectangle.
• There are five x tiles on the left side of your model. To solve the equation by using the model, you need to find the value of one x tile.
• To do this, divide each side of your model into five equal groups.

Solve the equation by drawing a model.

Question 7.
4x = 8
x = _______

Answer: 2

Question 8.
3x = 18
x = _______

Answer: 6

Problem Solving + Applications

Question 9.
Communicate Explain the steps you use to solve a multiplication equation with algebra tiles.
Type below:
_____________

Answer:
To solve an equation, model the terms of the equation on both sides of an equals sign.
Isolate the variable on one side by adding opposites and creating zero pairs.
To remove a factor from the variable, divide the sides into rows equal to the factor, and distribute the terms equally among all the rows.

Page No. 448

The bar graph shows the number of countries that competed in the first four modern Olympic Games. Use the bar graph for 10–11.

Question 10.
Naomi is doing a report about the 1900 and 1904 Olympic Games. Each page will contain info7rmation about 4 of the countries that competed each year. Write and solve an equation to find the number of pages Naomi will need.
_______ pages

Answer: 9 pages

Explanation:
By seeing the above table we can say that the equation is 4x = 36
The number of countries that competed in the 1900 summer Olympic games is 24.
The number of countries that competed in the 1904 summer Olympic games is 12.
The total number of countries competed in total is 36.
Each page of Naomi’s report contains information about 4 of the countries that competed each year.
4x = 36
x = 36/4
x = 9
Thus Naomi would require 9 pages to complete her report.

Question 11.
Pose a Problem Use the information in the bar graph to write and solve a problem involving a multiplication equation.
Type below:
_____________

Answer:
By seeing the above table we can say that the equation is 4x = 72
The number of countries that competed in the 1900 summer Olympic games is 24.
The number of countries that competed in the 1904 summer Olympic games is 12.
The number of countries that competed in the 1896 summer Olympic games is 14.
The number of countries that competed in the 1908 summer Olympic games is 22.
The total number of countries competed in total is 72.
4x = 72
x = 72/4
x = 18

Question 12.
The equation 7s = 21 can be used to find the number of snakes s in each cage at a zoo. Solve the equation. Then tell what the solution means.
s = _______

Answer: 3

Explanation:
The equation 7s = 21 can be used to find the number of snakes s in each cage at a zoo. Solve the equation.
7 × s = 21
s = 21/7 = 3
The solution s is 3.

Question 13.
A choir is made up of 6 vocal groups. Each group has an equal number of singers. There are 18 singers in the choir. Solve the equation 6p = 18 to find the number of singers in each group. Use a model.
_______ singers

Answer: 3 singers

Explanation:
A choir is made up of 6 vocal groups. Each group has an equal number of singers.
There are 18 singers in the choir.
The equation 6p = 18
p = 18/6 = 3
p = 3
The solution p is 3.

Model and Solve Multiplication Equations – Page No. 449

Model and solve the equation by using algebra tiles.

Question 1.
2x = 8
x = _______

Answer: 4

Explanation:

• Draw 2 rectangles on your Mathboard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model 2x in the left rectangle, and model 8 in the right rectangle.
• There are two x tiles on the left side of your model. To solve the equation by using the model, you need to find the value of one x tile.
• To do this, divide each side of your model into two equal groups.

Question 2.
5x = 10
x = _______

Answer: 2

Explanation:

• Draw 2 rectangles on your Mathboard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model 5x in the left rectangle, and model 10 in the right rectangle.
• There are five x tiles on the left side of your model. To solve the equation by using the model, you need to find the value of one x tile.
• To do this, divide each side of your model into five equal groups.

Question 3.
21 = 3x
x = _______

Answer: 7

Explanation:

• Draw 2 rectangles on your Mathboard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model 3x in the left rectangle, and model 21 in the right rectangle.
• There are three x tiles on the left side of your model. To solve the equation by using the model, you need to find the value of one x tile.
• To do this, divide each side of your model into three equal groups.

Solve the equation by drawing a model.

Question 4.
6 = 3x

Answer: 2

Question 5.
4x = 12
x = _______

Answer: 3

Problem Solving

Question 6.
A chef used 20 eggs to make 5 omelets. Model and solve the equation 5x = 20 to find the number of eggs x in each omelet.
_______ eggs

Answer: 4

Explanation:
A chef used 20 eggs to make 5 omelets.
The equation is 5x = 20
x = 50/5 = 4
Thus there are 4 eggs in each omelet.

Question 7.
Last month, Julio played 3 times as many video games as Scott did. Julio played 18 video games. Write and solve an equation to find the number of video games Scott played.
_______ video games

Answer: 6

Explanation:
Last month, Julio played 3 times as many video games as Scott did. Julio played 18 video games.
The equation will be 3x = 18
x = 18/3 = 6
x = 6
The number of video games Scott played is 6.

Question 8.
Write a multiplication equation, and explain how you can solve it by using a model.
Type below:
_____________

Answer:
15 = 5x
Explanation:

• Draw 2 rectangles on your Mathboard to represent the two sides of the equation.
• Use algebra tiles to model the equation. Model 5x in the left rectangle, and model 15 in the right rectangle.
• There are five x tiles on the left side of your model. To solve the equation by using the model, you need to find the value of one x tile.
• To do this, divide each side of your model into five equal groups.

Lesson Check – Page No. 450

Question 1.
What is the solution of the equation that is modeled by the algebra tiles?

x = 1 _______

Answer: 1

Explanation:
The equation for the above figure is 3x = 3
Substitute x = 1
3(1) = 3
3/3 = 1
Thus the solution is 1.

Question 2.
Carlos bought 5 tickets to a play for a total of $20. The equation 5c = 20 can be used to find the cost c in dollars of each ticket. How much does each ticket cost?
$ _______

Answer: 4

Explanation:
Carlos bought 5 tickets to a play for a total of $20.
The equation is 5c = 20
c = 20/5 = 4
c = 4
The cost of each ticket is $4.

Spiral Review

Question 3.
A rectangle is 12 feet wide and 96 inches long. What is the area of the rectangle?
_______ square feet

Answer: 1152

Explanation:
A rectangle is 12 feet wide and 96 inches long.
Area of rectangle is l × w
A = 12 × 96
A = 1152 square feet.
Thus the area of the rectangle is 1152 square feet.

Question 4.
Evaluate the algebraic expression 24 – x ÷ y for x = 8 and y = 2.
_______

Answer: 20

Explanation:
24 – x ÷ y for x = 8 and y = 2.
Substitute the value of x and y in the equation.
24 – (8 ÷ 2)
24 – 4 = 20

Question 5.
Ana bought a 15.5-pound turkey at the grocery store this month. The equation p – 15.5 = 2.5 can be used to find the weight p, in pounds, of the turkey she bought last month. What is the solution of the equation?
p = _______

Answer: 18

Explanation:
Ana bought a 15.5-pound turkey at the grocery store this month.
The equation is p – 15.5 = 2.5
p = 2.5 + 15.5
p = 18
The solution for the equation is 18.

Question 6.
A pet store usually keeps 12 birds per cage, and there are 7 birds in the cage now. The equation 7 + x = 12 can be used to find the remaining number of birds x that can be placed in the cage. What is the solution of the equation?
x = _______

Answer: 5

Explanation:
A pet store usually keeps 12 birds per cage, and there are 7 birds in the cage now.
The equation is 7 + x = 12
x = 12 – 7
x = 5
Thus the solution of the equation is 5.

Share and Show – Page No. 453

Question 1.
Solve the equation 2.5m = 10.
m = _______

Answer: 4

Explanation:
2.5m = 10
m = 10/2.5
m = 4

Solve the equation, and check the solution.

Question 2.
3x = 210
x = _______

Answer: 70

Explanation:
3x = 210
x = 210/3
x = 70

Question 3.
2.8 = 4t
t = _______

Answer: 0.7

Explanation:
2.8 = 4t
4t = 2.8
t = 2.8/4
t = 0.7

Question 4.
\(\frac{1}{3}\)n = 15
n = _______

Answer: 45

Explanation:
\(\frac{1}{3}\)n = 15
n = 15 × 3
n = 45

Question 5.
\(\frac{1}{2}\)y = \(\frac{1}{10}\)
y = _______

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

Explanation:
\(\frac{1}{2}\)y = \(\frac{1}{10}\)
y = \(\frac{1}{10}\) × 2
y = \(\frac{1}{5}\)

Question 6.
25 = \(\frac{a}{5}\)
a = _______

Answer: 125

Explanation:
25 = \(\frac{a}{5}\)
a = 25 × 5
a = 125

Question 7.
1.3 = \(\frac{c}{4}\)
c = _______

Answer: 5.2

Explanation:
1.3 = \(\frac{c}{4}\)
c = 1.3 × 4
c = 5.2

On Your Own

Practice: Copy and Solve Solve the equation, and check the solution.

Question 8.
150 = 6m
m = _______

Answer: 25

Explanation:
6m = 150
m = 150/6
m = 25

Question 9.
14.7 = \(\frac{b}{7}\)
b = _______

Answer: 102.9

Explanation:
14.7 = \(\frac{b}{7}\)
b = 14.7 × 7
b = 102.9

Question 10.
\(\frac{1}{4}\) = \(\frac{3}{5}\)s
s = \(\frac{□}{□}\)

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

Explanation:
\(\frac{1}{4}\) = \(\frac{3}{5}\)s
\(\frac{1}{4}\) × \(\frac{5}{3}\) = s
s = \(\frac{5}{12}\)

Question 11.
There are 100 calories in 8 fluid ounces of orange juice and 140 calories in 8 fluid ounces of pineapple juice. Tia mixed 4 fluid ounces of each juice. Write and solve an equation to find the number of calories in each fluid ounce of Tia’s juice mixture.
_______ calories

Answer: 15 calories

Explanation:
Number of calories in 8 ounces of orange juice = 100
Number of calories in 1 ounce of juice = 100/8
Number of calories in 4 ounces of juice 100/8 × 4 = 50 calories
Number of calories in 8 ounces of pineapple juice = 140
Number of calories in 1 ounce of juice = 140/8
Number of calories in 4 ounces of pineapple juice = 140/8 × 4 =70 calories
Now the mixture has 50 + 70 calories = 120 calories in 8 ounces
So, 1 ounce of the mixture has 120/8 = 15 calories.

Question 12.
Write a division equation that has the solution x = 16.
Type below:
_____________

Answer:
2x = 32
x = 32/2
x = 16
Thus the equation is x = 16.

Problem Solving + Applications – Page No. 454

What’s the Error?

Question 13.
Melinda has a block of clay that weighs 14.4 ounces. She divides the clay into 6 equal pieces. To find the weight w in ounces of each piece, Melinda solved the equation 6w = 14.4.
Look at how Melinda solved the equation. Find her error.
6w = 14.4
\(\frac{6 w}{6}\) = 6 × 14.4
w = 86.4
Correct the error. Solve the equation, and explain your steps.
Describe the error that Melinda made
Type below:
_____________

Answer:
Melinda has a block of clay that weighs 14.4 ounces. She divides the clay into 6 equal pieces.
The equation is 6w = 14.4
The error of Melinda is she used the multiplication equation to solve the equation.
She must have used the division equation to get the solution.
6w = 14.4
w = 14.4/6
w = 2.4

Question 14.
For numbers 14a−14d, choose Yes or No to indicate whether the equation has the solution x = 15.
14a. 15x = 30
14b. 4x = 60
14c. \(\frac{x}{5}\) = 3
14d. \(\frac{x}{3}\) = 5
14a. _____________
14b. _____________
14c. _____________
14d. _____________

Answer:
Given the value of x is 15
14a. 15x = 30
15 × 15 = 30
225 ≠ 30
The answer is No.
14b. 4x = 60
4 × 15 = 60
60 = 60
The answer is yes.
14c. \(\frac{x}{5}\) = 3
x/5 = 3
15/5 = 3
3 = 3
The answer is yes.
14d. \(\frac{x}{3}\) = 5
x/3 = 5
15/3 = 5
5 = 5
The answer is yes.

Solve Multiplication and Division Equations – Page No. 455

Solve the equation, and check the solution.

Question 1.
8p = 96
p = ________

Answer: 12

Explanation:
8p = 96
8 × p = 96
p = 96/8
p = 12
The solution is 12

Question 2.
\(\frac{z}{16}\) = 8
z = ________

Answer: 128

Explanation:
The given equation is
\(\frac{z}{16}\) = 8
z = 8 × 16
z = 128
The solution is 128.

Question 3.
3.5x = 14.7
x = ________

Answer: 4.2

Explanation:
The given equation is
3.5x = 14.7
x = 14.7/3.5
x = 4.2
The solution x is 4.2

Question 4.
32 = 3.2c
c = ________

Answer: 10

Explanation:
The given equation is
32 = 3.2c
3.2 × c = 32
c = 32/3.2
c = 1/0.1 = 10
The solution c is 10.

Question 5.
\(\frac{2}{5}\)w = 40
w = ________

Answer: 100

Explanation:
The given equation is
\(\frac{2}{5}\)w = 40
\(\frac{2}{5}\) × w = 40
w = 40 × 5/2
w = 200/2
w = 100

Question 6.
\(\frac{a}{14}\) = 6.8
a = ________

Answer: 95.2

Explanation:
The given equation is
\(\frac{a}{14}\) = 6.8
a = 6.8 × 14
a = 95.2

Question 7.
1.6x = 1.6
x = ________

Answer: 1

Explanation:
The given equation is
1.6x = 1.6
x = 1.6/1.6
x = 1
The solution x is 1

Question 8.
23.8 = 3.5b
b = ________

Answer: 6.8

Explanation:
The given equation is
23.8 = 3.5b
3.5b = 23.8
b = 23.8/3.5
b = 6.8
Thus the solution of the variable b is 6.8

Question 9.
\(\frac{3}{5}\) = \(\frac{2}{3}\)t
t = \(\frac{□}{□}\)

Answer: \(\frac{9}{10}\)

Explanation:
The given equation is
\(\frac{3}{5}\) = \(\frac{2}{3}\)t
t = \(\frac{3}{5}\) × \(\frac{3}{2}\)
t = \(\frac{9}{10}\)
Thus the solution of the variable t is \(\frac{9}{10}\)

Problem Solving

Question 10.
Anne runs 6 laps on a track. She runs a total of 1 mile, or 5,280 feet. Write and solve an equation to find the distance, in feet, that she runs in each lap.
________ feet

Answer: 880

Explanation:
Anne runs 6 laps on a track. She runs a total of 1 mile, or 5,280 feet.
Let the l represents the runs in each lap.
6 × l = 5280 feet
l = 5280/6
l = 880 feet
Therefore Anne runs 880 feets in each lap.

Question 11.
In a serving of 8 fluid ounces of pomegranate juice, there are 32.8 grams of carbohydrates. Write and solve an equation to find the amount of carbohydrates in each fluid ounce of the juice.
________ grams

Answer: 4.1

Explanation:
Given, In a serving of 8 fluid ounces of pomegranate juice, there are 32.8 grams of carbohydrates.
Let c represents the amount of carbohydrates in each fluid ounce of the juice
8 × c = 32.8 grams
c = 32.8/8
c = 4.1 grams

Question 12.
Write and solve a word problem that can be solved by solving a multiplication equation.
Type below:
_____________

Answer:
The quotient of 6 and p is 12
6 ÷ p = 12
p = 6/12
p = 1/2

Lesson Check – Page No. 456

Question 1.
Estella buys 1.8 pounds of walnuts for a total of $5.04. She solves the equation 1.8p = 5.04 to find the price p in dollars of one pound of walnuts. What does one pound of walnuts cost?
$ ________

Answer: 2.8

Explanation:
Given that, Estella buys 1.8 pounds of walnuts for a total of $5.04.
p represents the price in dollars of one pound of walnuts.
The equation to find one pound of walnuts cost is 1.8p = 5.04
1.8p = 5.04
p = 5.04/1.8
p = 2.8
Therefore the cost of one pound of walnuts is $2.8

Question 2.
Gabriel wants to solve the equation \(\frac{5}{8}\)m = 25. What step should he do to get m by itself on one side of the equation?
Type below:
_____________

Answer: 40

Explanation:
Gabriel wants to solve the equation \(\frac{5}{8}\)m = 25.
\(\frac{5}{8}\)m = 25
5m = 25 × 8
5 × m = 200
m = 200/5 = 40
Thus m = 40

Spiral Review

Question 3.
At top speed, a coyote can run at a speed of 44 miles per hour. If a coyote could maintain its top speed, how far could it run in 15 minutes?
________ miles

Answer: 11

Explanation:
At top speed, a coyote can run at a speed of 44 miles per hour.
Convert from minutes to hour.
60 minutes = 1 hour
15 minutes = 15 × 1/60 = 0.25 = 1/4
44 × 1/4 = 11 miles
A coyote can run at a speed of 11 miles for 15 minutes.

Question 4.
An online store sells DVDs for $10 each. The shipping charge for an entire order is $5.50. Frank orders d DVDs. Write an expression that represents the total cost of Frank’s DVDs.
Type below:
_____________

Answer: 10d + $5.50

Explanation:
An online store sells DVDs for $10 each.
The shipping charge for an entire order is $5.50. Frank orders d DVDs.
The expression will be the product of 10 and d more than 5.50
The expression is 10d + $5.50

Question 5.
A ring costs $27 more than a pair of earrings. The ring costs $90. Write an equation that can be used to find the cost c in dollars of the earrings.
Type below:
_____________

Answer: $90 – $27 = c

Explanation:
A ring costs $27 more than a pair of earrings.
The ring costs $90.
c represents the cost in dollars of the earrings.
Thus the equation is c + $27 = $90
c = $90 – $27.

Question 6.
The equation 3s = 21 can be used to find the number of students s in each van on a field trip. How many students are in each van?
________ students

Answer: 7 students

Explanation:
The equation 3s = 21 can be used to find the number of students s in each van on a field trip.
3s = 21
s = 21/3 = 7
s = 7
Thus there are 7 students in each van.

Share and Show – Page No. 459

Question 1.
Connor ran 3 kilometers in a relay race. His distance represents \(\frac{3}{10}\) of the total distance of the race. The equation \(\frac{3}{10}\)d = 3 can be used to find the total distance d of the race in kilometers. What was the total distance of the race?
________ kilometers

Answer: 10

Explanation:
Connor ran 3 kilometers in a relay race.
His distance represents \(\frac{3}{10}\) of the total distance of the race.
\(\frac{3}{10}\)d = 3
3 × d = 3 × 10
3 × d = 30
d = 30/3 = 10 kilometers
Therefore the total distance of the race is 10 kilometers.