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Go Math Grade 4 Chapter 11 Answer Key Pdf: Students who are looking for quick learning with basic fundamentals can Download Go Math Grade 4 Answer Key Chapter 11 Angles pdf for free. There are different types of questions with detailed and simple explanations here. So, the students of Grade 4 can make HMH Go Math Answer Key as a reference while practicing the problems. There is a scope to learn simple techniques to solve the problems. Go Math Grade 4 Answer Key helps the parents to explain the concepts in an easy manner to their children.

Angles Go Math Grade 4 Chapter 11 Answer Key Pdf

We have provided the solutions for not only the exercised but also for the mid-chapter checkpoint and review tests. So, the students can check the solutions after practicing from Go Math Grade Chapter 11 Answer Key. Check out the topics given below before starting your preparation. Get step by step procedure for each and every problem with suitable examples in our Go Math Answer Key for Grade 4 Chapter 11 Angles. Hence make use of the links and start practicing now.

Lesson 1:

• Investigate • Angles and Fractional Parts of a Circle Page No. 605
• Investigate • Angles and Fractional Parts of a Circle Lesson Check Page No. 606

Lesson 2:

• Degrees Page No. 609
• Degrees Lesson Check Page No. 610

Lesson 3: Measure and Draw Angles

• Common Core – New Measure and Draw Angles Page No. 611
• Common Core – New Measure and Draw Angles Lesson Check Page No. 612
• Measure and Draw Angles Page No. 615
• Measure and Draw Angles Page No. 616
• Measure and Draw Angles Page No. 617
• Measure and Draw Angles Lesson Check Page No. 618

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint Page No. 619
• Mid-Chapter Checkpoint Lesson Check Page No. 620

Lesson 4:

• Investigate • Join and Separate Angles Page No. 623
• Investigate • Join and Separate Angles Lesson Check Page No. 624

Common Core – New

• Common Core – New – Page No. 625
• Common Core – New Lesson Check – Page No. 626

Lesson 5:

• Problem Solving • Unknown Angle Measures Page No. 629
• Problem Solving • Unknown Angle Measures Page No. 630

Common Core – New

• Problem Solving Unknown Angle Measures Common Core – New – Page No. 631
• Problem Solving Unknown Angle Measures Common Core – New Lesson Check – Page No. 632

Chapter 11 Review/Test

• Review/Test Page No. 633
• Review/Test Page No. 634
• Review/Test Page No. 635
• Review/Test Page No. 636
• Review/Test Page No. 637
• Review/Test Page No. 638
• Review/Test Page No. 643
• Review/Test Page No. 644

Common Core – New – Page No. 605

Angles and Fractional Parts of a Circle

Tell what fraction of the circle the shaded angle represents.

Question 1.

The figure shows that the \(\frac{1}{4}\)th part of the circle is shaded. So, the fraction of the shaded angle is \(\frac{1}{4}\)

Question 2.

\(\frac{□}{□}\)

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

Explanation:

Half of the circle is shaded. Thus the fraction of the shaded angle is \(\frac{1}{2}\)

Question 3.

\(\frac{□}{□}\)

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

Explanation:

From the above figure, we can observe that the complete circle is shaded. So, the fraction of the shaded angle is \(\frac{1}{1}\) or 1.

Tell whether the angle on the circle shows a \(\frac{1}{4}, \frac{1}{2}, \frac{3}{4}\), or 1 full turn clockwise or counterclockwise.

Question 4.

\(\frac{□}{□}\)

Answer: \(\frac{1}{2}\) turn counter-clockwise

Explanation:

From the figure, we can see that the circle is rotating in the anti-clockwise direction. And it has completed the half-turn.
Thus the fraction is \(\frac{1}{2}\) turn counter-clockwise

Go Math Grade 4 Chapter 11 Answer Key Pdf Question 5.

\(\frac{□}{□}\)

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

Explanation:

The arrow is turned in a clockwise direction. It has completed \(\frac{3}{4}\) turn. So, the angle with direction is \(\frac{3}{4}\) turn clockwise.

Question 6.

_________

Answer: 1 full turn counter clockwise

Explanation:

From the above picture, we can observe that the circle has completed the full turn in the counter clockwise direction.

Problem Solving

Question 7.
Shelley exercised for 15 minutes. Describe the turn the minute hand made.

Type below:
_________

Answer: The minute hand made a turn of \(\frac{1}{4}\) clockwise.

Explanation:

Given that,

Shelley exercised for 15 minutes.
So, the fraction of the minute hand made is \(\frac{1}{4}\).
The direction of the minute hand made is clockwise.
So, the answer is the minute hand made a turn of \(\frac{1}{4}\) clockwise.

Question 8.
Mark took 30 minutes to finish lunch. Describe the turn the minute hand made.

Type below:
_________

Answer: The minute hand made a turn of \(\frac{1}{2}\) clockwise.

Explanation:

Given, Mark took 30 minutes to finish lunch.
The minute hand made a turn in the clockwise direction from 12 to 6.
That means the fraction of the angle is \(\frac{1}{2}\).
Thus the turn minute hand made is \(\frac{1}{2}\) clockwise.

Common Core – New – Page No. 606

Lesson Check

Question 1.
What fraction of the circle does the shaded angle represent

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

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

Explanation:

From the figure we can say that the fraction of the shaded angle is \(\frac{1}{4}\).
Thus the answer is option D.

Question 2.
Which describes the turn shown below?

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

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

Explanation:

From the figure, we can see that the circle is rotating in the clockwise direction. And it has completed the half turn.
So, the answer is \(\frac{1}{2}\) turn clockwise.

Spiral Review

Question 3.
Which shows \(\frac{2}{3}\) and \(\frac{3}{4}\) written as a pair of fractions with a common denominator?
Options:
a. \(\frac{2}{3} \text { and } \frac{4}{3}\)
b. \(\frac{6}{9} \text { and } \frac{6}{8}\)
c. \(\frac{2}{12} \text { and } \frac{3}{12}\)
d. \(\frac{8}{12} \text { and } \frac{9}{12}\)

Answer: \(\frac{8}{12} \text { and } \frac{9}{12}\)

Explanation:

\(\frac{2}{3}\) and \(\frac{3}{4}\)
The denomintors are different here. So you have to make the denominators common.
\(\frac{2}{3}\) × \(\frac{4}{4}\) = \(\frac{8}{12}\)
\(\frac{3}{4}\) × \(\frac{3}{3}\) = \(\frac{9}{12}\)
So the answer is option D.

Question 4.
Raymond bought \(\frac{3}{4}\) of a dozen rolls. How many rolls did he buy?
Options:
a. 3
b. 6
c. 7
d. 9

Answer: 9

Explanation:

Raymond bought \(\frac{3}{4}\) of a dozen rolls.
Dozen = 12
\(\frac{3}{4}\) × 12 = 9
Thus the correct answer is option D.

Question 5.
Which of the following lists all the factors of 18?
Options:
a. 1, 2, 4, 9, 18
b. 1, 2, 3, 6, 9, 18
c. 2, 3, 6, 9
d. 1, 3, 5, 9, 18

Answer: 1, 2, 3, 6, 9, 18

Explanation:

The factors of 18 are
1 × 18 = 18
2 × 9 = 18
3 × 6 = 18
6 × 3 = 18
9 × 2 = 18
18 × 1 = 18
Thus the correct answer is option B.

Question 6.
Jonathan rode 1.05 miles on Friday, 1.5 miles on Saturday, 1.25 miles on Monday, and 1.1 miles on Tuesday. On which day did he ride the shortest distance?
Options:
a. Monday
b. Tuesday
c. Friday
d. Saturday

Answer: Friday

Explanation:

Jonathan rode 1.05 miles on Friday, 1.5 miles on Saturday, 1.25 miles on Monday, and 1.1 miles on Tuesday.
The shortest among all is 1.05 miles.
Therefore the answer is option C.

Page No. 609

Question 1.
Find the measure of the angle.

Through what fraction of a circle does the angle turn?
\(\frac{1}{3}=\frac{■}{360}\)
Think: 3 × 12 = 36, so 3 × _____ = 360.
So, the measure of the angle is _____.
_____ degrees

Answer: 120°

Explanation:

The fraction of the shaded angle is \(\frac{1}{3}\)
To measure the angle we have to multiply the fraction of the shaded angle with the total angle.
That means, \(\frac{1}{3}\) × 360
360/3 = 120 degrees.
Thus the angle of the shaded part is 120°

Tell the measure of the angle in degrees.

Question 2.

____ °

Answer: 45°

Explanation:

The fraction of the shaded angle is \(\frac{45}{360}\)
Multiply the fraction with the complete angle
\(\frac{45}{360}\) × 360° = 45°
Thus the angle of the above figure is 45°

Question 3.

____ degrees

Answer: 30°

Explanation:

The figure shows the fraction of the shaded angle is \(\frac{1}{12}\)
Multiply the fraction with the complete angle
\(\frac{1}{12}\) × 360° = 30°
Therefore the measure of the shaded angle is 30°

Tell the measure of the angle in degrees.

Question 4.

____ °

Answer: 360°

Explanation:

We observe that the circle is shaded completely.
\(\frac{360}{360}\) × 360° = 360°
Thus the above figure is the complete angle.

Go Math Grade 4 Topic 11 Lesson 11.2 Question 5.

____ °

Answer: 36°

Explanation:

The fraction of the shaded angle is \(\frac{1}{10}\)
Multiply the fraction with the complete angle
\(\frac{1}{10}\) × 360° = 36°
Therefore the measure of the shaded angle is 36°

Classify the angle. Write acute, obtuse, right, or straight.

Question 6.

_________

Answer: Obtuse

An obtuse angle has a measurement greater than 90 degrees but less than 180 degrees. However, A reflex angle measures more than 180 degrees but less than 360 degrees.

Question 7.

_________

Answer: Right

A right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles.

Question 8.

_________

Answer: Acute

The acute angle is the small angle which is less than 90°.

Question 9.

_________

Answer: Straight

A straight angle is 180 degrees. A straight angle changes the direction to point the opposite way.

Question 10.
Is this an obtuse angle? Explain.

Type below:
_________

Answer: Obtuse

An obtuse angle has a measurement greater than 90 degrees but less than 180 degrees. However, A reflex angle measures more than 180 degrees but less than 360 degrees.

Question 11.
Alex cut a circular pizza into 8 equal slices. He removed 2 of the slices of pizza. What is the measure of the angle made by the missing slices of pizza?

____ °

Answer: 90°

Explanation:

Alex cut a circular pizza into 8 equal slices.
He removed 2 of the slices of pizza.
The fraction of the missing slices = \(\frac{2}{8}\) = \(\frac{1}{4}\)
The fraction of the missing slices is \(\frac{1}{4}\)
To know the angle we have to multiply the fraction with complete angle i.e., 360°
\(\frac{1}{4}\) × 360° = 90°
Thus the angle of the missing slices is 90°

Page No. 610

Question 12.
Ava started reading at 3:30 p.m. She stopped for a snack at 4:15 p.m. During this time, through what fraction of a circle did the minute hand turn? How many degrees did the minute hand turn?

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

Answer: I am asked to find the fraction of a circle did the minute hand turn and how many degrees did the minute hand turn

Question 12.
b. What information can you use to find the fraction of a circle through which the minute hand turned?
Type below:
_________

Answer: The fraction of a circle through which the minute hand-turned \(\frac{3}{4}\) Clockwise.

Question 12.
c. How can you use the fraction of a circle through which the minute hand turned to find how many degrees it turned?
Type below:
_________

Answer:

The figure shows that the fraction of a circle through which the minute hand turned is \(\frac{3}{4}\) Clockwise.
Let the shaded part be x
And the nonshaded part is 90°
x + 90° = 360°
x = 360°- 90°
x = 270°
Therefore the minute hand turns 270° clockwise.

Question 12.
d. Show the steps to solve the problem.
Step 1:
\(\frac{3 × ■}{4 × ■}=\frac{?}{360}\)
Step 2:
\(\frac{3 × 90}{4 × 90}=\frac{■}{360}\)
Type below:
_________

Answer:
\(\frac{3 × 90}{4 × 90}=\frac{■}{360}\)
\(\frac{270}{360} = \frac{■}{360}\)
If the denominators are equal then the numerators must be equated.
■ = 270

Question 12.
e. Complete the sentences. From 3:30 p.m. to 4:15 p.m., the minute hand made a ______ turn clockwise. The minute hand turned ______ degrees.
Type below:
_________

Answer:
From 3:30 p.m. to 4:15 p.m., the minute hand made a \(\frac{3}{4}\) turn clockwise. The minute hand turned 270 degrees.

Angles Grade 4 Pdf Chapter 11 Answer Key Question 13.
An angle represents \(\frac{1}{15}\) of a circle. Select the number to show how to find the measure of the angle in degrees.


\(\frac{1}{15}=\frac{1 × □}{15 × □}=\frac{□}{360}\)
Type below:
_________

Answer: 24°
\(\frac{1}{15} × 360° = 24°

Common Core – New – Page No. 611

Degrees

Tell the measure of the angle in degrees.

Question 1.

Answer: 60°

Explanation:

Given that the fraction of the shaded angle is [latex]\frac{60}{360}\)
\(\frac{60}{360}\) × 360 = 60°
Thus the angle for the above figure is 60°

Question 2.

____ °

Answer: 180°

Explanation:

Half of the circle is shaded. The fraction of the shaded angle is \(\frac{1}{2}\)
\(\frac{1}{2}\) × 360 = 360/2 = 180°

Question 3.

____ °

Answer: 90°

Explanation:

The fraction of the shaded angle is \(\frac{1}{4}\)
To find the angle we need to multiply the fraction with the total angle.
\(\frac{1}{4}\) × 360° = 90°

Classify the angle. Write acute, obtuse, right, or straight.

Question 4.

_________

Answer: Acute

Explanation:

25° < 90°
So, the above figure is an acute angle.

Question 5.

_________

Answer: Obtuse

Explanation:

110° > 90°
So, the figure shown above is an obtuse angle.

Question 6.

_________

Answer: Acute

Explanation:

60° < 90°
Acute angles measure less than 90 degrees. Thus the above angle is an acute angle.

Classify the triangle. Write acute, obtuse, or right.

Question 7.

_________

Answer: Right

Explanation:

65 + 25 = 90
The sum of two angles = 90°
Thus the above figure is a right-angled triangle.

Question 8.

_________

Answer: Obtuse

Explanation:

110° > 90°
So, the above triangle is an obtuse angle.

Question 9.

_________

Answer: Acute

Explanation:

50° is less than 90°
Thus the above triangle is an acute angle triangle.

Problem Solving

Ann started reading at 4:00 P.M. and finished at 4:20 P.M.

Question 10.
Through what fraction of a circle did the minute hand turn?
\(\frac{□}{□}\)

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

Explanation:

The fraction of the shaded clock is \(\frac{12}{4}\)
\(\frac{12}{4}\) = \(\frac{1}{3}\)
The minute hand turn clockwise direction.
So, the answer is \(\frac{1}{3}\) turn clockwise

Question 11.
How many degrees did the minute hand turn?
____ °

Answer: 120°

Explanation:

The fraction of the minute hand turn is \(\frac{1}{3}\)
\(\frac{1}{3}\) × 360° = 120°
The minute hand turn 120°

Common Core – New – Page No. 612

Lesson Check

Question 1.
What kind of angle is shown?

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

Answer: straight

A straight angle is 180 degrees. This is a straight angle. A straight angle changes the direction to point the opposite way.
So, the answer is option D.

Question 2.
How many degrees are in an angle that turns through \(\frac{1}{4}\) of a circle?
Options:
a. 45°
b. 90°
c. 180°
d. 270°

Answer: 90°

Explanation:

\(\frac{1}{4}\) × 360°
\(\frac{360}{4}\) = 90°
Thus the correct answer is option B.

Spiral Review

Question 3.
Mae bought 15 football cards and 18 baseball cards. She separated them into 3 equal groups. How many sports cards are in each group?
Options:
a. 5
b. 6
c. 11
d. 12

Answer: 11

Explanation:

Mae bought 15 football cards and 18 baseball cards.
She separated them into 3 equal groups.
Total number of cards = 15 + 18 = 33
33/3 = 11
There are 11 sports cards in each group.

Question 4.
Each part of a race is \(\frac{1}{10}\) mile long. Marsha finished 5 parts of the race. How far did Marsha race?
Options:
a. \(\frac{1}{10}\) mile
b. \(\frac{5}{12}\) mile
c. \(\frac{1}{2}\) mile
d. 5 \(\frac{1}{10}\) miles

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

Explanation:

Each part of a race is \(\frac{1}{10}\) mile long.
Marsha finished 5 parts of the race.
\(\frac{1}{10}\) × 5 = 5/10 = \(\frac{1}{2}\) mile
Thus the correct answer is option C.

Question 5.
Jeff said his city got \(\frac{11}{3}\) inches of snow. Which shows this fraction written as a mixed number?
Options:
a. 3 \(\frac{2}{3}\)
b. 3 \(\frac{1}{3}\)
c. 2 \(\frac{2}{3}\)
d. 1 \(\frac{2}{3}\)

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

Explanation:

Jeff said his city got \(\frac{11}{3}\) inches of snow.
The mixed fraction of \(\frac{11}{3}\) is 3 \(\frac{2}{3}\)
The correct answer is option A.

Go Math Grade 4 Chapter 11 Answer Key Question 6.
Amy ran \(\frac{3}{4}\) mile. Which decimal shows how many miles she ran?
Options:
a. 0.25 mile
b. 0.34 mile
c. 0.5 mile
d. 0.75 mile

Answer: 0.75 mile

Explanation:

Amy ran \(\frac{3}{4}\) mile.
\(\frac{3}{4}\) = \(\frac{75}{100}\)
The decimal form of \(\frac{75}{100}\) is 0.75
So, the answer is option D.

Page No. 615

Question 1.
Measure ∠ABC.

Place the center of the protractor on point ____.
Align ray BC with ____ .
Read where ____ intersects the same scale.
So, m∠ABC is _____.
Type below:
_________

Answer: 65°

Use a protractor to find the angle measure.

Question 2.

m∠ONM = ____ °

Answer: 55°

Question 3.

m∠TSR = ____ °

Answer: 105°

Use a protractor to draw the angle.

Question 4.
170°
Type below:
_________

Answer:

Question 5.
78°
Type below:
_________

Answer:

Use a protractor to find the angle measure.

Question 6.

m∠QRS = ____ °

Answer: 90°

Question 7.

m∠XYZ = ____ °

Answer: 155°

Use a protractor to draw the angle.

Question 8.
115°
Type below:
_________

Answer:

Question 9.
67°
Type below:
_________

Answer:

Draw an example of each. Label the angle with its measure.

Question 10.
an acute angle
Type below:
_________

Answer:

Question 11.
an obtuse angle
Type below:
_________

Answer:

Question 12.
Elizabeth is making a quilt with scraps of fabric. What is the difference between m∠ABC and m∠DEF?

____ °

Answer: 15°

Go Math Grade 4 Chapter 11 Pdf Question 13.
Draw an angle with a measure of 0°.
Describe your drawing.
Type below:
_________

Answer:

Page No. 616

Question 14.
Hadley wants to divide this angle into three angles with equal measure. What will the measure of each angle be?

____ °

Answer: 30°

Explanation:

Given,
Hadley wants to divide this angle into three angles with equal measure.
The above figure is a right angle = 90°
If he divides into three equal angles
90/3 = 30°
So, the measure of angle will be 30°

Question 15.
Tracy measured an angle as 50° that was actually 130°. Explain her error.
Type below:
_________

Answer: She has measured the angle in the counterclockwise direction. So, that is why she got 50°.

Question 16.
Choose the word or number to complete a true statement about ∠QRS.

∠QRS is a(n) angle that has a measure of
Type below:
_________

Answer: ∠QRS is an obtuse angle that has a measure of 135°.

Earth’s Axis Earth revolves around the sun yearly. The Northern Hemisphere is the half of Earth that is north of the equator. The seasons of the year are due to the tilt of Earth’s axis.

Use the diagrams and a protractor for 17–18.

Question 17.
In the Northern Hemisphere, Earth’s axis is tilted away from the sun on the first day of winter, which is often on December 21. What is the measure of the marked angle on the first day of winter, the shortest day of the year?
____ °

Answer: 115°

Explanation:

By seeing the above figure we can say that the angle is an obtuse angle. The mark is above 90° and the marked angle is 115°.
Therefore the measure of the marked angle on the first day of winter, the shortest day of the year is 115°.

Question 18.
Earth’s axis is not tilted away from or toward the sun on the first days of spring and fall, which are often on March 20 and September 22. What is the measure of the marked angle on the first day of spring or fall?
____ °

Answer: 90°

Explanation:

The mark is exactly 90°. So, the angle on the first day of spring or fall is 90°

Common Core – New – Page No. 617

Measure and Draw Angles

Use a protractor to find the angle measure.

Question 1.

m∠ABC = 120°

By using the protractor we can measure the angle m∠ABC i.e., 120°

Question 2.

m∠MNP = ____ °

Answer: m∠MNP = 90°

By observing the above figure we can say that the angle of m∠MNP is 90°

Question 3.

m∠RST = ____ °

Answer: m∠RST = 65°
By using the protractor we can measure m∠RST = 65°

Use a protractor to draw the angle.

Question 4.
40°

Answer:

Question 5.
170°

Answer:

Draw an example of each. Label the angle with its measure.

Question 6.
a right angle

Answer:

A right angle is an angle of exactly 90°

Question 7.
an acute angle

Answer:

The acute angle is the small angle which is less than 90°.

Problem Solving

The drawing shows the angles a stair tread makes with a support board along a wall. Use your protractor to measure the angles.

Question 8.
What is the measure of ∠A?
____ °

Answer: 45°

By using the protractor we can measure the angle for A = 45°

Question 9.
What is the measure of ∠B?
____ °

Answer: 135°

The same process is used to measure ∠B = 135°

Common Core – New – Page No. 618

Lesson Check

Question 1.
What is the measure of ∠ABC?

Options:
a. 15°
b. 25°
c. 155°
d. 165°

Answer: 15°

Explanation:

Step 1: Place the center point of the protractor on the point B.
Step 2: Align the 0° mark on the scale of the protractor with ray BC.
Step 3: Find the point where AC meets. Read the angle measure on that scale.
So, the measure of ∠ABC is 15°
Thus the correct answer is option A.

Question 2.
What is the measure of ∠XYZ?

Options:
a. 20°
b. 30°
c. 150°
d. 160°

Answer: 150°

Explanation:

Step 1: Place the center point of the protractor on the point Y.
Step 2: Align the 0° mark on the scale of the protractor with ray XY.
Step 3: Find the point where YZ meet. Read the angle measure on that scale.
So, ∠XYZ = 150°
Therefore the correct answer is option C.

Spiral Review

Question 3.
Derrick earned $1,472 during the 4 weeks he had his summer job. If he earned the same amount each week, how much did he earn each week?
Options:
a. $360
b. $368
c. $3,680
d. $5,888

Answer: $368

Explanation:

Given that, Derrick earned $1,472 during the 4 weeks he had his summer job.
Let the amount he earned per week = x
x × 4 = $1,472
x = 1472 ÷ 4
x = 1472/4 = 368
So, Derrick earned $368 per week.

Go Math Workbook Grade 4 Chapter 11 Review/Test Answer Key Question 4.
Arthur baked 1 \(\frac{7}{12}\) dozen muffins. Nina baked 1 \(\frac{1}{12}\) dozen muffins. How many dozen muffins did they bake in all?
Options:
a. 3 \(\frac{2}{3}\)
b. 2 \(\frac{2}{3}\)
c. 2 \(\frac{1}{2}\)
d. \(\frac{6}{12}\)

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

Explanation:

Given:
Arthur baked 1 \(\frac{7}{12}\) dozen muffins. Nina baked 1 \(\frac{1}{12}\) dozen muffins.
Add both the fractions
Convert mixed fraction into normal fractions
1 \(\frac{7}{12}\) = \(\frac{19}{12}\)
1 \(\frac{1}{12}\) = \(\frac{13}{12}\)
\(\frac{19}{12}\) + \(\frac{13}{12}\) = \(\frac{32}{12}\)
= \(\frac{8}{3}\)
Convert \(\frac{8}{3}\) into mixed fraction = 2 \(\frac{2}{3}\)
So, the answer is option B.

Question 5.
Trisha drew the figure below. What figure did she draw?

Options:
a. line segment ST
b. ray ST
c. ray TS
d. line TS

Answer: ray TS

A ray can be defined as a part of a line that has a fixed starting point but no endpoint.
Here the point starts from T and ends at S.
So, the figure Trisha drew is ray TS.
The correct answer is option C.

Question 6.
Which describes the turn shown by the angle?

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

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

Explanation:

The figure shows that the point turned \(\frac{1}{4}\) in a clockwise direction.
So, the answer is option D.

Page No. 619

Choose the best term from the box.

Question 1.
The unit used to measure an angle is called a ________.
________

Answer: The unit used to measure an angle is called a degree.

Question 2.
________ is the opposite of the direction in which the hands of a clock move.
________

Answer: Counterclockwise is the opposite of the direction in which the hands of a clock move.

Question 3.
A ________ is a tool for measuring the size of an angle.
________

Answer: A protractor is a tool for measuring the size of an angle.

Tell whether the angle on the circle shows a \(\frac{1}{4}, \frac{1}{2}, \frac{3}{4}\), or 1 full turn clockwise or counterclockwise.

Question 4.

\(\frac{□}{□}\)

Answer: \(\frac{1}{4}\) turn clockwise
The figure shows that the angle turn \(\frac{1}{4}\) in the clockwise direction.

Question 5.

\(\frac{□}{□}\)

Answer: \(\frac{1}{2}\) turn counterclockwise
From the above figure, we can see that the angle turn \(\frac{1}{2}\) in the counterclockwise direction.

Question 6.

\(\frac{□}{□}\)

Answer: \(\frac{3}{4}\) turn clockwise
The figure shows that the angle turn \(\frac{3}{4}\) in the clockwise direction.

Question 7.

____

Answer: \(\frac{1}{1}\) or 1 turn counterclockwise
From the above figure, we can see that the angle turn \(\frac{1}{1}\) or 1 in the counterclockwise direction.

Tell the measure of the angle in degrees.

Question 8.

____ °

Answer: 100°

\(\frac{100}{360}\) × 360° = 100°

Question 9.
____ °

Use a protractor to draw the angle.

Question 10.
75°
Type below:
________

Question 11.
127°
Type below:
________

Page No. 620

Question 12.
Phillip watched a beach volleyball game from 1:45 p.m. to 2:00 p.m. How many degrees did the minute hand turn?

____ °

Answer: 90°

Explanation:

Phillip watched a beach volleyball game from 1:45 p.m. to 2:00 p.m.
The minute hand turned for 15 minutes.
That means \(\frac{1}{4}\) turn clockwise.
Complete angle = 360°
\(\frac{1}{4}\) × 360° = 360°/4 = 90°
Therefore the minute hand turn 90°

Question 13.
What angle does this piece of pie form?

____ °

Answer: 180°

From the above figure, we can see that half of the pie is completed.
Complete angle = 360°
\(\frac{1}{2}\) × 360°
= 180°
The angle for the piece of pie form is 180°

Question 14.
What is m∠CBT? Use a protractor to help you.

____ °

Answer: 60°

By using the protractor we can say that the angle for the above figure is 60°

Question 15.
Matt cut a circle into 8 equal sections. He drew an angle that measures the same as the total measure of 3 of the sections in the circle. What is the measure of the angle Matt drew?
____ °

Answer: 135°

Explanation:

Matt cut a circle into 8 equal sections.
He drew an angle that measures the same as the total measure of 3 of the sections in the circle.
Complete angle = 360°
Divide the total number of sections by 360°
\(\frac{360}{8}\) = 45°
So, the angle for each section is 45°
The angle for 3 of the sections in the circle = 3 × 45° = 135°
Thus the measure of the angle Matt drew is 135°

Page No. 623

Add to find the measure of the angle. Write an equation to record your work.

Question 1.

∠PQT = ____ °

Answer: 80°

To find the ∠PQT you have to add 43° and 37°
∠PQT = 43° + 37°
∠PQT = 80°

Question 2.

∠JKL = ____ °

Answer: 100°
Let ∠JKL = x°
∠JKL = 90° + 10°
∠JKL = 100°

Question 3.

∠RHT = ____ °

Answer:
Let ∠RHT = x°
x = 55° + 27° + 78°
x = 160°
Therefore ∠RHT = 160°

Use a protractor to find the measure of each angle. Label each angle with its measure.
Write the sum of the angle measures as an equation.

Question 4.

Type below:
________

Answer:

By using the protractor we can measure the angles of the above figures.
m∠KLM = 160°
m∠KLJ = 80°
m∠LMJ = 120°

Question 5.

Type below:
________

Answer:

By using the protractor we can measure the angles of the above figures.

m∠WVZ = 90°
m∠YVZ = 90°
m∠WVX = 140°
m∠YVX = 40°

Question 6.
Use Diagrams What is m∠QRT?

∠QRT = ____ °

Answer: 20°

The above figure is a straight angle.
∠QRT + ∠LRD + ∠RLT = 180
∠QRT + 75° + 85° = 180°
∠QRT + 160° = 180°
∠QRT = 180°- 160°
∠QRT = 20°

Question 7.
Look back at Exercise 1. Suppose you joined an angle measuring 10° to ∠PQT. Draw the new angle, showing all three parts. What type of angle is formed?
Type below:
________

Page No. 624

Question 8.
Stephanie, Kay, and Shane each ate an equal-sized piece of a pizza. The measure of the angle of each piece was 45°. When the pieces were together, what is the measure of the angle they formed?

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

Answer: What is the measure of the angle for the pizza leftover?

Question 8.
b. What information do you need to use?
Type below:
________

Answer: I need the information about the angle for each piece of pizza.

Question 8.
c. Tell how you can use addition to solve the problem.
Type below:
________

Answer:
The measure of the angle of each piece was 45°
There are 3 pieces of pizza = 45° + 45° + 45° = 135°

Question 8.
d. Complete the sentence. The three pieces of pizza formed a _________ angle.
________

Answer: Obtuse angle

Question 9.
What is the measure of ∠XZW?

____ °

Answer: 113°

Explanation:

∠XZW = ∠XZY + ∠YZW
∠XZY = 42°
∠YZW = 71°
∠XZW = 42° + 71°
∠XZW = 113°

Go Math Grade 4 Chapter 11 Review Test Answer Key Question 10.
What is m∠PRS? Use equations to explain and check your answer.

____ °

Answer: 12°

Explanation:

The above figure is a straight angle.
The sum of the three angles must be equal to 180°
m∠PRS + m∠PRN + m∠TRN = 180°
m∠PRS + 90° + 78° = 180°
m∠PRS = 180° – 90° – 78°
m∠PRS = 12°

Common Core – New – Page No. 625

Join and Separate Angles

Add to find the measure of the angle. Write an equation to record your work.

Question 1.

50°+75° = 125°
m∠ABD = 125°

Explanation:

m∠ABC = 50°
m∠CBD = 75°
To find the measure of m∠ABD we have to add m∠ABC and m∠CBD
m∠ABD = 50°+75°
m∠ABD = 125°

Question 2.

____ ° + ____ ° = ____ ° ;   m∠FGJ = ____ °

Answer: 140° + 20° = 160°
m∠FGJ = 160°

Explanation:

m∠FGH = 140°
m∠JGH = 20°
To find the measure of m∠FGJ we need to add m∠FGH and m∠JGH
m∠FGJ = 140° + 20°
m∠FGJ = 160°

Question 3.

____ ° + ____ ° = ____ ° ; m∠KLN = ____ °

Answer: 30° + 90° + 45° = 165°
m∠KLN = 165°

Explanation:

m∠KLM = 30°
m∠MLP = 90°
m∠PLN = 45°
To find the measure of m∠KLN we need to add m∠KLM, m∠MLP and m∠PLN
m∠KLN = 30° + 90° + 45° = 165°
m∠KLN = 165°

Use a protractor to find the measure of each angle in the circle.

Question 4.
m∠ABC = ____ °

Answer: 115°

Question 5.
m∠DBE = ____ °

Answer: 90°

Question 6.
m∠CBD = ____ °

Answer: 75°

Question 7.
m∠EBA = ____ °

Answer: 80°

Question 8.
Write the sum of the angle measures as an equation.
____ ° + ____ ° + ____ ° + ____ ° = ____ °

Answer:

Sum all the angles = m∠DBE + m∠ABC + m∠CBD + m∠EBA
= 115° + 90° + 75° + 80° = 360°

Problem Solving

Question 9.
Ned made the design at the right. Use a protractor. Find and write the measure of each of the 3 angles.
____ ° ; ____ ° ; ____ ° ;

Answer: 50°; 60°; 70°

The above figure is a straight angle.
By using the protractor we can measure the angles of the above figure.
The angle of above 3 shades is 50°; 60°; 70°

Question 10.
Write an equation to find the measure of the total angle.
____ ° + ____ ° + ____ ° = ____ °

Answer: Sum of three angles = 50° + 60° + 70° = 180°

Common Core – New – Page No. 626

Lesson Check

Question 1.
What is the measure of m∠WXZ?

Options:
a. 32°
b. 83°
c. 88°
d. 97°

Answer: 83°

Explanation:

m∠WXZ = m∠WXY + m∠YXZ
Let m∠WXZ be x°
x° = 58° + 25°
x° = 83°
Thus the correct answer is option B.

Question 2.
Which equation can you use to find the m∠MNQ?

Options:
a. 148° – 24° = ■
b. 148° × 24° = ■
c. 148° ÷ 24° = ■
d. 148° + 24° = ■

Answer: 148° + 24° = ■

Explanation:

To measure the unknown angle we need to add both the angles
m∠MNQ = m∠MNP + m∠PNQ
■ = 148° + 24°
So, the correct answer is option D.

Spiral Review

Question 3.
Joe bought 6 packages of envelopes. Each package contains 125 envelopes. How many envelopes did he buy?
Options:
a. 750
b. 723
c. 720
d. 650

Answer: 750

Explanation:

Joe bought 6 packages of envelopes.
Each package contains 125 envelopes.
To find the total number of envelopes in all 6 packages
We have to multiply number of packages and number of envelopes
= 125 × 6 =750
Thus Joe bought 750 envelopes.
The correct answer is option A.

Question 4.
The Lake Trail is \(\frac{3}{10}\) mile long and the Rock Trail is \(\frac{5}{10}\) long. Bill hiked each trail once. How many miles did he hike in all?
Options:
a. \(\frac{1}{5}\) mile
b. \(\frac{4}{10}\) mile
c. \(\frac{1}{2}\) mile
d. \(\frac{8}{10}\) mile

Answer: \(\frac{8}{10}\) mile

Explanation:

The Lake Trail is \(\frac{3}{10}\) mile long and the Rock Trail is \(\frac{5}{10}\) long. Bill hiked each trail once.
We need to both the fractions
\(\frac{3}{10}\) +\(\frac{5}{10}\)
The denominators are common. So add the numerators.
= \(\frac{8}{10}\)
Bill hiked \(\frac{8}{10}\) miles in all.
Thus the correct answer is option D.

Question 5.
Ron drew a quadrilateral with 4 right angles and 4 sides with the same length. Which best describes the figure he drew?
Options:
a. square
b. rhombus
c. trapezoid
d. parallelogram

Answer: square

Explanation:

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

Question 6.
How many degrees are in an angle that turns through \(\frac{3}{4}\) of a circle?
Options:
a. 45°
b. 90°
c. 180°
d. 270°

Answer: 270°

Explanation:

Complete angle = 360°
To measure the angle that turns through is \(\frac{3}{4}\)
multiply \(\frac{3}{4}\) with 360°
360° × \(\frac{3}{4}\) = 270°
So, the answer is option D.

Page No. 629

Question 1.
Laura cuts a square out of scrap paper as shown. What is the angle measure of the piece left over?
First, draw a bar model to represent the problem.

Type below:
_________

Question 1.
Next, write the equation you need to solve.
Type below:
_________

Answer:

m∠MNQ + m∠QNP = m∠MNP
x + 90° = 115°
x = 115° – 90°

Question 1.
Last, find the angle measure of the piece left over.
m∠MNQ =
So, the angle measure of the piece left over is _____.
____ °

Answer:
x + 90° = 115°
x = 115° – 90°
x = 25°
So, the angle measure of the piece left over is 25°

Question 2.
Jackie trimmed a piece of scrap metal to make a straight edge as shown. What is the measure of the piece she trimmed off?

x = ____ °

Answer:
x + 180° = 225°
x = 225°- 180°
x = 45°
Thus the measure of the piece she trimmed off is 45°

Go Math Workbook Grade 4 Chapter 11 Answer Key Pdf Question 3.
What if Laura cut a smaller square as shown? Would m∠MNQ be different? Explain.

Type below:
_________

Answer: No
m∠MNQ would still be 25°. Only the size of the square changed the angle will be the same.
m∠PNQ and m∠MNP did not change.

Question 4.
The map shows Marco’s paper route. When Marco turns right onto Center Street from Main Street, what degree turn does he make? Hint: Draw a dashed line to extend Oak Street to form a 180° angle.

Answer:

x° + 125° + 180° = 360°
x° = 360° – 125° – 180°
x° = 360° – 215°
x° = 145°

Page No. 630

Question 5.
Write an Equation Two angles form a straight angle. One angle measures 89°. What is the measure of the other angle? Explain.
____ °

Answer: 91°

A straight angle measures 180°, so you can subtract 89° from 180°
180° – 89° = 91°

Question 6.
Pose a Problem Look back at Problem 5. Write a similar problem about two angles that form a right angle.
____ °

Answer: Two angles form a right angle. The measure of one angle is 25°. What is the measure of the other angle?
x + 25° = 90°
x °= 90° – 25°
x° = 65°
The measure of other angle is 65°

Question 7.
Sam paid $20 for two T-shirts. The price of each T-shirt was a multiple of 5. What are the possible prices of the T-shirts?
Type below:
_________

Answer:
Sam paid $20 for two T-shirts.
The price of each T-shirt was a multiple of 5.
$20 – 2 T-shirts
x – 1 T-shirt
x = $10
The possible prices of the T-shirts are $10, $10
Another possible price of the T-shirts are $5, $15

Question 8.
Zayna has 3 boxes with 15 art books in each box. She has 2 bags with 11 math books in each bag. If she gives 30 books away, how many art and math books does she have left?
_____ books

Answer: 37 art and math books

Explanation:

Zayna has 3 boxes with 15 art books in each box = 15 × 3 = 45
She has 2 bags with 11 math books in each bag = 11 × 2 = 22
Total number of books = 45 + 22 = 67
If she gives 30 books away, then we have to subtract 30 from 67
67 – 30 = 37
37 art and math books are left.

Question 9.
What’s the Question? It measures greater than 0° and less than 90°.
Type below:
_________

Answer: What is an acute angle?

Question 10.
Two angles, ∠A and ∠B, form a straight angle. ∠A measures 65°. For numbers 10a–10c, select True or False for the statement.
a. ∠B is an acute angle.
i. True
ii. False

Answer: False

Explanation:

Two angles, ∠A and ∠B, form a straight angle. ∠A measures 65°.
65° + ∠B = 180°
∠B = 180° – 65°
∠B = 115°
115° is not an acute angle.
So, the above statement is false.

Question 10.
b. The equation 180° – 65° = x° can be used to find the measure of ∠B.
i. True
ii. False

Answer: True

Question 10.
c. The measure of ∠B is 125°.
i. True
ii. False

Answer: False

65° + ∠B = 180°
∠B = 180° – 65°
∠B = 115°
So, the above statement is false.

Common Core – New – Page No. 631

Problem Solving Unknown Angle Measures

Solve each problem. Draw a diagram to help.

Question 1.

Question 2.
An artist is cutting a piece of metal as shown. What is the angle measure of the piece left over?

x = ____ °

Answer: 95°

x + 130° = 225°
x = 225° – 130°
x = 95°
Therefore the angle of the piece leftover is 95°.

Question 3.
Joan has a piece of material for making a costume. She needs to cut it as shown. What is the angle measure of the piece left over?

x = ____ °

Answer: 50°

Joan has a piece of material for making a costume. She needs to cut it as shown.
By seeing the above figure we can say that it is a right angle.|
The sum of two must be equal to 90°
Let the unknown angle be x
x + 40° = 90°
x = 90° – 40°
x = 50°
Thue the angle measure of the piece leftover is 50°

Common Core – New – Page No. 632

Lesson Check

Question 1.
Angelo cuts a triangle from a sheet of paper as shown. What is the measure of ∠x in the triangle?

Options:
a. 15°
b. 25°
c. 75°
d. 105°

Answer: 15°

Explanation:

The above figure is a right angle.
So, to measure the ∠x we have to subtract 75° from 90°
∠x + 75° = 90°
∠x = 90° – 75°
∠x = 15°
Thus the correct answer is option A.

Question 2.
Cindy cuts a piece of wood as shown. What is the angle measure of the piece left over?

Options:
a. 30°
b. 90°
c. 120°
d. 150°

Answer: 120°

Explanation:

x + 90° = 210°
x = 210° – 90°
x = 120°
120° is the measure of the piece leftover.
So, the correct answer is option C.

Spiral Review

Question 3.
Tyronne worked 21 days last month. He earned $79 each day. How much did Tyronne earn last month?
Options:
a. $869
b. $948
c. $1,659
d. $2,169

Answer: $1,659

Explanation:

Tyronne worked 21 days last month.
He earned $79 each day.
$79 × 21 = 1659
Thus Tyronne earned $1,659 last month.
So, the correct answer is option C.

Question 4.
Meg inline skated for \(\frac{7}{10}\) mile. Which shows this distance written as a decimal?
Options:
a. 0.07 mile
b. 0.1 mile
c. 0.7 mile
d. 7.1 miles

Answer: 0.7 mile

Explanation:

Meg inline skated for \(\frac{7}{10}\) mile.
The decimal of the fraction \(\frac{7}{10}\) is 0.7
So, the answer is option C.

Question 5.
Kerry ran 34 mile. Sherrie ran \(\frac{1}{2}\) mile. Marcie ran \(\frac{2}{3}\) mile. Which list orders the friends from least to greatest distance
run?
Options:
a. Kerry, Sherrie, Marcie
b. Kerry, Marcie, Sherrie
c. Sherrie, Kerry, Marcie
d. Sherrie, Marcie, Kerry

Answer: Sherrie, Marcie, Kerry

Explanation:

Kerry ran 34 miles. Sherrie ran \(\frac{1}{2}\) mile. Marcie ran \(\frac{2}{3}\) mile.
The order of the above fractions is Sherrie ran \(\frac{1}{2}\), \(\frac{2}{3}\), 34
The distance from least to greatest is Sherrie, Marcie, Kerry.
so, the correct answer is option D.

Question 6.
What is the measure of m∠ABC?

Options:
a. 32°
b. 84°
c. 88°
d. 94°

Answer: 84°

Explanation:

m∠ABC = m∠ABD + m∠DBC
m∠ABC = 58° + 26°
m∠ABC = 84°
So, the correct answer is option B.

Page No. 633

Question 1.
An angle represents \(\frac{1}{12}\) of a circle. Use the numbers to show how to find the measure of the angle in degrees.



The angle measure is ____ °

Answer: 30°
\(\frac{1}{12}\) × \(\frac{30}{30}\) = \(\frac{30}{360}\)
Thus the angle measure is 30°

Question 2.
Match the measure of each ∠C with the measure of ∠D that forms a straight angle.

Type below:
_________

i. 122° + 58° = 180°
ii. 35° + 145° = 180°
iii. 62° + 118° = 180°
iv. 105° + 75° = 180°

Question 3.
Katie drew an obtuse angle. Which could be the measure of the angle she drew? Mark all that apply.
Options:
a. 35°
b. 157°
c. 180°
d. 92°

Answer: 157° and 92°
An obtuse angle has a measurement greater than 90 degrees but less than 180 degrees.
From the above options, B and D are more than 90°
So, the answer is options B and D.

Go Math Grade 4 Chapter 11 Test Pdf Question 4.
Draw an angle that represents a \(\frac{1}{4}\) and turn counterclockwise on the circle.

Type below:
_________

Page No. 634

Question 5.
Renee drew the figure shown. For 5a–5c, select Yes or No to tell whether the statement is true.

a. The measure of a straight angle is 180°.
i. yes
ii. no

Answer: Yes

By seeing the above figure we can say that the angle is a straight angle.
So, the above statement is true.

Question 5.
b. To find the measure of x, Renee can subtract 75° from 180°.
i. yes
ii. no

Answer: Yes

To know the value of x we have to subtract 75° from 180°.
x = 180° – 75°
Thus the above statement is true.

Question 5.
c. The measure of x is 115°.
i. yes
ii. no

Answer: No
x = 180° – 75°
x = 105°
Thus the above statement is false.
So, the answer is no.

Question 6.
Trey drew this figure with a protractor.

Part A
Write an equation that can be used to find m∠KFG.
Type below:
_________

Answer: 55° + 80° + x = 180°

The figure is a straight angle.
So, the sum of the three angles must be equal to 180°
Let m∠KFG = x
55° + 80° + x = 180°

Question 6.
Part B
What is the measure of m∠KFG? Describe how you solved the equation and how you can check your answer.
____ °
Explain:
_________

Answer: 45°

Explanation:

55° + 80° + x = 180°
x = 180° – 80° – 55°
x = 45°

Question 7.
Use a protractor to find the measure of the angle.

The angle measures ____ °

Answer: 40°
By using a protractor we can measure the angle.
The angle of the above figure is 40°

Page No. 635

Question 8.
Alex drew this angle on the circle. Which describes the angle? Mark all that apply.

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

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

The above figure shows that it is straight angle. So, the fraction of the circle is \(\frac{1}{2}\) turn.
The correct answer is option C.

Question 9.
Miles has a piece of paper that is \(\frac{1}{4}\) of a large circle. He cuts the paper into three equal parts from the center point of the circle. What is the angle measure of each part?

The angle measure is ____ °

Answer: 30°

Explanation:

Miles has a piece of paper that is \(\frac{1}{4}\) of a large circle. He cuts the paper into three equal parts from the center point of the circle.
\(\frac{1}{4}\) of a large circle = 90°
Given that he cut into 3 equal parts = \(\frac{90}{3}\) = 30°
So, the angle for each part is 30°

Question 10.
Use a protractor to find the measure of each angle. Write each angle and its measure in a box ordered by the measure of the angles from least to greatest.

Answer:

Question 11.
Use the numbers and symbols to write an equation that can be used to find the measure of the unknown angle.

What is the measure of the unknown angle?
____ °

Answer: 57°

Explanation:

Let the unknown angle be x
It is a straight angle.
The sum of three angles = 180°
90° + 33° + x = 180°
x = 180° – 90° – 33°
x = 57°

Page No. 636

Question 12.
Choose the word or number to complete a true statement about m∠JKL.


m∠JKL is a(n) ______ angle that has a measure of ____ °.

Answer: m∠JKL is an Obtuse angle that has a measure of 120°.

Question 13.
Vince began practicing piano at 5:15 p.m. He stopped at 5:35 p.m. How many degrees did the minute hand turn during Vince’s practice time?
Explain how you found your answer.

____ °
Explain:
_________

Answer: 120°

I shaded the part of the clock that the minute hand turned from 5:15 p.m. to 5:35 p.m. anmd found that it is \(\frac{1}{3}\) of the circle.
Next, I multiplied \(\frac{1}{3}\) × 360° = 120°
Thus the minute hand moved 120°

Question 14.
An angle measures 125°. Through what fraction of a circle does the angle turn?
\(\frac{□}{□}\) of a circle

Answer: \(\frac{125}{360}\)

The fraction of the circle the angle turned is \(\frac{125}{360}\)

Question 15.
Write the letter for each angle measure in the correct box.

Type below:
__________

Answer:

Page No. 637

Question 16.
For numbers 16a–16b, select the fraction that makes a true statement about the figure.

Question 16.
a. The angle in Figure 1 represents a turn.
\(\frac{□}{□}\) turn

Answer: The angle in Figure 1 represents a \(\frac{3}{4}\) turn

The above figure shows that \(\frac{3}{4}\) part of the circle is shaded. So, the angle represents \(\frac{3}{4}\) turn.

Question 16.
b. The angle in Figure 2 represents a turn.
\(\frac{□}{□}\) turn

Answer: The angle in Figure 2 represents a \(\frac{1}{2}\) turn.
From the second figure, we observe that half of the circle is shaded. So, The angle in Figure 2 represents a \(\frac{1}{2}\) turn.

Question 17.
Melanie cuts a rectangle out of a piece of scrap paper as shown. She wants to calculate the angle measure of the piece that is left over.

Part A
Draw a bar model to represent the problem.

Question 17.
Part B
Write and solve an equation to find x.
The angle measures ____ °.

Answer: 36°
m∠RST = 90°
m∠RSN = 126°
m∠TSN = x°
x + 90° = 126°
x = 126° – 90°
x = 36°
m∠TSN = 36°

Page No. 638

Question 18.
Two angles, m∠A and m∠B, form a right angle. m∠A measures 32°.
For numbers, 18a–18c, select True or False for the statement.
a. m∠B is an acute angle.
i. True
ii. False

Answer: True

If the sum of two angles is 90°, if one angle is acute then the other angle will be acute.
So, the above statement is true.

Question 18.
b. The equation 180° − 32° = x° can be used to find the measure of m∠B.
i. True
ii. False

Answer: False

Explanation:

Given that the sum of 2 angles is 90°
The sum of m∠A and m∠B = 90°
90° – 32° = x°
So, the above statement is false.

Question 18.
c. The measure of m∠B is 58°.
i. True
ii. False

Answer: True

Explanation:

Let m∠B = x
x° + 32° = 90°
x = 90 – 32
x = 58°.
So, the above statement is true.

Question 19.
A circle is divided into parts. Which sum could represent the angle measures that make up the circle? Mark all that apply.
Options:
a. 120° + 120° + 120° + 120°
b. 25° + 40° + 80° + 105° + 110°
c. 33° + 82° + 111° + 50° + 84°
d. 40° + 53° + 72° + 81° + 90° + 34°

Answer: 25° + 40° + 80° + 105° + 110°; 33° + 82° + 111° + 50° + 84°

Explanation:

The sum of all the angles must be equal to 360°
i. 120° + 120° + 120° + 120° = 480° ≠ 360°
ii. 25° + 40° + 80° + 105° + 110° = 360°
iii. 33° + 82° + 111° + 50° + 84° = 360°
iv. 40° + 53° + 72° + 81° + 90° + 34° = 370° ≠ 360°
So, the correct answers are option B, C.

Question 20.
Use a protractor to find the measures of the unknown angles.

What do you notice about the measures of the unknown angles? Is this what you would have expected? Explain your reasoning.
m∠x = ____ ° m∠y = ____ °

Answer: m∠x = 70°; m∠y = 110°
By using a protractor we can find the measure of m∠y
m∠y = 110°
Let m∠x = x°
Sum of supplementary angles = 180°
110° + x = 180°
x = 180° – 110°
x = 70°
Therefore m∠x = 70°

Page No. 643

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

Question 1.
mass of a strawberry
__________

Answer: gram
The metric unit used to measure the mass of a strawberry is the gram.

Question 2.
length of a cell phone
__________

Answer: Centimeter
The metric unit used to measure the length of a cell phone is Centimeter.

Circle the better estimate.

Question 3.
width of a teacher’s desk
10 meters or 1 meter
__________

Answer: 1 meter
The estimation of the width of the teacher’s desk is 1 meter.

Question 4.
The amount of liquid a punch bowl holds
2 liters or 20 liters
__________

Answer: 2 liters

20 liters is greater than 2 liters.
The estimation of the amount of liquid a punch bowl holds is 2 liters.

Question 5.
distance between Seattle and San Francisco
6 miles or 680 miles
__________

Answer: 680 miles
The distance between Seattle and San Francisco is 680 miles.

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

Question 6.
length of a football field
__________

Answer: Yard
The units to measure the length of a football field is Yards.

Question 7.
weight of a pumpkin
__________

Answer: Pound
The customary unit I use to measure the weight of a pumpkin is pounds.

Circle the better estimate.

Question 8.
weight of a watermelon
4 pounds or 4 ounces
__________

Answer: 4 pounds
The estimation of the weight of the watermelon is 4 pounds.

Question 9.
The amount of liquid a fish tank holds
10 cups or 10 gallons
__________

Answer: 10 gallons
The estimation of the amount of liquid a fish tank holds is 10 gallons.

Complete the sentence. Write more or less.

Question 10.
Matthew’s large dog weighs ________ than one ton.
________

Answer: Less
1 ton = 1000 kgs
The weight of dogs can’t be more than a ton.
So, Matthew’s large dog weighs less than one ton.

Question 11.
The amount of liquid a sink can hold is _______ than one cup of water.
________

Answer: More
1 cup holds a very small amount of water.
So, The amount of liquid a sink can hold is more than one cup of water.

Go Math Grade 4 Chapter 11 Mid Chapter Checkpoint Answer Key Question 12.
A paper clip has a mass of _______ than one kilogram.
________

Answer: Less

The weight of a paper clip is about 1 gram.
So, A paper clip has a mass of less than one kilogram.

Page No. 644

For 13–15, use benchmarks to explain your answer.

Question 13.
Cristina is making macaroni and cheese for her family. Would Cristina use 1 pound of macaroni or 1 ounce of macaroni?
__________

Answer: Cristina should use 1 pound of macaroni.

Question 14.
Which is the better estimate for the length of a kitchen table, 200 centimeters or 200 meters?
__________

Answer: 200 centimeters

Centimeters are less than meters. The length of the kitchen will be measured in centimeters.
So, the answer is 200 centimeters.

Question 15.
Jodi wants to weigh her cat and measure its standing height. Which two units should she use?
weight: ________
height: ________

Answer:
The weight of the cat should be measured in Kilograms.
The height of the cat should be measured in Centimeters.

Question 16.
Evaluate Reasonableness Dalton used benchmarks to estimate that there are more cups than quarts in one gallon. Is Dalton’s estimate reasonable? Explain.
Type below:
__________

Answer: Dalton’s reasoning is correct because the measurement of cups is smaller than the measurement of quarts, therefore there would be more cups in a gallon than quarts.

Question 17.
Select the correct word to complete the sentence. Justine is thirsty after running two miles.
She should of water.
__________

Answer: 1 pint

The suitable word for the above sentence is the pint. A pint is a measure of liquid equal to about half a liter. There are eight pints in a gallon.

Conclusion

Make maths your favorite subject by solving the problems. If you understand the concepts you can prepare the questions on your own. It is an easy and scoring subject compared to all. So, go through the Go Math Grade 4 Solution Key Chapter 11 Angles to secure the highest marks in the exams. If you have doubts regarding the subject you can comment in the below comment box. All the best!!!!

Go Math Grade 4 Chapter 13 Answer Key Pdf: Hello students!!! Are you searching for the Grade 4 Answer Key of Go Math Chapter 13 Algebra: Perimeter and Area. Then what are you waiting for Download Go Math Grade 4 Answer Key Chapter 13 Algebra: Perimeter and Area pdf for free of cost here. Make our Go Math Grade 4 Chapter 13 Solution Key as a reference while practicing for your exams. Check out the topics covered in Go Math Grade 4 Answer Key Chapter 13 Algebra: Perimeter and Area from the below.

Algebra: Perimeter and Area Go Math Grade 4 Chapter 13 Answer Key Pdf

Students can get the solution for only for the exercises and homework problems but also for the Mid-Chapter checkpoint and review test. So, the students who are practicing seriously for the exams can go through the Go Math 4th Grade Key of Chapter 13 Perimeter and Area. You can test your knowledge by solving the problems in this HMH Go Math Grade 4 Answer Key Chapter Perimeter and Area.

Common Core – New – Page No. 721

Perimeter

Find the perimeter of the rectangle or square.

Question 1.

9+3+9+3=24
24 inches

Explanation:

Length = 9 inches
Width = 3 inches
Perimeter of the rectangle = l + w + l + w
9+3+9+3=24
Therefore the Perimeter of the rectangle = 24 inches.

Question 2.

_____ meters

Answer: 32 meters

Explanation:

Side of a square = 8 meters
The perimeter of a square = 4a
= 4 × 8 meters = 32 meters
Thus the perimeter of a square = 32 meters.

Class 4 Maths Chapter 13 Perimeter and Area Question 3.

_____ feet

Answer: 44 feet

Explanation:

Length = 10 ft
Width = 12 ft
Perimeter of the rectangle = l + w + l + w
P = 10 + 12 + 10 + 12 = 20 + 24 = 44 feets
Thus the perimeter of the rectangle = 44 feet.

Remember: perimeter is the total distance around the outside, which can be found by adding together the length of each side. In the case of a rectangle, opposite sides are equal in length, so the perimeter is twice its width plus twice its height.

Question 4.

_____ centimeters

Answer: 108 centimeters

Explanation:

Length = 30 cm
Width = 24 cm
Perimeter of the rectangle = l + w + l + w
= 30 + 24 + 30 + 24 = 60 + 48
= 108 centimeters
Therefore the perimeter of the rectangle = 108 centimeters

Question 5.

_____ inches

Answer: 216 inches

Explanation:

Length = 25 in.
Width = 83 in.
Perimeter of the rectangle = l + w + l + w
= 25 + 83 + 25 + 83
= 216 inches
Thus the perimeter of the rectangle = 216 inches

Question 6.

_____ meters

Answer: 240 meters

Explanation:

The side of a square = 60 meters
The perimeter of the square = 4a
= 4 × 60 meters = 240 meters
Thus the perimeter of the square = 240 meters.

Problem Solving

Question 7.
Troy is making a flag shaped like a square. Each side measures 12 inches. He wants to add ribbon along the edges. He has 36 inches of ribbon. Does he have enough ribbon? Explain.
_____

Answer: No. He needs 48 inches of ribbon.

Explanation:

Troy is making a flag shaped like a square. Each side measures 12 inches.
He wants to add a ribbon along the edges.
He has 36 inches of ribbon.
36 inches + 12 inches = 48 inches

Question 8.
The width of the Ochoa Community Pool is 20 feet. The length is twice as long as its width. What is the perimeter of the pool?
_____ feet

Answer: 120 feet

Explanation:

The width of the Ochoa Community Pool is 20 feet.
The length is twice as long as its width.
Length = 2 × 20 feet = 40 feet
Perimeter of the rectangle = l + w + l + w
= 40 + 20 + 40 + 20 = 120 feet
Thus the perimeter of the pool is 120 feet.

Common Core – New – Page No. 722

Lesson Check

Question 1.
What is the perimeter of a square window with sides 36 inches long?
Options:
a. 40 inches
b. 72 inches
c. 144 inches
d. 1,296 inches

Answer: 144 inches

Explanation:

Given, Side of a square = 36 inches
The perimeter of the square = 4 × side = 4a
= 4 × 36 inches = 144 inches
Thus the perimeter of the square = 144 inches
The correct answer is option C.

Question 2.
What is the perimeter of the rectangle below?

Options:
a. 11 meters
b. 14 meters
c. 18 meters
d. 400 meters

Answer: 18 meters

Explanation:

Length of the rectangle = 5 meter
Width of the rectangle = 4 meters
The perimeter of the rectangle = l + w + l + w
= 5 + 4 + 5 + 4 = 18 meters
Thus the correct answer is option C.

Spiral Review

Question 3.
Which is the most reasonable estimate for the measure of the angle Natalie drew?

Options:
a. 30°
b. 90°
c. 180°
d. 210°

Answer: 90°

Explanation:

By seeing the above figure we can say that it is the right angle.
The correct answer is option B.

Question 4.
Ethan has 3 pounds of mixed nuts. How many ounces of mixed nuts does Ethan have?
Options:
a. 30 ounces
b. 36 ounces
c. 48 ounces
d. 54 ounces

Answer: 48 ounces

Explanation:

Given that, Ethan has 3 pounds of mixed nuts.
1 pound = 16 ounces
3 pounds = 3 × 16 ounces = 48 ounces
Therefore the correct answer is option C.

Question 5.
How many lines of symmetry does the shape below appear to have?

Options:
a. 0
b. 1
c. 2
d. more than 2

Answer: 1

Explanation:

The above shape has 1 line of symmetry.
The correct answer is option B.

Go Math Grade 4 Chapter 13 Pdf Perimeter for a Square Question 6.
Which of the following comparisons is correct?
Options:
a. 0.70 > 7.0
b. 0.7 = 0.70
c. 0.7 < 0.70
d. 0.70 = 0.07

Answer: 0.7 = 0.70

Explanation:

a. 0.70 > 7.0
7.0 = 7
0.7 is less than 7

b. 0.7 = 0.70
0.7 is nothing but 0.70
So, the comparision is correct.
The answer is option B.

Page No. 725

Question 1.
Find the area of the rectangle.

A = _____ square cm

Answer: 143 square cm

Explanation:

Length = 11 cm
Width = 13 cm
Area of the rectangle = l × w
= 11 cm × 13 cm = 143 square cm
Therefore the area of the rectangle = 143 square cm

Find the area of the rectangle or square.

Question 2.

A = _____ square inches

Answer: 14 square inches

Explanation:

Length = 7 inches
Width = 2 inches
Area of the rectangle = l × w
= 7 inches × 2 inches = 14 inches
Therefore the area of the rectangle = 14 square inches

Question 3.

A = _____ square meters

Answer: 81 square meters

Explanation:

Side of the square = 9 m
Area of a square = s × s
= 9 m × 9 m = 81 square meters
Thus the area of a square = 81 square meters

Question 4.

A = _____ square feet

Answer: 112 square feet

Explanation:

Length = 8 feet
Width = 14 feet
Area of the rectangle = l × w
= 8 feet × 14 feet = 112 square feet
Therefore, area of the rectangle = 112 square feet

Find the area of the rectangle or square.

Question 5.

A = _____ square feet

Answer: 65 square feet

Explanation:

Length of the rectangle = 13 ft
Width of the rectangle = 5 feet
Area of a rectangle = l × w
= 13 feet × 5 feet = 65 square feet
Thus, the area of the rectangle = 65 square feet

Question 6.

A = _____ square yards

Answer: 169 square yards

Explanation:

Side of the square = 13 yards
Area of a square = s × s
= 13 yards × 13 yards = 169 square yards
Therefore, the area of a square = 169 square yards

Question 7.

A = _____ square centimeters

Answer: 40 square centimeters

Explanation:

Length of the rectangle = 20 cm
Width of the rectangle = 2 cm
Area of a rectangle = l × w
= 20 cm × 2 cm = 40 square centimeters
Therefore the area of the rectangle = 40 square centimeters.

Practice: Copy and Solve Find the area of the rectangle.

Question 8.
base: 16 feet
height: 6 feet
A = _____ square feet

Answer: 96 square feet

Explanation:

base: 16 feet
height: 6 feet
Area of a rectangle = b ×h
= 16 feet × 6 feet = 96 square feet
Thus the area of the rectangle = 96 square feet

Question 9.
base: 9 yards
height: 17 yards
A = _____ square yards

Answer: 153 square yards

Explanation:

base: 9 yards
height: 17 yards
Area of a rectangle = b × h
9 yards × 17 yards = 153 square yards
The area of the rectangle = 153 square yards

Question 10.
base: 14 centimeters
height: 11 centimeters
A = _____ square centimeters

Answer: 154 square centimeters

Explanation:

base: 14 centimeters
height: 11 centimeters
Area of a rectangle = b × h
14 centimeters × 11 centimeters = 154 square centimeters
The area of the rectangle = 154 square centimeters

Question 11.
Terry’s rectangular yard is 15 meters by 18 meters. Todd’s rectangular yard is 20 meters by 9 meters. How much greater is the area of Terry’s yard than Todd’s yard?
_____ square meters

Answer: 90 square meters

Explanation:

Given,
Terry’s rectangular yard is 15 meters by 18 meters.
Todd’s rectangular yard is 20 meters by 9 meters.
Terry’s rectangular yard:
Area of a rectangle = b × h
= 15 meters × 18 meters = 270 square meters
Todd’s rectangular yard:
Area of a rectangle = b × h
20 meters × 9 meters = 180 square meters
270 square meters – 180 square meters = 90 square meters
Terry’s yard is 90 square meters greater than Todd’s yard.

Question 12.
Reason Quantitatively Carmen sewed a square baby quilt that measures 36 inches on each side. What is the area of the quilt?
A = _____ square inches

Answer: 1296 square inches

Explanation:

Carmen sewed a square baby quilt that measures 36 inches on each side.
Area of a square = s × s
= 36 inches × 36 inches = 1296 square inches
Therefore the area of the quilt is 1296 square inches.

Page No. 726

Question 13.
Nancy and Luke are drawing plans for rectangular flower gardens. In Nancy’s plan, the garden is 18 feet by 12 feet. In Luke’s plan, the garden is 15 feet by 15 feet. Who drew the garden plan with the greater area? What is the area?
a. What do you need to find?
Type below:
__________

Answer: I need to find who drew the garden plan with the greater area.

Question 13.
b. What formula will you use?
Type below:
__________

Answer: I will Area of rectangle and Area of a square formula

Question 13.
c. What units will you use to write the answer?
Type below:
__________

Answer: Square feet units

Question 13.
d. Show the steps to solve the problem.
Type below:
__________

Answer:
First, we need to find the area of Nancy’s plan
Length = 18 feet
Width = 12 feet
Area of a rectangle = l × w
A = 18 feet × 12 feet = 216 square feet
And now we need to find the area of Luke’s plan
A = s × s
A = 15 feet × 15 feet = 225 square feet

Question 13.
e. Complete the sentences.
The area of Nancy’s garden is _______.
The area of Luke’s garden is _______.
_______ garden has the greater area.
Type below:
__________

Answer:
The area of Nancy’s garden is 216 square feet.
The area of Luke’s garden is 225 square feet.
Luke’s garden has a greater area.

Question 14.
Victor wants to buy fertilizer for his yard. The yard is 35 feet by 55 feet. The directions on the bag of fertilizer say that one bag will cover 1,250 square feet. How many bags of fertilizer should Victor buy to be sure that he covers the entire yard?
______ bags

Answer: 2 bags

Explanation:
Given that,
Victor wants to buy fertilizer for his yard. The yard is 35 feet by 55 feet.
The directions on the bag of fertilizer say that one bag will cover 1,250 square feet.
A = b × h
A = 35 feet × 55 feet
A = 1925 square feet
1925 square feet is greater than 1,250 square feet.
So, Victor has to buy 2 bags to be sure that he covers the entire yard.

Question 15.
Tuan is an artist. He is painting on a large canvas that is 45 inches wide. The height of the canvas is 9 inches less than the width. What is the area of Tuan’s canvas?
A = ______ square inches

Answer: 1620 square inches

Explanation:
Tuan is an artist. He is painting on a large canvas that is 45 inches wide.
The height of the canvas is 9 inches less than the width.
So, h = 45 – 9 = 36 inches
A = b × h
A = 45 inches × 36 inches
A = 1,620 square inches
Therefore the area of Tuan’s canvas is 1620 square inches.

Common Core – New – Page No. 727

Area

Find the area of the rectangle or square.

Question 1.

Question 2.

______ square yards

Answer: 64 square yards

Explanation:

Side of the square = 8 yards
Area of the square = s × s
8 yards × 8 yards = 64 square yards
Therefore, The area of the square is 64 square yards.

Question 3.

_____ square meters

Answer: 45 square meters

Explanation:

Length of the rectangle = 15 m
Width of the rectangle = 3 m
Area of the rectangle = b × h
= 15 m × 3 m = 45 square meters
Thus the area of the rectangle is 45 square meters.

Question 4.

______ square inches

Answer: 78 square inches

Explanation:

The base of the rectangle = 13 in.
Height of the rectangle = 6 in.
Area of the rectangle = b × h
13 in. × 6 in. = 78 square inches
Thus the area of the rectangle is 78 square inches.

Question 5.

______ square centimeters

Answer: 150 square centimeters

Explanation:

The base of the rectangle = 30 cm
Height of the rectangle = 5 cm
Area of the rectangle = b × h
30 cm × 5 cm = 150 square centimeters
Therefore, the area of the rectangle = 150 square centimeters

Go Math Grade 4 Book My Homework Chapter 13 Perimeter and Area Question 6.

______ square feet

Answer: 56 square feet

Explanation:

The base of the rectangle = 14 feet
Height of the rectangle = 4 feet
Area of the rectangle = b × h
14 feet × 4 feet = 56 square feet
Therefore, the area of the rectangle = 56 square feet.

Problem Solving

Question 7.
Meghan is putting wallpaper on a wall that measures 8 feet by 12 feet. How much wallpaper does Meghan need to cover the wall?
______ square feet wallpaper

Answer: 96 square feet

Explanation:

Meghan is putting wallpaper on a wall that measures 8 feet by 12 feet.
The base of the rectangle = 8 feet
Height of the rectangle = 12 feet
Area of the rectangle = b × h
8 feet × 12 feet = 96 square feet
Thus the Area of the rectangle = 96 square feet

Question 8.
Bryson is laying down sod in his yard to grow a new lawn. Each piece of sod is a 1-foot by 1-foot square. How many pieces of sod will Bryson need to cover his yard if his yard measures 30 feet by 14 feet?
______ pieces

Answer: 420 pieces

Explanation:

Bryson is laying down sod in his yard to grow a new lawn.
Each piece of sod is a 1-foot by 1-foot square.
The base of the rectangle = 30 feet
Height of the rectangle = 14 feet
Area of the rectangle = b × h
= 30 feet × 14 feet = 420 sq. ft.
Therefore Bryson needs 420 pieces of sod to cover his yard.

Common Core – New – Page No. 728

Lesson Check

Question 1.
Ellie and Heather drew floor models of their living rooms. Ellie’s model represented 20 feet by 15 feet. Heather’s model represented 18 feet by 18 feet. Whose floor model represents the greater area? How much greater?
Options:
a. Ellie; 138 square feet
b. Heather; 24 square feet
c. Ellie; 300 square feet
d. Heather; 324 square feet

Answer: Heather; 24 square feet

Explanation:

Given,
Ellie and Heather drew floor models of their living rooms.
Ellie’s model represented 20 feet by 15 feet.
Heather’s model represented 18 feet by 18 feet.
Area of Ellie’s model = 20 feet × 15 feet = 300 square feet
Area of Heather’s model = 18 feet × 18 feet = 324 square feet
Now subtract the area of Ellie’s model from Heather’s model = 324 square feet – 300 square feet = 24 square feet
Thus the area of Heather’s model is greater than Ellie’s model
The correct answer is option B.

Question 2.
Tyra is laying down square carpet pieces in her photography studio. Each square carpet piece is 1 yard by 1 yard. If Tyra’s photography studio is 7 yards long and 4 yards wide, how many pieces of square carpet will Tyra need?
Options:
a. 10
b. 11
c. 22
d. 28

Answer: 28

Explanation:

Tyra is laying down square carpet pieces in her photography studio.
Each square carpet piece is 1 yard by 1 yard. Tyra’s photography studio is 7 yards long and 4 yards wide
Area of the rectangle = b × h
= 7 yards × 4 yards
= 28 square yards
Thus the correct answer is option D.

Spiral Review

Question 3.
Typically, blood fully circulates through the human body 8 times each minute. How many times does blood circulate through the body in 1 hour?
Options:
a. 48
b. 240
c. 480
d. 4,800

Answer: 480

Explanation:

Blood fully circulates through the human body 8 times each minute.
1 minute = 60 seconds
8 × 60 seconds = 480 seconds
The correct answer is option C.

Question 4.
Each of the 28 students in Romi’s class raised at least $25 during the jump-a-thon. What is the least amount of money the class raised?
Options:
a. $5,200
b. $700
c. $660
d. $196

Answer: $700

Explanation:

Each of the 28 students in Romi’s class raised at least $25 during the jump-a-thon.
Multiply number od students with $25
28 × $25 = $700
The correct answer is option B.

Question 5.
What is the perimeter of the shape below if 1 square is equal to 1 square foot?

Options:
a. 12 feet
b. 14 feet
c. 24 feet
d. 28 feet

Answer: 28 feet

Explanation:

Given that 1 square is equal to 1 square foot
There are 14 squares
Length = 14 squares
Width = 2 squares
Area of the rectangle = l × w = 14 × 2 = 28 sq. feets
The correct answer is option D.

Question 6.
Ryan is making small meat loaves. Each small meat loaf uses \(\frac{3}{4}\) pound of meat. How much meat does Ryan need to make 8 small meat loaves?
Options:
a. 4 pounds
b. 6 pounds
c. 8 pounds
d. 10 \(\frac{2}{3}\) pounds

Answer: 6 pounds

Explanation:

Ryan is making small meatloaves.
Each small meatloaf uses \(\frac{3}{4}\) pound of meat.
Ryan need to make 8 small meatloaves.
\(\frac{3}{4}\) × 8 = 6 pounds
The correct answer is option B.

Page No. 731

Question 1.
Explain how to find the total area of the figure.

A = ______ square units

Answer: 23 square units

Explanation:
Rectangle:
Each square box = 1 unit
There are 7 units
Base = 7 units
Height = 2 units
The area of the figure = b × h
A = 7 units × 2 units = 14 square units
Square:
The side is 3 units
Area of the square = 3 units × 3 units = 9 square units
Add both the areas = 14 square units + 9 square units = 23 square units
Therefore the area of the above figure is 23 square units.

Find the area of the combined rectangles.

Question 2.

A = ______ square mm

Answer: 72 square mm

Explanation:
Area of top rectangle = b × h
Base = 12 mm
Height = 3 mm
A = 12 mm × 3 mm = 36 square mm
Area of square = s × s
s = 6 mm
A = 6 mm × 6 mm = 36 square mm
Area of the figure = 36 square mm + 36 square mm = 72 square mm
Thus the area of the above figure is 72 square mm.

Question 3.

A = ______ square miles

Answer: 146 square miles

Explanation:
Area of rectangle = b × h
Area of the first rectangle = 10 mi × 9 mi
A = 90 square miles
Area of the second rectangle = 8 mi × 7 mi
A = 56 square miles
Area of the figure = Area of first rectangle + Area of the second rectangle
Area of the figure = 90 square mi + 56 square miles
Thus the Area of the figure = 146 square miles

Question 4.

A = ______ square feet

Answer: 96 square feet

Explanation:
There are 2 squares and one rectangle in this figure
Area of the square = s × s
A = 4 ft × 4 ft = 16 square ft
Area of the square = s × s
A = 4 ft × 4 ft = 16 square ft
Area of the rectangle = b × h
A = 16 ft × 4 ft = 64 square ft
Area of the figure = 16 square ft + 16 square ft + 64 square ft
Thus the Area of the figure = 96 square feet.

Find the area of the combined rectangles.

Question 5.
Attend to Precision Jamie’s mom wants to enlarge her rectangular garden by adding a new rectangular section. The garden is now 96 square yards. What will the total area of the garden be after she adds the new section?

A = ______ square yards

Answer: 180 square yards

Explanation:

There are 2 rectangles in the above figure
Area of rectangle = b × h
A = 12 yard × 8 yards  = 96 square yards
Area of rectangle = b × h
A = 6 yards × 14 yards = 84 square yards
Area of the figure = 96 square yards + 84 square yards
Therefore the area of the figure = 180 square yards.

Go Math Workbook Grade 4 Area and Perimeter Answer Key Question 6.
Explain how to find the perimeter and area of the combined rectangles at the right.

P = ______ feet; A = ______ square feet

Answer: A = 92 square feet; P = 52 feet

Explanation:
There are 2 rectangle in the figure
Area of rectangle = b × h
A = 5 ft × 4 ft = 20 square ft
Area of rectangle = b × h
A = 8 ft × 9 ft = 72 square ft
Area of the figure = 20 square ft + 72 square ft = 92 square ft
Perimeter of the rectangle = 2l + 2w
P = 2 × 5 + 2 × 4 = 10 + 8 = 18 feet
Perimeter of the rectangle = 2l + 2w
P = 2 × 8 + 2 × 9 = 16 + 18 = 34 feet
Perimeter of the figure = 52 feet

Page No. 732

Question 7.
The diagram shows the layout of Mandy’s garden. The garden is the shape of combined rectangles. What is the area of the garden?
a. What do you need to find?
Type below:
__________

Answer: I need to find the area of the garden.

Question 7.
b. How can you divide the figure to help you find the total area?
Type below:
__________

Answer: I will divide the figure into 3 parts to find the total area

Question 7.
c. What operations will you use to find the answer?
Type below:
__________

Answer: I will use the addition operation to find the area.

Question 7.
d. Draw a diagram to show how you divided the figure. Then show the steps to solve the problem.
Type below:
__________

Answer:

There are 2 rectangles and 1 square in this figure.
Area of rectangle = b × h
Base = 1 ft
H = 7 ft
A = 1 ft × 7 ft = 7 square ft
Area of rectangle = b × h
Base = 5 ft
H = 2 ft
A = 5 ft × 2 ft = 10 square ft
Area of the square = s × s
A = 3 ft × 3 ft = 9 square ft
Total area = 7 square ft + 10 square ft + 9 square ft
= 26 square ft

Question 8.
Workers are painting a large letter L for an outdoor sign. The diagram shows the dimensions of the L. For numbers 8a–8c, select Yes or No to tell whether you can add the products to find the area that the workers will paint.

8a. 2 × 8 and 2 × 4
i. yes
ii. no

Answer: Yes
Explanation:
There are 2 rectangles in the above figure
B = 2 ft
H = 8 ft
A = 2 × 8
B = 4 ft
H = 2 ft
A = 4 × 2
Thus the above statement is correct.

Question 8.
8b. 2 × 6 and 2 × 8
i. yes
ii. no

Answer: No
There are 2 rectangles in the above figure
B = 6 ft
H = 2 ft
A = 2 × 6
Then 2 will be subtracted from 8 = 6
So, the above statement 2 × 6 and 2 × 8 is false.

Question 8.
8c. 2 × 6 and 6 × 2
i. yes
ii. no

Answer: Yes
Explanation:
There are 2 rectangles in the above figure
B = 6 ft
H = 2 ft
A = 6 × 2
B = 2 ft
H = 6 ft
A = 2 × 6
Thus the above statement is true.

Common Core – New – Page No. 733

Area of Combined Rectangles

Find the area of the combined rectangles.

Question 1.

Question 2.

______ square feet

Answer: 143 square feet

Explanation:

Area of A = 9 ft × 5 ft = 45 sq. ft.
Area of B = 14 ft. × 7 ft. = 98 sq. ft.
Total Area = Area of A + Area of B
= 45 sq. ft. + 98 sq. ft. = 143 square feet
Therefore the total Area = 143 square feet

Question 3.

______ square inches

Answer: 63 square inches

Explanation:

Area of A = 9 in. × 5 in. = 45 square inches
Area of B = 6 inches × 3 inches = 18 square inches
Total Area = Area of A + Area of B
Total Area = 45 square inches + 18 square inches
Total Area = 63 square inches

Question 4.

______ square feet

Answer: 50 square feet

Explanation:

Area of A = 4 feet × 2 feet = 8 square feet
Area of B = 7 feet × 6 feet = 42 square feet
Total Area = Area of A + Area of B
Total Area = 8 square feet + 42 square feet
Total Area = 50 square feet

Question 5.

______ square centimeters

Answer: 180 square centimeters

Explanation:

Area of A = 12 cm × 7 cm = 84 square cm
Area of B = 16 cm × 6 cm = 96 square cm
Total Area = Area of A + Area of B
Total Area = 84 square cm + 96 square cm
Total Area = 180 square centimeters

Question 6.

______ square yards

Answer: 68 square yards

Explanation:

Area of A = 14 yd × 1 yd = 14 square yards
Area of B = 9 yd × 6 yd = 54 square yards
Total Area = Area of A + Area of B
Total Area = 14 square yards + 54 square yards
Total Area = 68 square yards

Problem Solving

Use the diagram for 7–8.

Nadia makes the diagram below to represent the counter space she wants to build in her craft room.

Question 7.
What is the area of the space that Nadia has shown for scrapbooking?
______ square feet

Answer: 52 square feet

Explanation:

Length = 13 feet
Width = 9 feet – 5 feet = 4 feet
Area of scrapbooking = l × w
= 13 feet × 4 feet
= 52 square feet
Therefore the area of the space that Nadia has shown for scrapbooking is 52 square feet.

Question 8.
What is the area of the space she has shown for painting?
______ square feet

Answer: 25 square feet

Explanation:
The space for painting is a square.
Side of the square is 5 feet
Area of the square = 5 feet × 5 feet
= 25 square feet
Thus the area of the space she has shown for painting is 25 square feet.

Common Core – New – Page No. 734

Lesson Check

Question 1.
What is the area of the combined rectangles below?

Options:
a. 136 square yards
b. 100 square yards
c. 76 square yards
d. 64 square yards

Answer: 76 square yards

Explanation:
Area of 1st rectangle = 5 yards × 8 yards = 40 square yards
Area of 2nd rectangle = 12 yards × 3 yards = 36 square yards
Area of the figure = Area of 1st rectangle + Area of 2nd rectangle
Area of the figure = 40 square yards + 36 square yards
Therefore, the Area of the figure is 76 square yards.
So, the correct answer is option C.

Question 2.
Marquis is redecorating his bedroom. What could Marquis use the area formula to find?
Options:
a. how much space should be in a storage box
b. what length of wood is needed for a shelf
c. the amount of paint needed to cover a wall
d. how much water will fill up his new aquarium

Answer: the amount of paint needed to cover a wall

Spiral Review

Question 3.
Giraffes are the tallest land animals. A male giraffe can grow as tall as 6 yards. How tall would the giraffe be in feet?
Options:
a. 2 feet
b. 6 feet
c. 12 feet
d. 18 feet

Answer: 18 feet

Explanation:
Giraffes are the tallest land animals. A male giraffe can grow as tall as 6 yards.
6 yards + 6 yards + 6 yards = 18 yards
The correct answer is option D.

Question 4.
Drew purchased 3 books for $24. The cost of each book was a multiple of 4. Which of the following could be the prices of the 3 books?
Options:
a. $4, $10, $10
b. $4, $8, $12
c. $5, $8, $11
d. $3, $7, $14

Answer: $4, $8, $12

Explanation:
Given that,
Drew purchased 3 books for $24.
The cost of each book was a multiple of 4.
So, the prices of books will be multiple of 4.
That means $4 × 1, $4 × 2, $4 × 3
=  $4, $8, $12
The correct answer is option B.

Question 5.
Esmeralda has a magnet in the shape of a square. Each side of the magnet is 3 inches long. What is the perimeter of her magnet?
Options:
a. 3 inches
b. 7 inches
c. 9 inches
d. 12 inches

Answer: 12 inches

Explanation:
Esmeralda has a magnet in the shape of a square. Each side of the magnet is 3 inches long.
Side = 3 inches
The perimeter of the square = 4s
P = 4 × 3 = 12 inches
The correct answer is option D.

Question 6.
What is the area of the rectangle below?

Options:
a. 63 square feet
b. 32 square feet
c. 18 square feet
d. 16 square feet

Answer: 63 square feet

Explanation:
Area of the rectangle = base × height
Base = 9 feet
Height = 7 feet
A = 9 feet × 7 feet
A = 63 square feet
Thus the correct answer is option A.

Page No. 735

Choose the best term from the box.

Question 1.
A square that is 1 unit wide and 1 unit long is a ________.
__________

Answer: Square unit

Question 2.
The _______ of a two-dimensional figure can be any side.
__________

Answer: Base

Question 3.
A set of symbols that expresses a mathematical rule is called a ______.
__________

Answer: Formula

Question 4.
The ______ is the distance around a shape.
__________

Answer: Perimeter

Find the perimeter and area of the rectangle or square.

Question 5.

Perimeter = ______ cm
Area = ______ square cm

Answer:
Perimeter = 52 cm
Area = 169 square cm

Explanation:
P = 4s
P = 4 × 13 = 52 cm
A = s × s
A = 13 × 13 = 169 square cm

Go Math 4th Grade Answers Chapter 13 Area and Perimeter Question 6.

Perimeter = ______ ft
Area = ______ square ft

Answer:
Perimeter: 48 ft
Area = 63 square ft

Explanation:
Base = 21 ft
Height = 3 ft
P = 2l +2w
P = 2 (21 ft + 3 ft)
P = 2 × 24 = 48 feet
A = b × h
A = 21 × 3
A = 63 square ft

Question 7.

Perimeter = ______ in.
Area = ______ square in.

Answer:
Perimeter = 46 in.
Area = 120 square in.

Explanation:
P = 2l +2w
P = 2 × 15 + 2 × 8
P = 30 + 16 = 46 inches
A = l × w
A = 15 × 8 = 120 square inches

Question 8.

Area = ____ square yd

Answer:
Area of the rectangle = 20 yards × 5 yards = 100 square yards
Area of the rectangle = 18 yards × 5 yards = 90 square yards
Area of the figure = 100 square yards + 90 square yards = 190 square yards

Question 9.

Area = ____ square meters

Answer:
A = b × h
A = 5 m × 2 m = 10 square meters
A = b × h
A = 5 m × 2 m = 10 square meters
A = b × h
A = 4 m × 2 m = 8 square meters
Now add all the areas
10 square meters + 10 square meters + 8 square meters
= 28 square meters
Therefore the area of the figures is 28 square meters

Question 10.

Area = ____ square feet
Answer:
Area of the rectangle = b × h
A = 14 ft × 2 ft = 28 square feet
A = s × s
A = 8 ft × 8 ft = 64 square feet
Area of the figures = 64 square feet + 28 square feet
Therefore Area of the figure = 92 square feet

Page No. 736

Question 11.
Which figure has the greatest perimeter?




________

Answer: Figure B has the highest perimeter.

Explanation:

P = 2l +2w
P = 2 × 3 + 2 ×5 = 6 + 10 = 16

P = 2 × 6 + 2 × 3 = 12 + 6 = 18

P = 4a = 4 × 4 = 16

P = 2 × 4 + 2 × 3 = 8+ 6 = 14
Thus the greatest perimeter is figure B.

Question 12.
Which figure has an area of 108 square centimeters?




________

Answer: Figure C

Explanation:

A = 13 cm × 6 cm = 78 square cm.

A = 11 cm × 11 cm = 121 square cm.

A = 12 cm × 9 cm = 108 square cm.

A = 16 cm × 38 cm = 608 square cm.
Thus the area of 108 square centimeters is Figure C.

Question 13.
Which of the combined rectangles has an area of 40 square feet?




________

Answer: Figure A

Explanation:

Area of top rectangle = 6 ft × 2 ft = 12 square feet
Area of bottom rectangle = 6 ft × 2 ft = 12 square feet
Area of square = 4 ft × 4 ft = 16 square feet
Add Area of top rectangle, Area of bottom rectangle and Area of square
= 12 square feet +  12 square feet + 16 square feet = 40 square feet.
Thus the correct answer is option A.

Page No. 739

Question 1.
Find the unknown measure. The area of the rectangle is 36 square feet.

A = b × h
The base of the rectangle is ________ .
base = _____ ft

Answer: 12 feet

Explanation:
Given,
The area of the rectangle = 36 square feet
Height = 3 feet
Base =?
A = b × h
36 square feet = b × 3 feet
b × 3 feet = 36 square feet
b = 36/3 = 12 feet
The base of the rectangle is 12 feets.

Find the unknown measure of the rectangle.

Question 2.

Perimeter = 44 centimeters
width = _____ cm

Answer: 10 cm

Explanation:
Given,
Perimeter = 44 centimeters
Length = 12 cm
width =?
The perimeter of the rectangle = 2 (l + w)
P = 2l + 2w
44 cm = 24 cm + 2w
2w = 44 cm – 24 cm
2w = 20 cm
w = 20/2 = 10
Therefore width = 10 cm

Question 3.

Area = 108 square inches
height = _____ in.

Answer: 12 inches

Explanation:
Given,
Area = 108 square inches
Base = 9 inches
height = _____ in.
A = b × h
108 square inches = 9 inches × h
h = 108/9
Height = 12 inches
Therefore the height of the rectangle = 12 inches

Question 4.

Area = 90 square meters
base = _____ cm

Answer: 18 meters

Explanation:
Given,
Area = 90 square meters
Height = 5 meters
base = _____ cm
A = b × h
90 square meters = b × 5 meters
b × 5 meters = 90 square meters
b = 90/5 = 18 meters
Therefore the base of the rectangle = 18 meters

Question 5.

Perimeter = 34 yards
length = _____ yd

Answer: 12 yards

Explanation:
Given,
Perimeter = 34 yards
Width = 5 yards
Length =?
The perimeter of the rectangle = 2 (l + w)
P = 2l + 2w
34 yards = 2 × l + 2 × 5 yards
34 yards = 2 × l + 10 yards
2 × l + 10 yards = 34 yards
2l = 34 yards – 10 yards
2l = 24 yards
l = 24/2 = 12 yards
Therefore the length of the rectangle = 12 yards.

Question 6.

Area = 96 square feet
base = ______ ft

Answer: 12 feet

Explanation:
Given,
Area = 96 square feet
Height = 8 feet
Base =?
A = b × h
96 square feet = b × 8 feet
b × 8 feet = 96 square feet
b = 96/8 = 12 feet
Thus base of the rectangle = 12 feet.

Question 7.

Area = 126 square centimeters
height = _____ centimeters

Answer: 14 centimeters

Explanation:
Given,
Area = 126 square centimeters
Base = 9 cm
height = _____ centimeters
A = b × h
126 square centimeters = 9 cm × h
9 cm × h = 126 square centimeters
h = 126/9 = 14 centimeters
Therefore the Height of the rectangle = 14 centimeters

Question 8.
A square has an area of 49 square inches. Explain how to find the perimeter of the square.
Type below:
________

Answer:

Explanation:
Given that,
A square has an area of 49 square inches.
A = 49 square inches
s^2 = 49 square inches
The square root of 49 is 7
So, each side of the square is 7 inches
The perimeter of the square = 4 × s
4 × 7 inches = 28 inches.
Therefore the perimeter of the square is 28 inches.

Page No. 740

Question 9.
Identify Relationships The area of a swimming pool is 120 square meters. The width of the pool is 8 meters. What is the length of the pool in centimeters?
length = _____ centimeters

Answer:
Given that the area of a swimming pool is 120 square meters.
The width of the pool is 8 meters.
We have to find the length of the pool in centimeters.
We know that Area of the rectangle = l × w
A = l × w
120 square meters = l × 8 meters
l × 8 meters = 120 square meters
l = 120/8 = 15 meters
Therefore, the length of the pool = 15 meters
Convert meters to centimeters
1 meter = 100 centimeters
15 meters = 1500 centimeters.
The length of the pool in centimeters = 1500 centimeters

Go Math Grade 4 Additional Practice 13.6 Answer Key Question 10.
An outdoor deck is 7 feet wide. The perimeter of the deck is 64 feet. What is the length of the deck? Use the numbers to write an equation and solve it. A number may be used more than once.

P=(2 × l) + (2 × w)
So, the length of the deck is _______ feet.
length = _____ ft

Answer:
An outdoor deck is 7 feet wide.
The perimeter of the deck is 64 feet.
We know that,
P=(2 × l) + (2 × w)
64 feet = (2 × l) + (2 × 7)
64 feet = 2l + 14 feet
2 × l = 64 feet – 14 feet
2 × l = 50 feet
l = 50/2 = 25 feet
Therefore the length of the deck = 25 feet.

Question 11.
A male mountain lion has a rectangular territory with an area of 96 square miles. If his territory is 8 miles wide, what is the length of his territory?

length = _____ miles

Answer:
A male mountain lion has a rectangular territory with an area of 96 square miles.
Width = 8 miles
Length =?
A = l × w
96 square miles = l × 8 miles
l × 8 miles = 96 square miles
l = 96/8
l = 12 miles
Therefore, length of his territory = 12 miles

Common Core – New – Page No. 741

Find Unknown Measures

Find the unknown measure of the rectangle.

Question 1.

Perimeter = 54 feet
width = 7 feet
Think: P = (2 × l) + (2 × w)
54 = (2 × 20) + (2 × w)
54 = 40 + (2 × w)
Since 54 = 40 + 14, 2 × w = 14, and w = 7.

Question 2.

Perimeter = 42 meters
length = _____ meters

Answer: length = 12 meters

Explanation:

Given, Perimeter = 42 meters
Width = 9 meters
P = (2 × l) + (2 × w)
P = (2 × l) + (2 × 9 m)
42 m = 2l + 18 m
42 m – 18 m = 2l
2l = 24 meters
l = 24 meters/2 = 12 meters
Therefore length = 12 meters

Question 3.

Area = 28 square centimeters
height = _____ centimeters

Answer: height = 7 centimeters

Explanation:

Given,
Area = 28 square centimeters
Base = 4 cm
A = b × h
28 square centimeters = 4 cm × h
4 × h = 28
h = 28/4 = 7 cm
The height of the rectangle = 7 centimeters

Question 4.

Area = 200 square inches
base = _____ inches

Answer: base = 8 inches

Explanation:

Given,
Area = 200 square inches
Height = 25 inches
Base = ?
Area of the rectangle = b × h
200 square inches = b × 25 inches
b × 25 inches = 200 square inches
b = 200/25 = 8 inches
The base of the rectangle = 8 inches.

Problem Solving

Question 5.
Susie is an organic vegetable grower. The perimeter of her rectangular vegetable garden is 72 yards. The width of the vegetable garden is 9 yards. How long is the vegetable garden?
length = _____ yards

Answer: 27 yards

Explanation:

Susie is an organic vegetable grower.
The perimeter of her rectangular vegetable garden is 72 yards.
The width of the vegetable garden is 9 yards.
P = 72 yards
W = 9 yards
L =?
We know that,
P = (2 × l) + (2 × w)
72 yards = (2 × l) + (2 × 9)
72 yards – 18 yards = (2 × l)
(2 × l) = 72 yards – 18 yards
2l = 54 yards
l = 54/2 = 27 yards
Thus the vegetable garden is 27 yards long.

Question 6.
An artist is creating a rectangular mural for the Northfield Community Center. The mural is 7 feet tall and has an area of 84 square feet. What is the length of
the mural?
length = _____ feet

Answer: 12 feet

Explanation:

An artist is creating a rectangular mural for the Northfield Community Center.
The mural is 7 feet tall and has an area of 84 square feet.
A = 84 square feet
W = 7 feet
L =?
A = l × w
84 square feet = l × 7 feet
l × 7 feet = 84 square feet
l = 84/7 = 12 feet
Thus the length of Murali is 12 feet.

Common Core – New – Page No. 742

Lesson Check

Question 1.
The area of a rectangular photograph is 35 square inches. If the width of the photo is 5 inches, how tall is the photo?
Options:
a. 5 inches
b. 7 inches
c. 25 inches
d. 30 inches

Answer: 7 inches

Explanation:

The area of a rectangular photograph is 35 square inches.
Width = 5 inches
A = l × w
35 square inches = l × 5 inches
Length = 35/5 = inches
Thus the photo is 7 inches tall.
The correct answer is option B.

Question 2.
Natalie used 112 inches of blue yarn as a border around her rectangular bulletin board. If the bulletin board is 36 inches wide, how long is it?
Options:
a. 20 inches
b. 38 inches
c. 40 inches
d. 76 inches

Answer: 20 inches

Explanation:

Natalie used 112 inches of blue yarn as a border around her rectangular bulletin board.
Width = 36 inches
A = 112 inches
A = l × w
112 inches = l × 36 inches
l × 36 inches = 112 inches
l = 112/36 = 20 inches
Length = 20 inches
The correct answer is option A.

Spiral Review

Question 3.
A professional basketball court is in the shape of a rectangle. It is 50 feet wide and 94 feet long. A player ran one time around the edge of the court. How far did the player run?
Options:
a. 144 feet
b. 194 feet
c. 238 feet
d. 288 feet

Answer: 288 feet

Explanation:

A professional basketball court is in the shape of a rectangle.
It is 50 feet wide and 94 feet long.
A player ran one time around the edge of the court.
P = (2 × l) + (2 × w)
P = (2 × 94 feet) + (2 × 50 feet)
P = 188 feet + 100 feet = 288 feet
Therefore the perimeter of the rectangle is 288 feet.

Question 4.
On a compass, due east is a \(\frac{1}{4}\) turn clockwise from due north. How many degrees are in a \(\frac{1}{4}\) turn?
Options:
a. 45°
b. 60°
c. 90°
d. 180°

Answer: 90°

Explanation:

On a compass, due east is a \(\frac{1}{4}\) turn clockwise from due north.
\(\frac{1}{4}\) × 360° = 360°/4 = 90°
The correct answer is option C.

Question 5.
Hakeem’s frog made three quick jumps. The first was 1 meter. The second jump was 85 centimeters. The third jump was 400 millimeters. What was the total length of the frog’s three jumps?
Options:
a. 189 centimeters
b. 225 centimeters
c. 486 centimeters
d. 585 millimeters

Answer: 225 centimeters

Explanation:

Hakeem’s frog made three quick jumps.
The first was 1 meter. The second jump was 85 centimeters. The third jump was 400 millimeters.
Convert other units to centimeters
1 meter = 100 centimeters
400 millimeters = 40 centimeters
100 + 85 + 40 = 225 centimeters
Thus the correct answer is option B.

Question 6.
Karen colors in squares on a grid. She colored \(\frac{1}{8}\) of the squares blue and \(\frac{5}{8}\) of the squares red. What fraction of the squares are not colored in?
Options:
a. \(\frac{1}{8}\)
b. \(\frac{1}{4}\)
c. \(\frac{1}{2}\)
d. \(\frac{3}{4}\)

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

Explanation:

Karen colors in squares on a grid.
She colored \(\frac{1}{8}\) of the squares blue and \(\frac{5}{8}\) of the squares red.
\(\frac{1}{8}\) + \(\frac{5}{8}\) = \(\frac{6}{8}\)
Total number of fractions = \(\frac{8}{8}\)
\(\frac{8}{8}\) – \(\frac{6}{8}\) = \(\frac{2}{8}\)
\(\frac{1}{4}\) fraction of the squares are not colored.

Page No. 745

Question 1.
Lila is wallpapering one wall of her bedroom, as shown in the diagram. She will cover the whole wall except for the doorway. How many square feet of wall does Lila need to cover?

First, find the area of the wall.
A = b × h
A_wall = _____ square feet

Answer:
Base = 12 feet
Height = 8 feet
A = b × h
A_wall = 12 feet × 8 feet
A_wall = 96 square feet

Question 1.
Next, find the area of the door.
A = b × h
A_door = _____ square feet

Answer:
Base = 3 feet
Height = 7 feet
A = b × h
A_door = 3 feet × 7 feet
A_door = 21 square feet

Question 1.
Last, subtract the area of the door from the area of the wall.
_____ – _____ = _____ square feet
So, Lila needs to cover _____ of wall.
Type below:
________

Answer:
A_door = 21 square feet
A_wall = 96 square feet
Last, subtract the area of the door from the area of the wall.
A = A_wall – A_door
A = 96 square feet – 21 square feet
A = 75 square feet
So, Lila needs to cover 75 square feet

Question 2.
What if there was a square window on the wall with a side length of 2 feet? How much wall would Lila need to cover then? Explain.
______ square feet

Answer:
If there is a square window of length 2 feet
Area of square = s × s
A_window = 2 × 2 = 4 square feet
Now Subtract the area of the door, area of the window from the area of the wall.
A = 96 square feet – 21 square feet – 4 square feet
A = 71 square feet
Therefore Lila need to cover 71 square feet.

Question 3.
Ed is building a model of a house with a flat roof, as shown in the diagram. There is a chimney through the roof. Ed will cover the roof with square tiles. If the area of each tile is 1 square inch, how many tiles will he need? Explain.

_____ tiles

Answer:
Roof:
Base = 20 inches
Height = 30 inches
Area of the roof = b × h
A_roof = 20 inches × 30 inches
A_roof = 600 inches
Chimney:
Base = 3 inches
Height = 4 inches
Area of the chimney = b × h
A_chimney = 3 × 4 = 12 inches
Now subtract Area of Chimney from Area of the roof
A = 600 inches – 12 inches
A = 588 inches
Therefore Ed needs 588 tiles.

Page No. 746

Question 4.
Make Sense of Problems Lia has a dog and a cat. Together, the pets weigh 28 pounds. The dog weighs 3 times as much as the cat. How much does each pet weigh?
cat weight = _____  pounds dog weight = _____ pounds

Answer:
Given that, the pets weigh 28 pounds.
28 = 7 + 7 + 7 + 7
The dog weighs 3 times as much as the cat.
= 3 × 7 = 21 pounds
The dog weighs 21 pounds
28 – 21 = 7
The cat weighs = 7 pounds.

Question 5.
Mr. Foster is covering two rectangular pictures with glass. One is 6 inches by 4 inches and the other one is 5 inches by 5 inches. Does he need the same number of square inches of glass for each picture? Explain.
_____

Answer: No

Explanation:
Mr. Foster is covering two rectangular pictures with glass.
One is 6 inches by 4 inches and the other one is 5 inches by 5 inches.
Area of first rectangular picture = 6 × 4 = 24 square inches
Area of second rectangular picture = 5 × 5 = 25 square inches
Area of two rectangular pictures = 25 square inches – 24 square inches
1 square inch.
Therefore, he doesn’t need the same number of square inches of glass for each picture.

Question 6.
Claire says the area of a square with a side length of 100 centimeters is greater than the area of a square with a side length of 1 meter. Is she correct? Explain.
_____

Answer: No

Explanation:
Claire says the area of a square with a side length of 100 centimeters is greater than the area of a square with a side length of 1 meter.
Her statement is not correct because 1 meter = 100 centimeters.
So, the area of a square with a side length of 100 centimeters is equal to the area of a square with a side length of 1 meter.

Question 7.
A rectangular floor is 12 feet long and 11 feet wide. Janine places a rug that is 9 feet long and 7 feet wide and covers part of the floor in the room. Select the word(s) to complete the sentence.
To find the number of square feet of the floor that is NOT covered by the rug,
the the area of the floor.
_____ square feet

Answer:
Length = 12 feet
Width = 11 feet
Area of the rectangular floor = l × w
= 12 feet × 11 feet = 132 square feet
Room:
Length = 9 feet
Width = 7 feet
Area of the floor in the room = l × w
= 9 feet × 7 feet
= 63 square feet
Subtract the area of the rug from the area of the floor
= 132 square feet – 63 square feet = 69 square feet
The number of square feet of the floor that is NOT covered by the rug is 69 square feet.

Common Core – New – Page No. 747

Problem Solving Find the Area

Solve each problem.

Question 1.
A room has a wooden floor. There is a rug in the center of the floor. The diagram shows the room and the rug. How many square feet of the wood floor still shows?

82 square feet
Area of the floor: 13 × 10 = 130 square feet
Area of the rug: 8 × 6 = 48 square feet
Subtract to find the area of the floor still showing: 130 – 48 = 82 square feet

Question 2.
A rectangular wall has a square window, as shown in the diagram.

What is the area of the wall NOT including the window?
The area of the wall NOT including the window = _____ square feet

Answer: 96 square feet

Explanation:
Wall:
Base = 14 feet
Height = 8 feet
Area of the wall = b × h
A = 14 feet × 8 feet
A = 112 square feet
Window:
Length = 4 feet
Area of the square = s × s
Area of the window = 4 feet × 4 feet = 16 square feet
Now subtract Area of the window from the area of the rectangular wall
= 112 square feet – 16 square feet
= 96 square feet
Therefore the area of the wall NOT including the window = 96 square feet.

Question 3.
Bob wants to put down new sod in his backyard, except for the part set aside for his flower garden. The diagram shows Bob’s backyard and the flower garden.

How much sod will Bob need?
The area covered with new sod = _____ square yards

Answer: 235 square yards

Flower Garden:
Base = 20 yards
Height = 14 yards
Area of the rectangular flower garden = b × h
A = 20 yards × 14 yards
A = 280 square yards
Sod:
Base = 5 yards
Height = 9 yards
Area of sod = b × h
= 5 yards × 9 yards = 45 square yards
Now subtract area of sod from area of flower garden
= 280 square yards – 45 square yards
= 235 square yards
Thus the area covered with new sod = 235 square yards

Question 4.
A rectangular painting is 24 inches wide and 20 inches tall without the frame. With the frame, it is 28 inches wide and 24 inches tall. What is the area of the frame not covered by the painting?
The area of the frame = _____ square inches

Answer: 192 square inches

Explanation:
A rectangular painting is 24 inches wide and 20 inches tall without the frame.
A = b × h
A = 24 inches × 20 inches
A = 480 square inches
With the frame, it is 28 inches wide and 24 inches tall.
A = b × h
A = 28 inches × 24 inches
A = 672 square inches
The area of the frame not covered by the painting
= 672 square inches – 480 square inches
= 192 square inches
Therefore, The area of the frame = 192 square inches

Question 5.
One wall in Jeanne’s bedroom is 13 feet long and 8 feet tall. There is a door 3 feet wide and 6 feet tall. She has a poster on the wall that is 2 feet wide and 3 feet tall. How much of the wall is visible?
The area of the wall visible = _____ square feet

Answer: 80 square feet

Explanation:
One wall in Jeanne’s bedroom is 13 feet long and 8 feet tall.
Area of Jeanne’s bedroom = 13 feet × 8 feet = 104 square feet
Area of door = 3 feet × 6 feet = 18 square feet
Area of the wall = 2 feet × 3 feet = 6 square feet
To find the area of the wall visible we have to subtract Area of the wall, Area of the door from Area of Jeanne’s bedroom.
104 square feet – 18 square feet – 6 square feet
= 80 square feet
The area of the wall visible = 80 square feet

Common Core – New – Page No. 748

Lesson Check

Question 1.
One wall in Zoe’s bedroom is 5 feet wide and 8 feet tall. Zoe puts up a poster of her favorite athlete. The poster is 2 feet wide and 3 feet tall. How much of the wall is not covered by the poster?
Options:
a. 16 square feet
b. 34 square feet
c. 35 square feet
d. 46 square feet

Answer: 34 square feet

Explanation:
One wall in Zoe’s bedroom is 5 feet wide and 8 feet tall.
Area of the wall in Zoe’s bedroom = b × h
A = 5 feet × 8 feet
A = 40 square feet
Zoe puts up a poster of her favorite athlete. The poster is 2 feet wide and 3 feet tall.
Area of the poster = b × h
A = 2 feet × 3 feet = 6 square feet
Now subtract Area of the poster from the Area of the wall in Zoe’s bedroom
= 40 square feet – 6 square feet
= 34 square feet
Thus the area of the wall is not covered by the poster = 34 square feet.
The correct answer is option B.

Question 2.
A garage door is 15 feet wide and 6 feet high. It is painted white, except for a rectangular panel 1 foot high and 9 feet wide that is brown. How much of the garage door is white?
Options:
a. 22 square feet
b. 70 square feet
c. 80 square feet
d. 81 square feet

Answer: 81 square feet

Explanation:
A garage door is 15 feet wide and 6 feet high.
Area of the garage door = b × h
A = 15 feet × 6 feet
A = 90 square feet
It is painted white, except for a rectangular panel 1 foot high and 9 feet wide that is brown.
b = 9 feet
h = 1 foot
A = b × h
A = 9 feet × 1 feet
A = 9 square feet
Area of the garage door is white = 90 square feet – 9 square feet
Area of the garage door is white = 81 square feet
The correct answer is option D.

Spiral Review

Question 3.
Kate baked a rectangular cake for a party. She used 42 inches of frosting around the edges of the cake. If the cake was 9 inches wide, how long was the cake?
Options:
a. 5 inches
b. 12 inches
c. 24 inches
d. 33 inches

Answer: 12 inches

Explanation:
Kate baked a rectangular cake for a party. She used 42 inches of frosting around the edges of the cake.
Width = 9 inches
P = (2 × l) + (2 × w)
42 inches = (2 × l) + (2 × 9)
(2 × l) + (2 × 9) = 42 inches
(2 × l) = 42 inches – 18 inches
2l = 24 inches
l = 24/2 = 12 inches
Therefore the cake is 12 inches long.
Thus the correct answer is option B.

Question 4.
Larry, Mary, and Terry each had a full glass of juice. Larry drank \(\frac{3}{4}\) of his. Mary drank \(\frac{3}{8}\) of hers. Terry drank \(\frac{7}{10}\) of his. Who drank less than \(\frac{1}{2}\) of their juice?
Options:
a. Larry
b. Mary
c. Mary and Terry
d. Larry and Terry

Answer: Mary

Explanation:
Larry, Mary, and Terry each had a full glass of juice.
Larry drank \(\frac{3}{4}\), Mary drank \(\frac{3}{8}\) and Terry drank \(\frac{7}{10}\) of \(\frac{1}{2}\)
\(\frac{3}{8}\) is less than \(\frac{1}{2}\) of their juice.
The correct answer is Option B.

Question 5.
Which of the following statements is NOT true about the numbers 7 and 9?
Options:
a. 7 is a prime number.
b. 9 is a composite number.
c. 7 and 9 have no common factors other than 1.
d. 27 is a common multiple of 7 and 9.

Answer: 27 is a common multiple of 7 and 9

Explanation:
a. 7 is a prime number is true.
b. 9 is a composite number is true
c. 7 and 9 have no common factors other than 1 is true.
d. 27 is a common multiple of 7 and 9 is not true because 7 is not the multiple of 27.
Thus the correct answer is option D.

Question 6.
Tom and some friends went to a movie. The show started at 2:30 P.M. and ended at 4:15 P.M. How long did the movie last?
Options:
a. 1 hour 35 minutes
b. 1 hour 45 minutes
c. 1 hour 55 minutes
d. 2 hours 15 minutes

Answer: 1 hour 45 minutes

Explanation:
Tom and some friends went to a movie. The show started at 2:30 P.M. and ended at 4:15 P.M.
Subtract 2:30 P.M. from 4:15 P.M.
4 hour 15 minutes
-2 hour 30 minutes
1 hour 45 minutes
The movie last for 1 hour 45 minutes
Thus the correct answer is option B.

Page No. 749

Question 1.
For numbers 1a–1e, select Yes or No to indicate if a rectangle with the given dimensions would have a perimeter of 50 inches.
a. length: 25 inches; width: 2 inches
i. yes
ii. no

Answer: No

Explanation:
P = (2 × l) + (2 × w)
50 inches = (2 × 25 in.) + (2 × w)
(2 × w) = 50 inches – 50 inches
w = 0
Thus the above statement is false

Question 1.
b. length: 20 inches; width: 5 inches
i. yes
ii. no

Answer: Yes

Explanation:
P = (2 × l) + (2 × w)
50 inches = (2 × 20 in.) + (2 × 5)
50 inches = 40 in. + 10 in.
Thus the above statement is true.

Question 1.
c. length: 17 inches; width: 8 inches
i. yes
ii. no

Answer: Yes

Explanation:
P = (2 × l) + (2 × w)
50 inches = (2 × 17 in.) + (2 × 8 in.)
50 inches = 34 in. + 16 in.
Thus the above statement is true.

Question 1.
d. length: 15 inches; width: 5 inches
i. yes
ii. no

Answer: No

Explanation:
P = (2 × l) + (2 × w)
50 inches = (2 × 15 in.) + (2 × 5 in.)
50 inches = 30 in. + 10 in.
50 inches = 40 inches
Thus the above statement is false.

Question 1.
e. length: 15 inches; width: 10 inches
i. yes
ii. no

Answer: Yes

Explanation:
P = (2 × l) + (2 × w)
50 inches = (2 × 15 in.) + (2 × 10 in.)
50 inches = 30 in. + 20 in.
50 inches = 50 inches
Thus the above statement is true.

Question 2.
The swimming club’s indoor pool is in a rectangular building.
Marco is laying tile around the rectangular pool.

Part A
What is the area of the pool and the area of the pool and the walkway? Show your work.
A(pool) = ____ m²    A(building) = ____ m²

Answer:
Pool:
Base = 20 m
Height = 16 m
A = b × h
Area of the pool = 20 m × 16 m = 320 square meters
Pool and the walkway:
Area of the pool and the walkway = 26 m × 22 m = 572 square meters

Question 2.
Part B
How many square meters of tile will Marco need for the walkway?
Explain how you found your answer.
A(walkway) = ____ m²

Answer: 252 square meters

Explanation:
Area of walkway = Area of the pool and the walkway – Area of pool
Area of the walkway = 572 square meters – 320 square meters
= 252 square meters
Therefore the Area of walkway = 252 square meters

Page No. 750

Question 3.
Match the dimensions of the rectangles in the top row with the correct area or perimeter in the bottom row

Answer:

Question 4.
Kyleigh put a large rectangular sticker on her notebook. The height of the sticker measures 18 centimeters. The base is half as long as the height. What area of the notebook does the sticker cover?
________ square centimeters

Answer: 162 square centimeters

Explanation:
Kyleigh put a large rectangular sticker on her notebook.
The height of the sticker measures 18 centimeters.
The base is half as long as the height.
Base = h/2 = 18/2 = 9 centimeters
Area of the rectangle = b × h
A = 9 cm × 18 cm
A = 162 square centimeters
Thus the area of the notebook the sticker cover is 162 square centimeters.

Question 5.
A rectangular flower garden in Samantha’s backyard has 100 feet around its edge. The width of the garden is 20 feet. What is the length of the garden? Use the numbers to write an equation and solve. A number may be used more than once.

□ = (2 × l) + (2 × □)
□ = 2 × l + □
□ = 2 × l
□ = l
So, the length of the garden _____ feet.

Answer:
P = (2 × l) + (2 × w)
100 = (2 × l) + (2 × 20)
100 – 40 = 2 × l
2 × l = 60
l = 60/2 = 30 feet
Length = 30 feet
So, the length of the garden 30 feet.

Question 6.
Gary drew a rectangle with a perimeter of 20 inches. Then he tried to draw a square with a perimeter of 20 inches.
Draw 3 different rectangles that Gary could have drawn. Then draw the square, if possible.
Type below:
__________

Answer:
The possible rectangles with a perimeter of 20 inches are:

The possible square with a perimeter of 20 inches is:

Page No. 751

Question 7.
Ami and Bert are drawing plans for rectangular vegetable gardens. In Ami’s plan, the garden is 13 feet by 10 feet. In Bert’s plan, the garden is 12 feet by 12 feet. For numbers 7a−7d, select True or False for each statement.
a. The area of Ami’s garden is 130 square feet.
i. True
ii. False

Answer: True

Explanation:
A = b × h
Area of Ami’s garden = 13 feet × 10 feet =
Area of Ami’s garden = 130 square feet
The above statement is true.

Question 7.
b. The area of Bert’s garden is 48 square feet.
i. True
ii. False

Answer: False

Explanation:
Area of Bert’s garden = 12 feet × 12 feet = 144 square feet
The above statement is false.

Question 7.
c. Ami’s garden has a greater area than Bert’s garden.
i. True
ii. False

Answer: False

Explanation:
Area of Ami’s garden = 13 feet × 10 feet = 130 square feet
Area of Bert’s garden = 12 feet × 12 feet = 144 square feet
130 square feet is less than 144 square feet
The area of Ami’s garden is less than Area of Bert’s garden.
The above statement is false.

Question 7.
d. The area of Bert’s garden is 14 square feet greater than Ami’s.
i. True
ii. False

Answer: True

Explanation:
Area of Ami’s garden = 13 feet × 10 feet = 130 square feet
Area of Bert’s garden = 12 feet × 12 feet = 144 square feet
144 square feet – 130 square feet = 14 square feet
The above statement is true.

Question 8.
A farmer planted corn in a square field. One side of the field measures 32 yards. What is the area of the cornfield? Show your work.
_______ square yards

Answer: 1024 square yards

Explanation:
A farmer planted corn in a square field. One side of the field measures 32 yards.
Area of the square = 32 yards × 32 yards
A = 1,024 square yards
Therefore the area of the cornfield is 1,024 square yards.

Question 9.
Harvey bought a frame in which he put his family’s picture.

What is the area of the frame not covered by the picture?
_______ square inches

Answer: 136 square inches

Explanation:
Area of the picture = 12 in. × 18 in.
A = 216 square inches
Area of the frame = 16 in. × 22 in.
A = 352 square inches
The area of the frame not covered by the picture = 352 square inches – 216 square inches
= 136 square inches
Therefore the area of the frame not covered by the picture is 136 square inches.

Question 10.
Kelly has 236 feet of fence to use to enclose a rectangular space for her dog. She wants the width to be 23 feet. Draw a rectangle that could be the space for Kelly’s dog. Label the length and width.
Type below:
________

Answer:

Kelly has 236 feet of fence to use to enclose a rectangular space for her dog.
She wants the width to be 23 feet.
Perimeter = (2 × l) + (2 × w)
236 = (2 × l) + (2 × w)
236 = (2 × l) + (2 × 23)
236 – 46 = (2 × l)
(2 × l) = 190
l = 190/2
l = 95 feet
Therefore length = 95 feet.

Page No. 752

Question 11.
The diagram shows the dimensions of a new parking lot at Helen’s Health Food store.

Use either addition or subtraction to find the area of the parking lot. Show your work.
_______ square yards

Answer: 1100 square yards

Explanation:
Addition:
Top:
Base = 40 yards
Height = 20 yards
Area of the top rectangle = b × h
A = 40 yards × 20 yards = 800 square yards
Bottom:
Base = 30 yards
Height = 10 yards
Area of the rectangle = b × h
A = 30 yards × 10 yards = 300 square yards
Area of the parking = Area of top + Area of bottom
A = 800 square yards + 300 square yards
Area of parking = 1100 square yards.

Question 12.
Chad’s bedroom floor is 12 feet long and 10 feet wide. He has an area rug on his floor that is 7 feet long and 5 feet wide. Which statement tells how to find the amount of the floor that is not covered by the rug? Mark all that apply.
Options:
a. Add 12 × 10 and 7 × 5.
b. Subtract 35 from 12 × 10
c. Subtract 10 × 5 from 12 × 7.
d. Add 12 + 10 + 7 + 5.
e. Subtract 7 × 5 from 12 × 10.
f. Subtract 12 × 10 from 7 × 5.

Answer: B, F

Chad’s bedroom floor is 12 feet long and 10 feet wide.
A = 12 feet × 10 feet = 120 square feet
Area rug on his floor = 7 feet × 5 feet = 35 square feet
To find the amount of the floor that is not covered by the rug we have to subtract 120 square feet from 35 square feet or 35 square feet from 12 × 10.
So, the correct answers are B and F.

Question 13.
A row of plaques covers 120 square feet of space along a wall. If the plaques are 3 feet tall, what length of the wall do they cover?
____ feet

Answer: 40 feet

Explanation:
Given that,
A row of plaques covers 120 square feet of space along a wall.
Height = 3 feet
A = b × h
120 square feet = b × 3 feet
b = 120/3 = 40
Therefore the base is 40 feet.

Page No. 753

Question 14.
Ms. Bennett wants to buy carpeting for her living room and dining room.

Explain how she can find the amount of carpet she needs to cover the floor in both rooms. Then find the amount of carpet she will need.
____ square feet

Answer:
She can find the area of each rectangle and then find the sum. The area of the living room is 20 × 20 = 400 square feet.
The area of the dining room is 15 × 10 = 150 square feet.
The sum of the two rooms = 400 + 150 = 550 square feet.
She needs 550 square feet of carpeting.

Question 15.
Lorenzo built a rectangular brick patio. He is putting a stone border around the edge of the patio. The width of the patio is 12 feet. The length of the patio is two feet longer than the width.
How many feet of stone will Lorenzo need? Explain how you found your answer.
____ feet

Answer: 52 feet

Explanation:
Width = 12 feet
Length = 2 × width
Length = 2 + 12 feet = 14 feet
Perimeter = (2 × l) + (2 × w)
P = (2 × 14) + (2 × 12)
P = 28 + 24
P = 52 feet

Page No. 754

Question 16.
Which rectangle has a perimeter of 10 feet? Mark all that apply.

Rectangle: ____
Rectangle: ____

Answer: A, C

Explanation:
i. Perimeter of A = (2 × l) + (2 × w)
P = (2 × 1) + (2 × 4) = 2 + 8 = 10 feet
ii. Perimeter of B = (2 × l) + (2 × w)
P = (2 × 2) + (2 × 5) = 4 + 10 = 14 feet
iii. Perimeter of C = (2 × l) + (2 × w)
P = (2 × 2) + (2 × 3) = 4 + 6 = 14 feet
iv. Perimeter of D = (2 × l) + (2 × w)
P = (2 × 4) + (2 × 6) = 8 + 12 = 20 feet
The correct answer is option A and C.

Question 17.
A folder is 11 inches long and 8 inches wide. Alyssa places a sticker that is 2 inches long and 1 inch wide on the notebook. Choose the words that correctly complete the sentence.
To find the number of square inches of the folder that is NOT covered by the sticker,

Type below:
________

Answer: Subtract the area of the sticker from the area of the notebook.

Question 18.
Tricia is cutting her initial from a piece of felt. For numbers 18a–18c, select Yes or No to tell whether you can add the products to find the number of square centimeters Tricia needs.

a. 1 × 8 and 5 × 2 _______
b. 3 × 5 and 1 × 8 _______
c. 2 × 5 and 1 × 3 and 1 × 3 _______

Answer:
a. 1 × 8 and 5 × 2 _______
Yes
b. 3 × 5 and 1 × 8 _______
No
c. 2 × 5 and 1 × 3 and 1 × 3 _______
No

Question 19.
Mr. Butler posts his students’ artwork on a bulletin board.

The width and length of the bulletin board are whole numbers. What could be the dimensions of the bulletin board Mr. Butler uses?
Type below:
________

Answer: 5 feet long by 3 feet wide
Area of the rectangle = l × w
A = 15 square feet
The factor of 15 is 5 and 3.
So, the length = 5 feet long
Width = 3 feet long.

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Lesson 1: Multiples of Unit Fractions

• Multiples of Unit Fractions – Page No. 459
• Multiples of Unit Fractions Lesson Check – Page No. 460

Lesson 2: Multiples of Fractions

• Multiples of Fractions – Page No. 463
• Multiples of Fractions Lesson Check – Page No. 464
• Multiples of Fractions Lesson Check 1 – Page No. 465
• Multiples of Fractions Lesson Check 2 – Page No. 466

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Page No. 467
• Mid-Chapter Checkpoint Lesson Check – Page No. 468

Lesson 3: Multiply a Fraction by a Whole Number Using Models

• Multiply a Fraction by a Whole Number Using Models – Page No. 471
• Multiply a Fraction by a Whole Number Using Models Lesson Check – Page No. 472
• Multiply a Fraction by a Whole Number Using Models Lesson Check 1 – Page No. 473
• Multiply a Fraction by a Whole Number Using Models Lesson Check 2 – Page No. 474

Lesson 4: Multiply a Fraction or Mixed Number by a Whole Number

• Multiply a Fraction or Mixed Number by a Whole Number – Page No. 477
• Multiply a Fraction or Mixed Number by a Whole Number Lesson Check – Page No. 478
• Multiply a Fraction or Mixed Number by a Whole Number Lesson Check 1 – Page No. 479
• Multiply a Fraction or Mixed Number by a Whole Number Lesson Check 2- Page No. 480

Lesson 5: Problem Solving • Comparison Problems with Fractions

• Comparison Problems with Fractions – Page No. 483
• Comparison Problems with Fractions Lesson Check – Page No. 484
• Comparison Problems with Fractions Lesson Check 1 – Page No. 485
• Comparison Problems with Fractions Lesson Check 2 – Page No. 486

Review/Test

• • Review/Test – Page No. 487
  • Review/Test – Page No. 488
  • Review/Test – Page No. 489
  • Review/Test – Page No. 490
  • Review/Test – Page No. 491
  • Review/Test – Page No. 492
  • Review/Test – Page No. 497
  • Review/Test – Page No. 498

Common Core – New – Page No. 459

Multiples of Unit Fractions

Write the fraction as a product of a whole number and a unit fraction.

Question 1.

Answer:
5 x 1/6

Explanation:
Given that 5/6 or 5 sixth-size parts.
Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.
You can use unit fractions to show 5/6
5/6 = 5 x 1/6.

Question 2.
\(\frac{7}{8}\) =
Type below:
__________

Answer:
7 x 1/8

Explanation:
Given that 7/8 or 7 eighth-size parts.
Each eighth-size part of the given fraction can be shown by the unit fraction 1/8.
You can use unit fractions to show 7/8
7/8 = 7 x 1/8.

Question 3.
\(\frac{5}{3}\) =
Type below:
__________

Answer:
5 x 1/3

Explanation:
Given that 5/3 or 5 third-size parts.
Each third-size part of the given fraction can be shown by the unit fraction 1/3.
You can use unit fractions to show 5/6
5/3 = 5 x 1/3.

Go Math Grade 4 Chapter 8 Lesson 8.1 Answer Key Question 4.
\(\frac{9}{10}\) =
Type below:
__________

Answer:
9 x 1/10

Explanation:
Given that 9/10 or 9-tenth-size parts.
Each tenth-size part of the given fraction can be shown by the unit fraction 1/10.
You can use unit fractions to show 9/10
9/10 = 9 x 1/10.

Question 5.
\(\frac{3}{4}\) =
Type below:
__________

Answer:
3 x 1/4

Explanation:
Given that 3/4 or 3 fourth-size parts.
Each fourth-size part of the given fraction can be shown by the unit fraction 1/4.
You can use unit fractions to show 5/6
3/4 = 3 x 1/4.

Question 6.
\(\frac{11}{12}\) =
Type below:
__________

Answer:
11 x 1/12

Explanation:
Given that 11/12 or 11 twelve-size parts.
Each twelve-size part of the given fraction can be shown by the unit fraction 1/12.
You can use unit fractions to show 5/6
11/12 = 11 x 1/12.

Question 7.
\(\frac{4}{6}\) =
Type below:
__________

Answer:
4 x 1/6

Explanation:
Given that 4/6 or 4 sixth-size parts.
Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.
You can use unit fractions to show 4/6
4/6 = 4 x 1/6.

Question 8.
\(\frac{8}{20}\) =
Type below:
__________

Answer:
8 x 1/20

Explanation:
Given that 8/20 or 8 twenty-size parts.
Each twenty-size part of the given fraction can be shown by the unit fraction 1/20.
You can use unit fractions to show 8/20
8/20 = 8 x 1/20.

Question 9.
\(\frac{13}{100}\) =
Type below:
__________

Answer:
13 x 1/100

Explanation:
Given that 13/100 or 13 hundred-size parts.
Each hundred-size part of the given fraction can be shown by the unit fraction 1/100.
You can use unit fractions to show 13/100
13/100 = 13 x 1/100.

List the next four multiples of the unit fraction.

Question 10.
\(\frac{1}{5}\) ,
Type below:
__________

Answer:
2/5, 3/5, 4/5, 5/5

Explanation:

2/5, 3/5, 4/5, 5/5

Question 11.
\(\frac{1}{8}\) ,
Type below:
__________

Answer:
2/8, 3/8, 4/8, 5/8

Explanation:

2/8, 3/8, 4/8, 5/8

Problem Solving

Question 12.
So far, Monica has read \(\frac{5}{6}\) of a book. She has read the same number of pages each day for 5 days. What fraction of the book does Monica read each day?
\(\frac{□}{□}\) of the book

Answer:
1/6 of the book

Explanation:
Monica has read 5/6 of a book. She has read the same number of pages each day for 5 days.
For 1 day, she read one page. In total, she read 5 pages in 5 days. So, Monica read 1/6 of a book each day.

Question 13.
Nicholas buys \(\frac{3}{8}\) pound of cheese. He puts the same amount of cheese on 3 sandwiches. How much cheese does Nicholas put on each sandwich?
\(\frac{□}{□}\) pound of cheese

Answer:
1/8 pound of cheese

Explanation:
Nicholas buys 3/8 pound of cheese. He bought 3 sandwiches. Then, he applied 3/8 pound of cheese on 3 sandwiches. So, 3 x 1/8 cheese he put on 3 sandwiches. So, for one sandwich he put 1/8 pound of cheese.

Common Core – New – Page No. 460

Lesson Check

Question 1.
Selena walks from home to school each morning and back home each afternoon. Altogether, she walks \(\frac{2}{3}\) mile each day. How far does Selena live from school?
Options:
a. \(\frac{1}{3}\) mile
b. \(\frac{2}{3}\) mile
c. 1 \(\frac{1}{3}\) mile
d. 2 miles

Answer:
a. \(\frac{1}{3}\) mile

Explanation:
Selena walks from home to school each morning and back home each afternoon. Altogether, she walks 2/3 miles each day. The distance between home and school will remain the same. So, 2/3 x 1/2 = 1/3 mile far Selena live from the school.

Go Math Lesson 8.1 4th Grade Question 2.
Will uses \(\frac{3}{4}\) cup of olive oil to make 3 batches of salad dressing. How much oil does Will use for one batch of salad dressing?
Options:
a. \(\frac{1}{4}\) cup
b. \(\frac{1}{3}\) cup
c. 2 \(\frac{1}{3}\) cups
d. 3 cups

Answer:
1/8 pound of cheesa. \(\frac{1}{4}\) cup

Explanation:
Will uses 34 cups of olive oil to make 3 batches of salad dressing. To know the one batch of salad dressing, we need to take one part of salad dressing = 1/3. So, 3/4 x 1/3 = 1/4 cup of olive oil will use for one batch of salad dressing.

Spiral Review

Question 3.
Liza bought \(\frac{5}{8}\) pound of trail mix. She gives \(\frac{2}{8}\) pound of trail mix to Michael. How much trail mix does Liza have left?
Options:
a. \(\frac{1}{8}\) pound
b. \(\frac{2}{8}\) pound
c. \(\frac{3}{8}\) pound
d. \(\frac{4}{8}\) pound

Answer:
c. \(\frac{3}{8}\) pound

Explanation:
Liza bought 58 pound of trail mix. She gives 28 pound of trail mix to Michael.
So, Liza have left 5/8 – 2/8 = 3/8 trail mix.

Question 4.
Leigh has a piece of rope that is 6 \(\frac{2}{3}\) feet long. How do you write 6 \(\frac{2}{3}\) as a fraction greater than 1?
Options:
a. \(\frac{11}{3}\)
b. \(\frac{15}{3}\)
c. \(\frac{20}{3}\)
d. \(\frac{62}{3}\)

Answer:
c. \(\frac{20}{3}\)

Explanation:
Multiply the denominator with the whole number. i.e Multiply 3 with 6 in the given example, 6 (2/3).
3 x 6 =18.
Add 18 + 2 =20.
Keep the Denominator the same i.e. 3.
The obtained fraction is 20/3.

Question 5.
Randy’s house number is a composite number. Which of the following could be Randy’s house number?
Options:
a. 29
b. 39
c. 59
d. 79

Answer:
b. 39

Explanation:
The composite numbers can be defined as whole numbers that have more than two factors. Whole numbers that are not prime are composite numbers because they are divisible by more than two numbers. 39 is the composite number. 39 is divided by 13 and 3.

Question 6.
Mindy buys 12 cupcakes. Nine of the cupcakes have chocolate frosting and the rest have vanilla frosting. What fraction of the cupcakes have vanilla frosting?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{2}{3}\)
d. \(\frac{3}{4}\)

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

Explanation:
Mindy buys 12 cupcakes.
Nine of the cupcakes have chocolate frosting = 9/12.
The rest have vanilla frosting. So, there are 3 cups remaining = 3/12 = 1/4.
1/4 cupcakes have vanilla frosting.

Page No. 463

Question 1.
Write three multiples of \(\frac{3}{8}\).

1 × \(\frac{3}{8}\) = \(\frac{■}{8}\)
2 × \(\frac{3}{8}\) = \(\frac{■}{8}\)
3 × \(\frac{3}{8}\) = \(\frac{■}{8}\)
Multiples of \(\frac{3}{8}\) are ____ , ____ , and ____ .
Type below:
__________

Answer:
3/8, 6/8, 9/8, 12/8.

Explanation:
1 x 3/8 = 3/8.
2 x 3/8 = 6/8.
3 x 3/8 = 9/8.
4 x 3/8 = 12/8.
Multiples of 3/8 are 3/8, 6/8, 9/8, 12/8.

List the next four multiples of the fraction.

Question 2.
\(\frac{3}{6}\) ,
Type below:
__________

Answer:
6/6, 9/6, 12/6, 20/6

Explanation:
1 x 3/6 = 3/6.
2 x 3/6 = 6/6.
3 x 3/6 = 9/6.
4 x 3/6 = 12/6.
5 x 4/6 = 20/6.
Next four multiples of 3/6 are 6/6, 9/6, 12/6, 20/6.

Question 3.
\(\frac{2}{10}\) ,
Type below:
__________

Answer:
4/10, 6/10, 8/10, 10/10

Explanation:
1 x 2/10 = 2/10.
2 x 2/10 = 4/10.
3 x 2/10 = 6/10.
4 x 2/10 = 8/10.
5 x 2/10 = 10/10.
The next four multiples of 2/10 are 4/10, 6/10, 8/10, 10/10.

Write the product as the product of a whole number and a unit fraction.

Question 4.

3 × \(\frac{3}{4}\) =
Type below:
__________

Answer:
9/4 = 9 x 1/4

Explanation:
1 group of 3/4 = 3/4
2 groups of 3/4 = 6/4
3 groups of 3/4 = 9/4
3 x 3/4 = 9/4.

Question 5.

2 × \(\frac{4}{6}\) =
Type below:
__________

Answer:
8/6 = 8 x 1/6

Explanation:
1 group of 4/6 = 4/6
2 groups of 4/6 = 8/6
2 x 4/6 = 8/6 = 8 x 1/6.

List the next four multiples of the fraction.

Question 6.
\(\frac{4}{5}\) ,
Type below:
__________

Answer:
8/5, 12/5, 16/5, 20/5

Explanation:
1 x 4/5 = 4/5.
2 x 4/5 = 8/5.
3 x 4/5 = 12/5.
4 x 4/5 = 16/5.
5 x 4/5 = 20/5.
The next four multiples of 4/5 are 8/5, 12/5, 16/5, 20/5.

Question 7.
\(\frac{2}{4}\) ,
Type below:
__________

Answer:
4/4, 6/4, 8/4, 10/4

Explanation:
1 x 2/4 = 2/4.
2 x 2/4 = 4/4.
3 x 2/4 = 6/4.
4 x 2/4 = 8/4.
5 x 2/4 = 10/4.
The next four multiples of 2/4 are 4/4, 6/4, 8/4, 10/4.

Write the product as the product of a whole number and a unit fraction.

Question 8.

4 × \(\frac{2}{8}\) =
Type below:
__________

Answer:
8/8 = 8 x 1/8

Explanation:
1 group of 2/8 = 2/8
2 groups of 2/8 = 4/8
3 groups of 2/8 = 6/8
4 groups of 2/8 = 8/8
4 x 2/8 = 8/8 = 8 x 1/8.

Question 9.

3 × \(\frac{3}{5}\) =
Type below:
__________

Answer:
9/5 = 9 x 1/5

Explanation:
1 group of 3/5 = 3/5
2 groups of 3/5 = 6/5
3 groups of 3/5 = 9/5
3 x 3/5 = 9/5 = 9 x 1/5.

Question 10.
Use Repeated Reasoning Are \(\frac{6}{10}\) and \(\frac{6}{30}\) multiples of \(\frac{3}{10}\)?
Explain.
Type below:
__________

Answer:
3/30

Explanation:
Use Repeated Reasoning Are 6/10 and 6/30 multiples of 3/10 and 3/30.

Question 11.
Which is greater, 4 × \(\frac{2}{7}\) or 3 × \(\frac{3}{7}\)? Explain.
4 × \(\frac{2}{7}\) _____ 3 × \(\frac{3}{7}\)

Answer:
4 × \(\frac{2}{7}\) __<___ 3 × \(\frac{3}{7}\)

Explanation:
8/7 < 9/7
So, 4 x 2/7 < 3 x 3/7

Page No. 464

Question 12.
Josh is watering his plants. He gives each of 2 plants \(\frac{3}{5}\) pint of water. His watering can holds \(\frac{1}{5}\) pint. How many times will he fill his watering can to water both plants?

a. What do you need to find?
Type below:
__________

Answer:
We need to find how many times Josh needs to fill his watering can to water both plants.

Question 12.
b. What information do you need to use?
Type below:
__________

Answer:
Use the Number of plants = 2.
He gives each plant a 3/5 pint of water.
His watering can hold 1/5 pint.

Question 12.
c. How can drawing a model help you solve the problem?
Type below:
__________

Answer:

Question 12.
d. Show the steps you use to solve the problem.
Type below:
__________

Answer:
If Josh gives each plant 3/5 pint, then that’s a total of 6/5 pint.
6/5 = 6 x 1/5.

Question 12.
e. Complete the sentence. Josh will fill his watering can ____ times.
____ times

Answer:
Josh will fill his watering can 6 times.

Go Math 4th Grade Pdf Practice and Homework Lesson 8.2 Question 13.
Alma is making 3 batches of tortillas. She adds \(\frac{3}{4}\) cup of water to each batch. The measuring cup holds \(\frac{1}{4}\) cup. How many times must Alma measure \(\frac{1}{4}\) cup of water to have enough for the tortillas? Shade the model to show your answer.

Alma must measure \(\frac{1}{4}\) cup ______ times.
____ times

Answer:
12 times

Explanation:
Alma is making 3 batches of tortillas. She adds a 3/4 cup of water to each batch. The measuring cup holds 1/4 cup.
Alma must measure 1/4 cup 12 times.

Common Core – New – Page No. 465

Multiples of Fractions

List the next four multiples of the fraction.

Question 1.
\(\frac{3}{5}\) ,
Type below:
__________

Answer:
6/5, 9/5, 12/5, 20/5

Explanation:
1 x 3/5 = 3/5.
2 x 3/5 = 6/5.
3 x 3/5 = 9/5.
4 x 3/5 = 12/5.
5 x 4/5 = 20/5.
The next four multiples of 3/5 are 6/5, 9/5, 12/5, 20/5.

Question 2.
\(\frac{2}{6}\) ,
Type below:
__________

Answer:
4/6, 6/6, 8/6, 10/6

Explanation:
1 x 2/6 = 2/6.
2 x 2/6 = 4/6.
3 x 2/6 = 6/6.
4 x 2/6 = 8/6.
5 x 2/6 = 10/6.
The next four multiples of 2/6 are 4/6, 6/6, 8/6, 10/6.

Question 3.
\(\frac{4}{8}\) ,
Type below:
__________

Answer:
8/8, 12/8, 16/8, 20/8

Explanation:
1 x 4/8 = 4/8.
2 x 4/8 = 8/8.
3 x 4/8 = 12/8.
4 x 4/8 = 16/8.
5 x 4/8 = 20/8.
The next four multiples of 4/8 are 8/8, 12/8, 16/8, 20/8.

Question 4.
\(\frac{5}{10}\) ,
Type below:
__________

Answer:
10/10, 15/10, 20/10, 25/10

Explanation:
1 x 5/10 = 5/10.
2 x 5/10 = 10/10.
3 x 5/10 = 15/10.
4 x 5/10 = 20/10.
5 x 5/10 = 25/10.
The next four multiples of 5/10 are 10/10, 15/10, 20/10, 25/10.

Write the product as the product of a whole number and a unit fraction.

Question 5.

2 × \(\frac{4}{5}\) =
Type below:
__________

Answer:
8/5 = 8 x 1/5

Explanation:
1 group of 4/5 = 4/5
2 groups of 4/5 = 8/5
2 x 4/5 = 8/5 = 8 x 1/5.

Question 6.

5 × \(\frac{2}{3}\) =
Type below:
__________

Answer:
10/3 = 10 x 1/3

Explanation:
1 group of 2/3 = 2/3
2 group of 2/3 = 4/3
3 group of 2/3 = 6/3
4 group of 2/3 = 8/3
5 group of 2/3 = 10/3
5 x 2/3 = 10/3 = 10 x 1/3.

Problem Solving

Question 7.
Jessica is making 2 loaves of banana bread. She needs \(\frac{3}{4}\) cup of sugar for each loaf. Her measuring cup can only hold \(\frac{1}{4}\) cup of sugar. How many times will Jessica need to fill the measuring cup in order to get enough sugar for both loaves of bread?
_____ times

Answer:
6 times

Explanation:
Jessica is making 2 loaves of banana bread. She needs a 3/4 cup of sugar for each loaf.
For 2 loaves, she needs 2 x 3/4 = 6/4 cups of sugar.
Her measuring cup can only hold 1/4 cup of sugar. So, to get the 3/4 cup of sugar, she needs to fill the cup 3 times. 1/4 + 1/4 + 1/4 = 3/4.
So, to fill 2 loaves, she needs to fill cup 3 x 2 = 6 times.

Question 8.
A group of four students is performing an experiment with salt. Each student must add \(\frac{3}{8}\) teaspoon of salt to a solution. The group only has a \(\frac{1}{8}\) teaspoon measuring spoon. How many times will the group need to fill the measuring spoon in order to perform the experiment?
_____ times

Answer:
12 times

Explanation:
A group of four students is performing an experiment with salt. Each student must add a 3/8 teaspoon of salt to a solution. 4 x 3/8 = 12/8 teaspoon of salt required to finish the experiment.
If they have 1/8 teaspoon measuring spoon, 12 x 1/8.
So, the group needs to fill the measuring spoon 12 times in order to perform the experiment.

Common Core – New – Page No. 466

Lesson Check

Question 1.
Eloise made a list of some multiples of \(\frac{5}{8}\). Which of the following lists could be Eloise’s list?
Options:
a. \(\frac{5}{8}, \frac{10}{16}, \frac{15}{24}, \frac{20}{32}, \frac{25}{40}\)
b. \(\frac{5}{8}, \frac{10}{8}, \frac{15}{8}, \frac{20}{8}, \frac{25}{8}\)
c. \(\frac{5}{8}, \frac{6}{8}, \frac{7}{8}, \frac{8}{8}, \frac{9}{8}\)
d. \(\frac{1}{8}, \frac{2}{8}, \frac{3}{8}, \frac{4}{8}, \frac{5}{8}\)

Answer:
b. \(\frac{5}{8}, \frac{10}{8}, \frac{15}{8}, \frac{20}{8}, \frac{25}{8}\)

Explanation:
1 x 5/8 = 5/8.
2 x 5/8 = 10/8.
3 x 5/8 = 15/8.
4 x 5/8 = 20/8.
5 x 5/8 = 25/8.
The next four multiples of 5/8 are 10/8, 15/8, 20/8, 25/8.

Go Math Workbook Grade 4 Pdf Multiples of Fractions Lesson 8.2 Question 2.
David is filling five \(\frac{3}{4}\) quart bottles with a sports drink. His measuring cup only holds \(\frac{1}{4}\) quart. How many times will David need to fill the measuring cup in order to fill the 5 bottles?
Options:
a. 5
b. 10
c. 15
d. 20

Answer:
c. 15

Explanation:
David is filling five 3/4 quart bottles with a sports drink = 5 x 3/4 = 15/4.
His measuring cup only holds 1/4 quart.
So, 15 x 1/4. David needs to fill the measuring cup 15 times in order to fill the 5 bottles.

Spiral Review

Question 3.
Ira has 128 stamps in his stamp album. He has the same number of stamps on each of the 8 pages. How many stamps are on each page?
Options:
a. 12
b. 14
c. 16
d. 18

Answer:
c. 16

Explanation:
Ira has 128 stamps in his stamp album. He has the same number of stamps on each of the 8 pages.
128/8 = 16 stamps on each page.

Question 4.
Ryan is saving up for a bike that costs $198. So far, he has saved $15 per week for the last 12 weeks. How much more money does Ryan need in order to be able to buy the bike?
Options:
a. $ 8
b. $ 18
c. $ 48
d. $ 180

Answer:
b. $ 18

Explanation:
Ryan is saving up for a bike that costs $198.
So far, he has saved $15 per week for the last 12 weeks = $15 x 12 = $180.
$198 – $180 = $18 needed in order to buy the bike.

Question 5.
Tina buys 3 \(\frac{7}{8}\) yards of material at the fabric store. She uses it to make a skirt. Afterward, she has 1 \(\frac{3}{8}\) yards of the fabric left over. How many yards of material did Tina use?
Options:
a. 1 \(\frac{4}{8}\)
b. 2 \(\frac{1}{8}\)
c. 2 \(\frac{4}{8}\)
d. 5 \(\frac{2}{8}\)

Answer:
c. 2 \(\frac{4}{8}\)

Explanation:
Tina buys 3 7/8 yards of material at the fabric store. She uses it to make a skirt. Afterward, she has 1 3/8 yards of the fabric left over.
3 -1 = 2; 7/8 – 3/8 = 4/8. So, the answer is 2 4/8.

Question 6.
Which list shows the fractions in order from least to greatest?
Options:
a. \(\frac{2}{3}, \frac{3}{4}, \frac{7}{12}\)
b. \(\frac{7}{12}, \frac{3}{4}, \frac{2}{3}\)
c. \(\frac{3}{4}, \frac{2}{3}, \frac{7}{12}\)
d. \(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)

Answer:
d. \(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)

Explanation:
2/3 = 0.666
3/4 = 0.75
7/12 = 0.5833
7/12, 2/3, 3/4

Page No. 467

Choose the best term from the box.

Question 1.
A __________ of a number is the product of the number and a counting number.
__________

Answer:
Multiple

Question 2.
A _________ always has a numerator of 1.
_________

Answer:
Unit Fraction

List the next four multiples of the unit fraction.

Question 3.
\(\frac{1}{2}\) ,
Type below:
_________

Answer:
2/2, 3/2, 4/2, 5/2

Explanation:
1 x 1/2 = 1/2.
2 x 1/2 = 2/2.
3 x 1/2 = 3/2.
4 x 1/2 = 4/2.
5 x 1/2 = 5/2.
The next four multiples of 1/2 are 2/2, 3/2, 4/2, 5/2.

Question 4.
\(\frac{1}{5}\) ,
Type below:
_________

Answer:
2/5, 3/5, 4/5, 5/5

Explanation:
1 x 1/5 = 1/5.
2 x 1/5 = 2/5.
3 x 1/5 = 3/5.
4 x 1/5 = 4/5.
5 x 1/5 = 5/5.
The next four multiples of 1/5 are 2/5, 3/5, 4/5, 5/5.

Write the fraction as a product of a whole number and a unit fraction.

Question 5.
\(\frac{4}{10}\) = _____ × \(\frac{1}{10}\)

Answer:
4

Explanation:
4/10 = 4 x 1/10

Question 6.
\(\frac{8}{12}\) = _____ × \(\frac{1}{12}\)

Answer:
8

Explanation:
8/12 = 8 x 1/12

Question 7.
\(\frac{3}{4}\) = _____ × \(\frac{1}{4}\)

Answer:
3

Explanation:
3/4 = 3 x 1/4

List the next four multiples of the fraction.

Question 8.
\(\frac{2}{5}\) ,
Type below:
_________

Answer:
4/5, 6/5, 8/5, 10/5

Explanation:
1 x 2/5 = 1/5.
2 x 2/5 = 4/5.
3 x 2/5 = 6/5.
4 x 2/5 = 8/5.
5 x 2/5 = 10/5.
The next four multiples of 1/5 are 4/5, 6/5, 8/5, 10/5.

Question 9.
\(\frac{5}{6}\) ,
Type below:
_________

Answer:
10/6, 15/6, 20/6, 25/6

Explanation:
1 x 5/6 = 5/6.
2 x 5/6 = 10/6.
3 x 5/6 = 15/6.
4 x 5/6 = 20/6.
5 x 5/6 = 25/6.
The next four multiples of 5/6 are 10/6, 15/6, 20/6, 25/6.

Write the product as the product of a whole number and a unit fraction.

Question 10.

4 × \(\frac{2}{6}\) =
Type below:
_________

Answer:
8/6 = 8 x 1/6

Explanation:
1 group of 2/6 = 2/6
2 groups of 2/6 = 4/6
3 groups of 2/6 = 6/6
4 groups of 2/6 = 8/6
4 x 2/6 = 8/6 = 8 x 1/6.

Question 11.

3 × \(\frac{3}{8}\) =
Type below:
_________

Answer:
9/8 = 9 x 1/8

Explanation:
1 group of 3/8 = 3/8
2 groups of 3/8 = 6/8
3 groups of 3/8 = 9/8
3 x 3/8 = 9/8 = 9 x 1/8.

Page No. 468

Question 12.
Pedro cut a sheet of poster board into 10 equal parts. His brother used some of the poster board and now \(\frac{8}{10}\) is left. Pedro wants to make a sign from each remaining part of the poster board. How many signs can he make?
______ signs

Answer:
8 signs

Explanation:
Pedro cut a sheet of poster board into 10 equal parts.
His brother uses some of the poster board and now an 8/10 is left.
So, the remaining part of the b\poster board is 8/10 parts.
Pedro can use 8/ 10 parts of the board to make signs.
So, he can make 8 signs.

Question 13.
Ella is making 3 batches of banana milkshakes. She needs \(\frac{3}{4}\) gallon of milk for each batch. Her measuring cup holds \(\frac{1}{4}\) gallon. How many times will she need to fill the measuring cup to make all 3 batches of milkshakes?
______ times

Answer:
9 times

Explanation:
Ella is making 3 batches of banana milkshakes. She needs 3/4 gallon of milk for each batch. So, she needs 3 x 3/4 = 9/4 cups for 3 batches of banana milkshakes. Her measuring cup holds 1/4 gallon.
9/4 = 9 x 1/4.
So, Ella needs to fill the measuring cup 9 times to make all 3 batches of milkshakes.

Question 14.
Darren cut a lemon pie into 8 equal slices. His friends ate some of the pie and now \(\frac{5}{8}\) is left. Darren wants to put each slice of the leftover pie on its own plate. What part of the pie will he put on each plate?
\(\frac{□}{□}\) of the pie on each plate.

Answer:
5/8 of the pie on each plate

Explanation:
Darren cut a lemon pie into 8 equal slices. His friends ate some of the pie and now 5/8 is left. So, 5 pie slices leftover.
Darren can put 5/8 parts of the pie on each plate.

Question 15.
Beth is putting liquid fertilizer on the plants in 4 flowerpots. Her measuring spoon holds \(\frac{1}{8}\) teaspoon. The directions say to put \(\frac{5}{8}\) teaspoon of fertilizer in each pot. How many times will Beth need to fill the measuring spoon to fertilize the plants in the 4 pots?
______ times

Answer:
20 times

Explanation:
Beth is putting liquid fertilizer on the plants in 4 flowerpots. Her measuring spoon holds 1/8 teaspoon.
The directions say to put 5/8 teaspoons of fertilizer in each pot. So, 4 x 5/8 = 20/8.
20/8 = 20 x 1/8. Beth needs to fill the measuring spoon 20 times to fertilize the plants in the 4 pots.

Page No. 471

Question 1.
Find the product of 3 × \(\frac{5}{8}\).
1 group of \(\frac{5}{8}\) = \(\frac{□}{8}\)
2 groups of \(\frac{5}{8}\) = \(\frac{□}{8}\)
3 groups of \(\frac{5}{8}\) = \(\frac{□}{8}\)
3 × \(\frac{5}{8}\) = \(\frac{□}{□}\)

Answer:
15/8

Explanation:
1 group of 5/8 = 2/8
2 groups of 5/8 = 4/8
3 groups of 5/8 = 6/8
3 x 5/8 = 15/8.

Multiply.

Question 2.
2 × \(\frac{4}{5}\) = \(\frac{□}{□}\)

Answer:
8/5

Explanation:
1 group of 4/5 = 4/5
2 groups of 4/5 = 8/5
2 x 4/5 = 8/5.

Question 3.
4 × \(\frac{2}{3}\) = \(\frac{□}{□}\)

Answer:
8/3

Explanation:
1 group of 2/3 = 2/3
2 groups of 2/3 = 4/3
3 groups of 2/3 = 6/3
4 groups of 2/3 = 8/3
4 x 2/3 = 8/3

Question 4.
5 × \(\frac{3}{10}\) = \(\frac{□}{□}\)

Answer:
15/10

Explanation:
1 group of 3/10 = 3/10
2 groups of 3/10 = 6/10
3 groups of 3/10 = 9/10
4 groups of 3/10 = 12/10
5 groups of 3/10 = 15/10
5 x 3/10 = 15/10

Question 5.
4 × \(\frac{5}{6}\) = \(\frac{□}{□}\)

Answer:
20/6

Explanation:
1 group of 5/6 = 5/6
2 groups of 5/6 = 10/6
3 groups of 5/6 = 15/6
4 groups of 5/6 = 20/6
4 x 5/6 = 20/6

Multiply.

Question 6.
2 × \(\frac{7}{12}\) = \(\frac{□}{□}\)

Answer:
7/6

Explanation:
1 group of 7/12 = 7/12
2 groups of 7/12 = 14/12
2 x 7/12 = 14/12 = 7/6

Question 7.
6 × \(\frac{3}{8}\) = \(\frac{□}{□}\)

Answer:
9/4

Explanation:
1 group of 3/8 = 3/8
2 groups of 3/8 = 6/8
3 groups of 3/8 = 9/8
4 groups of 3/8 = 12/8
5 groups of 3/8 = 15/8
6 groups of 3/8 = 18/8
6 x 3/8 = 18/8 = 9/4

Question 8.
5 × \(\frac{2}{4}\) = \(\frac{□}{□}\)

Answer:
5/2

Explanation:
1 group of 2/4 = 2/4
2 groups of 2/4 = 4/4
3 groups of 2/4 = 6/4
4 groups of 2/4 = 8/4
5 groups of 2/4 = 10/4
5 x 2/4 = 10/4 = 5/2

Question 9.
3 × \(\frac{4}{6}\) = \(\frac{□}{□}\)

Answer:
2

Explanation:
1 group of 4/6 = 4/6
2 groups of 4/6 = 8/6
3 groups of 4/6 = 12/6
3 x 4/6 = 12/6 = 2

Question 10.
2 × \(\frac{5}{10}\) = \(\frac{□}{□}\)

Answer:
2

Explanation:
1 group of 5/10 = 5/10
2 groups of 5/10 = 10/10
2 x 10/10 = 2 x 1 = 2

Question 11.
4 × \(\frac{2}{8}\) = \(\frac{□}{□}\)

Answer:
1

Explanation:
1 group of 2/8 = 2/8
2 groups of 2/8 = 4/8
3 groups of 2/8 = 6/8
4 groups of 2/8 = 8/8
4 x 2/8 = 8/8 = 1

Look for a Pattern Algebra Write the unknown number.

Question 12.
□ × \(\frac{2}{3}\) = \(\frac{12}{3}\)
□ = ____

Answer:
6

Explanation:
Let the unknown number is s.
s x 2/3 = 12/3
s = 12/3 x 3/2 = 6.

Question 13.
5 × \(\frac{□}{4}\) = \(\frac{10}{4}\)
□ = ____

Answer:
2

Explanation:
Let the unknown number is s.
5 x s/4 = 10/4
5/4 x s = 10/4
s = 10/4 x 4/5 =2.

Question 14.
2 × \(\frac{7}{□}\) = \(\frac{14}{8}\)
□ = ____

Answer:
8

Explanation:
Let the unknown number is s.
2 x 7/s = 14/8
14/s = 14/8
s x 14/8 = 14
s = 14 x 8/14
s = 8.

Page No. 472

Question 15.
Lisa makes clothes for pets. She needs \(\frac{5}{6}\) yard of fabric to make 1 dog coat. How much fabric does she need to make 3 dog coats?
a. What do you need to find?
Type below:
_________

Answer:
The number of fabric yards required for 3 dog coats

Question 15.
b. What information do you need?
Type below:
_________

Answer:
How much she needs of fabric for 1 dog coat can help to find 3 dog coats.

Question 15.
c. Show the steps you use to solve the problem.
Type below:
_________

Answer:
Lisa makes clothes for pets. She needs a 5/6 yard of fabric to make 1 dog coat.
For 3 dogs = 5/6 x 3 =5/2

Question 15.
d. Complete the sentence.
Lisa needs _____ yards of fabric to make 3 dog coats.
\(\frac{□}{□}\)

Answer:
Lisa needs a 5/2 yard of fabric to make 3 dog coats.

Go Math Grade 4 Chapter 8 Answer Key Pdf Question 16.
Manuel’s small dog eats \(\frac{2}{4}\) bag of dog food in 1 month. His large dog eats \(\frac{3}{4}\) bag of dog food in 1 month. How many bags do both dogs eat in 6 months?
\(\frac{□}{□}\) bags

Answer:
2 bags

Explanation:
Manuel’s small dog eats a 2/4 bag of dog food in 1 month. His large dog eats a 3/4 bag of dog food in 1 month.
In total 2/4 + 3/4 = 5/4 bag of dog food eaten in 1 month.
So, for 6 months = 6 x 5/4 = 30/4 = 15/2.
So, 2 bags are needed for 6 months.

Question 17.
Select the correct product for the equation.
9 × \(\frac{2}{12}\) = □
3 × \(\frac{6}{7}\) = □
6 × \(\frac{4}{7}\) = □
8 × \(\frac{3}{12}\) = □
Type below:
_________

Answer:
8 × \(\frac{3}{12}\) = 2

Explanation:
9 × \(\frac{2}{12}\) = 3/2
3 × \(\frac{6}{7}\) = 18/7
6 × \(\frac{4}{7}\) = 24/7
8 × \(\frac{3}{12}\) = 2

Common Core – New – Page No. 473

Multiply a Fraction by a Whole Number Using Models

Multiply.

Question 1.

Answer:

Question 2.
3 × \(\frac{2}{5}\) = \(\frac{□}{□}\)

Answer:

3 x 2/5 = 6/5

Question 3.
7 × \(\frac{3}{10}\) = \(\frac{□}{□}\)

Answer:

7 x 3/10 = 21/10

Question 4.
3 × \(\frac{5}{12}\) = \(\frac{□}{□}\)

Answer:

3 x 5/12 = 15/12

Question 5.
6 × \(\frac{3}{4}\) = \(\frac{□}{□}\)

Answer:

6 x 3/4 = 18/4

Question 6.
4 × \(\frac{2}{8}\) = \(\frac{□}{□}\)

Answer:

4 x 2/8 = 8/8

Question 7.
5 × \(\frac{2}{3}\) = \(\frac{□}{□}\)

Answer:

5 x 2/3 = 10/3

Question 8.
2 × \(\frac{7}{8}\) = \(\frac{□}{□}\)

Answer:

2 x 7/8 = 14/8

Question 9.
6 × \(\frac{4}{5}\) = \(\frac{□}{□}\)

Answer:

6 x 4/5 = 28/5

Problem Solving

Question 10.
Matthew walks \(\frac{5}{8}\) mile to the bus stop each morning. How far will he walk in 5 days?
\(\frac{□}{□}\)

Answer:
25/8 miles

Explanation:
Matthew walks 5/8 mile to the bus stop each morning.
In 5 days, 5 x 5/8 = 25/8 miles.

Question 11.
Emily uses \(\frac{2}{3}\) cup of milk to make one batch of muffins. How many cups of milk will Emily use if she makes 3 batches of muffins?
\(\frac{□}{□}\)

Answer:
6/3 cups of milk

Explanation:
Emily uses a 2/3 cup of milk to make one batch of muffins.
Emily use 3 x 2/3 = 6/3 cups of milk to make 3 batches of muffins

Common Core – New – Page No. 474

Lesson Check

Question 1.
Aleta’s puppy gained \(\frac{3}{8}\) pound each week for 4 weeks. Altogether, how much weight did the puppy gain during the 4 weeks?
Options:
a. \(\frac{8}{12}\) pound
b. 1 \(\frac{2}{8}\) pounds
c. \(\frac{12}{8}\) pounds
d. 4 \(\frac{3}{8}\) pounds

Answer:
6/3 cups of milk

Explanation:
Aleta’s puppy gained 3/8 pound each week.
It gained 4 x 3/8 = 12/8 pounds in 4 weeks.

Question 2.
Pedro mixes \(\frac{3}{4}\) teaspoon of plant food into each gallon of water. How many teaspoons of plant food should Pedro mix into 5 gallons of water?
Options:
a. \(\frac{3}{20}\) teaspoon
b. \(\frac{4}{15}\) teaspoon
c. \(\frac{8}{4}\) teaspoons
d. \(\frac{15}{4}\) teaspoons

Answer:
d. \(\frac{15}{4}\) teaspoons

Explanation:
If Pedro mixes 3/4 teaspoon of plant food into each gallon of water, then 5 x 3/4 = 15/4 teaspoon of plant food mix into 5 gallons of water.

Spiral Review

Question 3.
Ivana has \(\frac{3}{4}\) pound of hamburger meat. She makes 3 hamburger patties. Each patty weighs the same amount. How much does each hamburger patty weigh?
Options:
a. \(\frac{1}{4}\) pound
b. \(\frac{1}{3}\) pound
c. 2 \(\frac{1}{4}\) pounds
d. 3 pounds

Answer:
a. \(\frac{1}{4}\) pound

Explanation:
Ivana has 3/4 pound of hamburger meat. She makes 3 hamburger patties.
Each patty weighs the same amount. So, each hamburger patty weight 1/4 pound.

Question 4.
Which of the following expressions is NOT equal to \(\frac{7}{10}\)?
Options:
a. \(\frac{5}{10}+\frac{1}{10}+\frac{1}{10}\)
b. \(\frac{2}{10}+\frac{2}{10}+\frac{3}{10}\)
c. \(\frac{3}{10}+\frac{3}{10}+\frac{2}{10}\)
d. \(\frac{4}{10}+\frac{2}{10}+\frac{1}{10}\)

Answer:
c. \(\frac{3}{10}+\frac{3}{10}+\frac{2}{10}\)

Explanation:
a. \(\frac{5}{10}+\frac{1}{10}+\frac{1}{10}\) = 7/10
b. \(\frac{2}{10}+\frac{2}{10}+\frac{3}{10}\) = 7/10
c. \(\frac{3}{10}+\frac{3}{10}+\frac{2}{10}\) = 8/10
d. \(\frac{4}{10}+\frac{2}{10}+\frac{1}{10}\) = 7/10

Question 5.
Lance wants to find the total length of 3 boards. He uses the expression 3 \(\frac{1}{2}\) + (2 + 4 \(\frac{1}{2}\)). How can Lance rewrite the expression using both the Associative and Commutative Properties of Addition?
Options:
a. 5 + 4 \(\frac{1}{2}\)
b. (3 \(\frac{1}{2}\) + 2) + 4 \(\frac{1}{2}\)
c. 2 + (3 \(\frac{1}{2}\) + 4 \(\frac{1}{2}\))
d. 3 \(\frac{1}{2}\) + (4 \(\frac{1}{2}\) + 2)

Answer:
She can write as (3 \(\frac{1}{2}\) + 2) + 4 \(\frac{1}{2}\)

Question 6.
Which of the following statements is true?
Options:
a. \(\frac{5}{8}>\frac{9}{10}\)
b. \(\frac{5}{12}>\frac{1}{3}\)
c. \(\frac{3}{6}>\frac{4}{5}\)
d. \(\frac{1}{2}>\frac{3}{4}\)

Answer:
6/3 cups of milk

Explanation:
0.625 > 0.9
0.416 > 0.333
0.5 > 0.8
0.5 > 0.75

Page No. 477

Question 1.
2 × 3 \(\frac{2}{3}\) = □
_____ \(\frac{□}{□}\)

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

Explanation:
3 \(\frac{2}{3}\) = 11/3
2 x 11/3 = 22/3
22/3 = 7 and remainder 1. So, 22/3 = 7 (1/3)

Multiply. Write the product as a mixed number.

Question 2.
6 × \(\frac{2}{5}\) = _____ \(\frac{□}{□}\)

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

Explanation:
6 × \(\frac{2}{5}\) = 12/5. 12/5 = 2 and remainder. So, 12/5 = 2 2/5

Question 3.
3 × 2 \(\frac{3}{4}\) = _____ \(\frac{□}{□}\)

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

Explanation:
2 \(\frac{3}{4}\) = 11/4
3 x 11/4 = 33/4. 33/4 = 8 and the remainder 1. So, 33/4 = 8 1/4

Go Math 4th Grade Lesson 8.4 Homework Answer Key Question 4.
4 × 1 \(\frac{5}{6}\) = _____ \(\frac{□}{□}\)

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

Explanation:
1 \(\frac{5}{6}\) = 11/6
4 x 11/6 = 44/6. 44/6 = 7 and the remainder 2. So, 44/6 = 7 2/6

Question 5.
4 × \(\frac{5}{8}\) = _____ \(\frac{□}{□}\)

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

Explanation:
4 × \(\frac{5}{8}\) = 5/2. 5/2 = 2 and remainder 1. So, 5/2 = 2 1/2

Question 6.
6 × \(\frac{5}{12}\) = _____ \(\frac{□}{□}\)

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

Explanation:
6 × \(\frac{5}{12}\) = 5/2. 5/2 = 2 and remainder 1. So, 5/2 = 2 1/2

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

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

Explanation:
3 \(\frac{1}{2}\) = 7/2
3 x 7/2 = 21/2. 21/2 = 10 and remainder 1. So, 21/2 = 10 1/2

Question 8.
2 × 2 \(\frac{2}{3}\) = _____ \(\frac{□}{□}\)

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

Explanation:
2 \(\frac{2}{3}\) = 8/3
2 x 8/3 = 16/3. 16/3 = 5 and remainder 1. So, 16/3 = 5 1/3

Question 9.
5 × 1 \(\frac{2}{4}\) = _____ \(\frac{□}{□}\)

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

Explanation:
1 \(\frac{2}{4}\) = 6/4
5 x 6/4 = 30/4 = 15/2. 15/2 = 7 and remainder 1. So, 15/2 = 7 1/2

Question 10.
4 × 2 \(\frac{2}{5}\) = _____ \(\frac{□}{□}\)

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

Explanation:
2 \(\frac{2}{5}\) = 12/5
4 x 12/5 = 48/5. 48/5 = 9 and remainder 3. So, 48/5 = 9 3/5

Look for a Pattern Algebra Write the unknown number.

Question 11.
□ × 2 \(\frac{1}{3}\) = 9 \(\frac{1}{3}\)
□ = ______

Answer:
4

Explanation:
2 \(\frac{1}{3}\) = 7/3
9 \(\frac{1}{3}\) = 28/3
Let the unknown numer s.
s x 7/3 = 28/3
s = 4

Question 12.
3 × 2 \(\frac{2}{□}\) = 7 \(\frac{2}{4}\)
□ = ______

Answer:
4

Explanation:
7 \(\frac{2}{4}\) = 30/4
Let the unknown number s. If s is 4, 3 × 2 \(\frac{2}{4}\) = 3 x 10/4 = 30/4.
So, the unknown number is 4.

Question 13.
3 × □ \(\frac{3}{8}\) = 4 \(\frac{1}{8}\)
□ = ______

Answer:
1

Explanation:
4 \(\frac{1}{8}\) = 33/8
Let the unknown number is s. If s is 1, 3 × 1 \(\frac{3}{8}\) = 3 x 11/8 = 33/8.

Question 14.
Describe two different ways to write \(\frac{7}{3}\) as a mixed number.
Type below:
_________

Answer:
One is 2\(\frac{1}{3}\)
Another one is 2 + 1/3

Explanation:
7/3 = 2 and the remainder is 1. So, 2 1/3 is one mixed fraction.
Seond method is 3/3 + 3/3 + 1/3 = 2 + 1/3.

Page No. 478

Use the recipe for 15–18.

Question 15.
Otis plans to make 3 batches of sidewalk chalk. How much plaster of Paris does he need?
______ \(\frac{□}{□}\) cups plaster of Paris

Answer:
4\(\frac{1}{2}\) cups plaster of Paris

Explanation:
1\(\frac{1}{2}\) = 3/2 + 3/2 + 3/2 = 9/2
9/2 = 4, the remainder is 1. So, 4 1/2 cups plaster of Paris need for 3 batches of sidewalk chalk.

Question 16.
What’s the Question? The answer is \(\frac{32}{3}\).
Type below:
_________

Answer:
How many tablespoons of powdered paint are needed for 4 batches of chalk?

Question 17.
Patty has 2 cups of warm water. Is that enough water to make 4 batches of sidewalk chalk? Explain how you know without finding the exact product.
______

Answer:
No. 4 x 1/2 = 2 and also 3/4 is greater than 1/2. So, 4 x 3/4 is greater than 2.

Go Math Lesson 8.4 4th Grade Question 18.
Rita makes sidewalk chalk 2 days a week. Each of those days, she spends 1 \(\frac{1}{4}\) hours making the chalk. How much time does Rita spend making sidewalk chalk in 3 weeks?
______ \(\frac{□}{□}\) hours

Answer:
7\(\frac{1}{2}\) hours

Explanation:
Rita makes sidewalk chalk 2 days a week. Each of those days, she spends 1 1/4 hours making the chalk.
1 week = 2 x 5/4 = 10/4 = 5/2.
3 weeks = 3 x 5/2 = 15/2 = 7 1/2.

Question 19.
Oliver has music lessons Monday, Wednesday, and Friday. Each lesson is \(\frac{3}{4}\) of an hour. Oliver says he will have lessons for 3 \(\frac{1}{2}\) hours this week. Without multiplying, explain how you know Oliver is incorrect.
Type below:
__________

Answer:
3/4 is less than 1, and 1 × 3 = 3. So 3/4 × 3 will also be less than 3.
Oliver’s answer, 3 1/2 is greater than 3, so it is incorrect.

Common Core – New – Page No. 479

Multiply a Fraction or Mixed Number by a Whole Number.

Multiply. Write the product as a mixed number.

Question 1.

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

Explanation:
5 x 3/10 = 15/10 = 1 and remainder is 5. So, the mixed fraction is 1 5/10

Question 2.
3 × \(\frac{3}{5}\) =
______ \(\frac{□}{□}\)

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

Explanation:
3 x 3/5 = 9/5 = 1 and remainder is 4. So, the mixed fraction is 1 4/5

Question 3.
5 × \(\frac{3}{4}\) =
______ \(\frac{□}{□}\)

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

Explanation:
15/4 = 3 and remainder is 3. So, the mixed fraction is 3 3/4

Question 4.
4 × 1 \(\frac{1}{5}\) =
______ \(\frac{□}{□}\)

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

Explanation:
1 \(\frac{1}{5}\) = 6/5.
4 x 6/5 = 24/5 = 4 and the remainder is 4. So, the mixed fraction is 4 4/5

Question 5.
2 × 2 \(\frac{1}{3}\) =
______ \(\frac{□}{□}\)

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

Explanation:
2 \(\frac{1}{3}\) = 7/3.
2 x 7/3 = 14/3.
14/3 = 4 and the remainder is 2. So, the mixed fraction is 4 2/3

Question 6.
5 × 1 \(\frac{1}{6}\) =
______ \(\frac{□}{□}\)

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

Explanation:
1 \(\frac{1}{6}\) = 7/6
5 x 7/6 = 35/6.
35/6 = 5 and the remainder is 5. So, the mixed fraction is 5 5/6

Question 7.
2 × 2 \(\frac{7}{8}\) =
______ \(\frac{□}{□}\)

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

Explanation:
2 \(\frac{7}{8}\) = 23/8
2 x 23/8 = 46/8 = 6 1/1

Question 8.
7 × 1 \(\frac{3}{4}\) =
______ \(\frac{□}{□}\)

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

Explanation:
1 \(\frac{3}{4}\) = 7/4
7 x 7/4 = 39/4
39/4 = 9 and the remainder is 3. So, the mixed fraction is 9 3/4

Question 9.
8 × 1 \(\frac{3}{5}\) =
______ \(\frac{□}{□}\)

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

Explanation:
1 \(\frac{3}{5}\) = 8/5
8 x 8/5 = 64/5
64/5 = 12 and the remainder is 4. So, the mixed fraction is 12 4/5

Problem Solving

Question 10.
Brielle exercises for \(\frac{3}{4}\) hour each day for 6 days in a row. Altogether, how many hours does she exercise during the 6 days?
______ \(\frac{□}{□}\)

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

Explanation:
6 x 3/4 = 18/4 = 4 and the remainder is 2. So, the mixed fraction is 4 2/4.

Question 11.
A recipe for quinoa calls for 2 \(\frac{2}{3}\) cups of milk. Conner wants to make 4 batches of quinoa. How much milk does he need?
______ \(\frac{□}{□}\)

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

Explanation:
quinoa calls for 8/3 cups of milk. Conner wants to make 4 batches of quinoa.
So, 4 x 8/3 = 32/3 = 10 and the remainder is 2. So, the mixed fraction is 10 2/3

Common Core – New – Page No. 480

Lesson Check

Question 1.
A mother is 1 \(\frac{3}{4}\) times as tall as her son. Her son is 3 feet tall. How tall is the mother?
Options:
a. 4 \(\frac{3}{4}\) feet
b. 5 \(\frac{1}{4}\) feet
c. 5 \(\frac{1}{2}\) feet
d. 5 \(\frac{3}{4}\) feet

Answer:
b. 5 \(\frac{1}{4}\) feet

Explanation:
A mother is 1 3/4 times as tall as her son. Her son is 3 feet tall.
So, 3 x 7/4 = 21/4 = 5 and the remainder is 1. The mixed fraction is 5 1/4 feet.

Question 2.
The cheerleaders are making a banner that is 8 feet wide. The length of the banner is 1 \(\frac{1}{3}\) times the width of the banner. How long is the banner?
Options:
a. 8 \(\frac{1}{3}\) feet
b. 8 \(\frac{3}{8}\) feet
c. 10 \(\frac{1}{3}\) feet
d. 10 \(\frac{2}{3}\) feet

Answer:
d. 10 \(\frac{2}{3}\) feet

Explanation:
The cheerleaders are making a banner that is 8 feet wide. he length of the banner is 1 1/3 times the width of the banner.
So, 8 x 4/3 = 32/3 =10 and the remainder is 2. The mixed fraction is 10 2/3 feet.

Spiral Review

Question 3.
Karleigh walks \(\frac{5}{8}\) mile to school every day. How far does she walk to school in 5 days?
Options:
a. \(\frac{5}{40}\) mile
b. \(\frac{25}{40}\) mile
c. \(\frac{10}{8}\) miles
d. \(\frac{25}{8}\) miles

Answer:
d. \(\frac{25}{8}\) miles

Explanation:
5 x 5/8 = 25/8.

Question 4.
Which number is a multiple of \(\frac{4}{5}\)?
Options:
a. \(\frac{8}{10}\)
b. \(\frac{12}{15}\)
c. \(\frac{16}{20}\)
d. \(\frac{12}{5}\)

Answer:
d. \(\frac{12}{5}\)

Explanation:
The multiple of \(\frac{4}{5}\) has the denominator 5. So, \(\frac{12}{5}\) is the correct answer.

Go Math Chapter 8 Grade 4 Answer Key Question 5.
Jo cut a key lime pie into 8 equal-size slices. The next day, \(\frac{7}{8}\) of the pie is left. Jo puts each slice on its own plate. How many plates does she need?
Options:
a. 5
b. 6
c. 7
d. 8

Answer:
c. 7

Explanation:
Jo cut a key lime pie into 8 equal-size slices. The next day, \(\frac{7}{8}\) of the pie is left. Jo puts each slice on its own plate. She needs 7 plates.

Question 6.
Over the weekend, Ed spent 1 \(\frac{1}{4}\) hours doing his math homework and 1 \(\frac{3}{4}\) hours doing his science project. Altogether, how much time did Ed spend doing homework over the weekend?
Options:
a. 3 hours
b. 2 \(\frac{3}{4}\) hours
c. 2 \(\frac{1}{2}\) hours
d. 2 hours

Answer:
a. 3 hours

Explanation:
5/4 + 7/4 = 12/4 = 3 hours

Page No. 483

Question 1.
Komodo dragons are the heaviest lizards on Earth. A baby Komodo dragon is 1 \(\frac{1}{4}\) feet long when it hatches. Its mother is 6 times as long. How long is the mother?
First, draw a bar model to show the problem.
Type below:
_________

Answer:

Question 1.
Then, write the equation you need to solve.
Type below:
_________

Answer:
A baby Komodo dragon is 5/4 feet.
Her mother is 6 x 5/4 = 30/4 feet long.

Question 1.
Finally, find the length of the mother Komodo dragon.
The mother Komodo dragon is _____ feet long.
______ \(\frac{□}{□}\)

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

Explanation:
30/4 = 7 and the remainder is 2. The mixed fraction is 7 2/4 feet.

Question 2.
What if a male Komodo dragon is 7 times as long as the baby Komodo dragon? How long is the male? How much longer is the male than the mother?
______ \(\frac{□}{□}\) feet long
______ \(\frac{□}{□}\) feet longer

Answer:
35/4 feet long
5/4 feet longer

Explanation:
If a male Komodo dragon is 7 times as long as the baby Komodo dragon, then 7 x 5/4 = 35/4.
35/4 – 30/4 = 5/4 feet male Komodo dragon is grater than female Komodo dragon.

Question 3.
The smallest hummingbird is the Bee hummingbird. It has a mass of about 1 \(\frac{1}{2}\) grams. A Rufous hummingbird’s mass is 3 times the mass of the Bee hummingbird. What is the mass of a Rufous hummingbird?
______ \(\frac{□}{□}\) grams

Answer:
9/2 grams

Explanation:

The smallest hummingbird is the Bee hummingbird. It has a mass of about 1 \(\frac{1}{2}\) grams. A Rufous hummingbird’s mass is 3 times the mass of the Bee hummingbird.
3 x 3/2 = 9/2 grams.

Question 4.
Sloane needs \(\frac{3}{4}\) hour to drive to her grandmother’s house. It takes her 5 times as long to drive to her cousin’s house. How long does it take to drive to her cousin’s house?
______ \(\frac{□}{□}\) hours

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

Explanation:
5 x 3/4 = 15/4
To drive to her cousin’s house, it takes 15/4 hours.

Page No. 484

Use the table for 5 and 6.

Payton has a variety of flowers in her garden. The table shows the average heights of the flowers.

tulip = 5/4 = 1.25
daisy = 5/2 = 2.5
tiger lily = 10/3 = 3.33
sunflower = 31/4 = 7.75

Question 5.
Make Sense of Problems What is the difference between the height of the tallest flower and the height of the shortest flower in Payton’s garden?
______ \(\frac{□}{□}\) feet

Answer:
6\(\frac{2}{4}\) feet

Explanation:
tallest flower = sunflower
shortest flower = tulip
The difference between the tallest flower and shortest flower = 31/4 – 5/4 = 26/4 =6 and the remainder is 2. So, the mixed fraction is 6 2/4 feet.

Question 6.
Payton says her average sunflower is 7 times the height of her average tulip. Do you agree or disagree with her statement? Explain your reasoning.
Type below:
_________

Answer:
I will disagree with her statement. Tulip = 5/4. 7 x 5/4 = 35/4. 31/4 is smaller than 35/4. So the statement is not correct.

Question 7.
Miguel ran 1 \(\frac{3}{10}\) miles on Monday. On Friday, Miguel ran 3 times as far as he did on Monday. How much farther did Miguel run on Friday than he did on Monday?
______ \(\frac{□}{□}\) miles

Answer:
3\(\frac{9}{10}\) miles

Explanation:
Miguel ran 13/10 miles on Monday.
On Friday, 3 x 13/10 = 39/10 miles = 3 and the remainder is 9. the mixed fraction is 3 9/10 miles

Question 8.
The table shows the lengths of different types of turtles at a zoo.

For numbers 8a–8d, select True or False for each statement.
a. Daisy is 4 times as long as Tuck.
i. True
ii. False

Answer:
ii. False

Explanation:
Tuck = 7/6
Lolly = 35/6
Daisy = 7/2
7/6 x 4 = 28/6.
So, the statement is false.

Question 8.
b. Lolly is 5 times as long as Tuck.
i. True
ii. False

Answer:
i. True

Explanation:
5 x 7/6 = 35/6.
So, the statement is true.

Question 8.
c. Daisy is 3 times as long as Tuck.
i. True
ii. False

Answer:
i. True

Explanation:
3 x 7/6 = 21/6 = 7/2
So, the statement is true.

Question 8.
d. Lolly is 2 times as long as Daisy.
i. True
ii. False

Answer:
ii. False

Explanation:
2 x 7/2 = 7.
So, the statement is false.

Common Core – New – Page No. 485

Problem Solving Comparison

Problems with Fractions

Read each problem and solve.

Question 1.
A shrub is 1 \(\frac{2}{3}\) feet tall. A small tree is 3 times as tall as the shrub. How tall is the tree?

Answer:
5 feet

Explanation:

Question 2.
You run 1 \(\frac{3}{4}\) miles each day. Your friend runs 4 times as far as you do. How far does your friend run each day?
__________ miles

Answer:
7 miles

Explanation:
4 x 7/4 = 7 miles each day

Question 3.
At the grocery store, Ayla buys 1 \(\frac{1}{3}\) pounds of ground turkey. Tasha buys 2 times as much ground turkey as Ayla. How much ground turkey does Tasha buy?
______ \(\frac{□}{□}\) pounds

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

Explanation:
2 x 4/3 = 8/3 = 2 and the remainder is 2. The mixed fraction is 2 2/3 pounds

Go Math Grade 4 Chapter 8 Review Test Answers Question 4.
When Nathan’s mother drives him to school, it takes \(\frac{1}{5}\) hour. When Nathan walks to school, it takes him 4 times as long to get to school. How long does it take Nathan to walk to school?
\(\frac{□}{□}\) hours

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

Explanation:
4 x 1/5 = 4/5 hour

Common Core – New – Page No. 486

Lesson Check

Question 1.
A Wilson’s Storm Petrel is a small bird with a wingspan of 1 \(\frac{1}{3}\) feet. A California Condor is a larger bird with a wingspan almost 7 times as wide as the wingspan of the petrel. About how wide is the wingspan of the California Condor?
Options:
a. \(\frac{4}{21}\) foot
b. 2 \(\frac{1}{3}\) feet
c. 7 \(\frac{1}{3}\) feet
d. 9 \(\frac{1}{3}\) feet

Answer:
d. 9 \(\frac{1}{3}\) feet

Explanation:
1 1/3 = 4/3.
7 x 4/3 = 28/3 feet = 9 and the remainder is 1. The mixed fraction is 9 1/3

Question 2.
The walking distance from the Empire State Building in New York City to Times Square is about \(\frac{9}{10}\) mile. The walking distance from the Empire State Building to Sue’s hotel is about 8 times as far. About how far is Sue’s hotel from the Empire State Building?
Options:
a. \(\frac{9}{80}\) mile
b. \(\frac{72}{80}\) mile
c. 1 \(\frac{7}{10}\) miles
d. 7 \(\frac{2}{10}\) miles

Answer:
d. 7 \(\frac{2}{10}\) miles

Explanation:
8 x 9/10 mile = 72/10 mile = 7 and the remainder is 2. The mixed fraction is 7 2/10 miles.

Spiral Review

Question 3.
Which of the following expressions is NOT equal to 3 × 2 \(\frac{1}{4}\)?
Options:
a. 3 × \(\frac{9}{4}\)
b. (3 × 2) + (3 × \(\frac{1}{4}\))
c. 6 \(\frac{3}{4}\)
d. 3 × 2 + \(\frac{1}{4}\)

Answer:
d. 3 × 2 + \(\frac{1}{4}\)

Explanation:
3 × 2 \(\frac{1}{4}\) = 3 x 9/4 = 27/4
a. 3 × \(\frac{9}{4}\) = 27/4
b. (3 × 2) + (3 × \(\frac{1}{4}\)) = 6 + 3/4 = 27/4
c. 6 \(\frac{3}{4}\) = 27/4
d. 3 × 2 + \(\frac{1}{4}\) = 6 + 1/4 = 25/4

Question 4.
At a bake sale, Ron sells \(\frac{7}{8}\) of an apple pie and \(\frac{5}{8}\) of a cherry pie. Altogether, how much pie does he sell at the bake sale?
Options:
a. \(\frac{2}{8}\)
b. \(\frac{12}{16}\)
c. \(\frac{12}{8}\)
d. \(\frac{35}{8}\)

Answer:
c. \(\frac{12}{8}\)

Explanation:
7/8 + 5/8 = 12/8
The bake sale 12/8 pie.

Question 5.
On a ruler, which measurement is between \(\frac{3}{16}\) inch and \(\frac{7}{8}\) inch?
Options:
a. \(\frac{1}{16}\) inch
b. \(\frac{1}{8}\) inch
c. \(\frac{11}{16}\) inch
d. \(\frac{15}{16}\) inch

Answer:
c. \(\frac{11}{16}\) inch

Question 6.
Which of the following numbers is composite?
Options:
a. 4
b. 3
c. 2
d. 1

Answer:
a. 4

Explanation:
4 has more than 2 factors.

Page No. 487

Question 1.
What are the next four multiples of \(\frac{1}{8}\)?
Type below:
_________

Answer:
2/8, 3/8, 4/8, 5/8

Explanation:
1 x 1/8 = 1/8.
2 x 1/8 = 2/8.
3 x 1/8 = 3/8.
4 x 1/8 = 4/8.
5 x 1/8 = 5/8.
Next four multiples of 1/8 are 2/8, 3/8, 4/8, 5/8.

Question 2.
Marta is making 3 servings of fruit salad. She adds \(\frac{3}{8}\) cup blueberries for each serving. Her measuring cup holds \(\frac{1}{8}\) cup. How many times must Marta measure \(\frac{1}{8}\) cup of blueberries to have enough for the fruit salad? Shade the models to show your answer.

Marta must measure \(\frac{1}{8}\) _________ cup times.
_________

Answer:

Marta must measure \(\frac{1}{8}\) 9 cup times.

Question 3.
Mickey exercises \(\frac{3}{4}\) hour every day. How many hours does he exercise in 8 days?
_____ hours

Answer:
6 hours

Explanation:
8 x 3/4 = 24/4 = 6

Page No. 488

Question 4.
Molly is baking for the Moms and Muffins event at her school. She will bake 4 batches of banana muffins. She needs 1 \(\frac{3}{4}\) cups of bananas for each batch of muffins.
Part A
Molly completed the multiplication below and said she needed 8 cups of bananas for 4 batches of muffins. What is Molly’s error?
\(4 \times 1 \frac{3}{4}=4 \times \frac{8}{4}=\times \frac{32}{4}=8\)
Type below:
_________

Answer:
4 x 1 3/4 = 4 x 8/4 = 8
Molly did not write the mixed number, 1 3/4 as a fraction correctly. 1 3/4 is not equal to 8/4.

Question 4.
Part B
What is the correct number of cups Molly needs for 4 batches of muffins? Explain how you found your answer.
_____ cups

Answer:
7 cups

Explanation:
She will bake 4 batches of banana muffins. She needs 7/4 cups of bananas for each batch of muffins.
So, if she prepares 4 batches of muffins = 4 x 7/4 = 7 cups of banana.

Question 5.
Which fraction is a multiple of \(\frac{1}{9}\)? Mark all that apply.
Options:
a. \(\frac{3}{9}\)
b. \(\frac{9}{12}\)
c. \(\frac{2}{9}\)
d. \(\frac{4}{9}\)
e. \(\frac{9}{10}\)
f. \(\frac{9}{9}\)

Answer:
a. \(\frac{3}{9}\)
c. \(\frac{2}{9}\)
d. \(\frac{4}{9}\)
f. \(\frac{9}{9}\)

Explanation:
The multiples of \(\frac{1}{9}\) have the denominator of 9.

Question 6.
Mimi recorded a soccer game that lasted 1 \(\frac{2}{3}\) hours. She watched it 3 times over the weekend to study the plays. How many hours did Mimi spend watching the soccer game? Show your work.
_____ hours

Answer:
5 hours

Explanation:
3 x 1 2/3 = 3 x 5/3 = 5 hours.

Question 7.
Theo is comparing shark lengths. He learned that a horn shark is 2 \(\frac{3}{4}\) feet long. A blue shark is 4 times as long. Complete the model. Then find the length of a blue shark.

A blue shark is ____ feet long.
_____

Answer:

4 x 11/4 = 11.
A blue shark is 11 feet long.

Page No. 489

Question 8.
Joel made a number line showing the multiples of \(\frac{3}{5}\).

The product 2 × \(\frac{3}{5}\) is shown by the fraction _________ on the number line.
\(\frac{□}{□}\)

Answer:
The product 2 × \(\frac{3}{5}\) is shown by the fraction \(\frac{6}{5}\) on the number line.

Question 9.
Bobby has baseball practice Monday, Wednesday, and Friday. Each practice is 2 \(\frac{1}{2}\) hours. Bobby says he will have practice for 4 hours this week.
Part A
Without multiplying, explain how you know Bobby is incorrect.
Type below:
_________

Answer:
Bobby needs to find 3 × 2 1/2. If he estimates 3 × 2 hours, then he finds the practice is at least 6 hours. 6 is greater than 4, so Bobby’s answer is incorrect.

Question 9.
Part B
How long will Bobby have baseball practice this week? Write your answer as a mixed number. Show your work.
______ \(\frac{□}{□}\) hours

Answer:
7\(\frac{1}{2}\) hours

Explanation:
3 x 2 1/2 = 3 x 5/2 = 15/2 = 7 1/2

Question 10.
Look at the number line. Write the missing fractions.

Type below:
_________

Answer:
9/6, 10/6, 11/6, 12/6

Go Math Grade 4 Pdf Chapter 8 Review/Test Answer Key Question 11.
Ana’s dachshund weighed 5 \(\frac{5}{8}\) pounds when it was born. By age 4, the dog weighed 6 times as much. Fill each box with a number or symbol from the list to show how to find the weight of Ana’s dog at age 4. Not all numbers and symbols may be used.


Type below:
_________

Answer:

Page No. 490

Question 12.
Asta made a fraction number line to help her find 3 × \(\frac{4}{5}\).

Select a way to write 3 × \(\frac{4}{5}\) as the product of a whole number and a unit fraction.

Type below:
_________

Answer:

12 × \(\frac{1}{5}\)

Explanation:
3 x 4/5 = 12/5 = 12 x 1/5.

Question 13.
Yusif wanted to give \(\frac{1}{3}\) of his total toy car collection to 2 of his friends. How many of his toy cars will he give away?
\(\frac{□}{□}\)

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

Explanation:
Yusif wanted to give \(\frac{1}{3}\) of his total toy car collection to 2 of his friends. He has three toy cars in total. He has given 2 cars out of 3 cars. So, the answer is \(\frac{2}{3}\).

Question 14.
Select the correct product for the equation.

4 × \(\frac{5}{8}\) = □ 4 × \(\frac{4}{8}\) = □
Type below:
_________

Answer:
4 × \(\frac{5}{8}\) = \(\frac{20}{8}\)
4 × \(\frac{4}{8}\) = \(\frac{16}{8}\)

Page No. 491

Question 15.
The lengths of different types of snakes at a zoo are shown in the table.

For numbers 15a–15d, select True or False for the statement.
a. Bobby is 4 times as long as Kenny.
i. True
ii. False

Answer:
ii. False

Explanation:
Kenny = 3/2
Bobby = 9/2
Puck = 15/2
4 x 3/2 =6
So, the statement is false.

Question 15.
b. Bobby is 3 times as long as Kenny.
i. True
ii. False

Answer:
i. True

Explanation:
3 x 3/2 = 9/2
So, the statement is true.

Question 15.
c. Puck is 5 times as long as Kenny.
i. True
ii. False

Answer:
i. True

Explanation:
5 x 3/2 = 15/2
So, the statement is true.

Question 15.
d. Puck is 2 times as long as Bobby.
i. True
ii. False

Answer:
ii. False

Explanation:
2 x 9/2 = 9
So, the statement is false.

Question 16.
Hank used 3 \(\frac{1}{2}\) bags of seed to plant grass in his front yard. He used 3 times as much seed to plant grass in his back yard. How much seed did Hank need for the backyard?
_____ \(\frac{□}{□}\)

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

Explanation:
3 x 7/2 = 21/2 = 10 and the remainder is 1. The answer is 10 1/2.

Question 17.
Jess made a big kettle of rice and beans. He used 1 \(\frac{1}{2}\) cups of beans. He used 4 times as much rice.
Part A
Draw a model to show the problem.
Type below:
_________

Answer:

Question 17.
Part B
Use your model to write an equation. Then solve the equation to find the amount of rice Jess needs.
Type below:
_________

Answer:
6 cups

Explanation:
Rice = 4 x 3/2 = 12/2 = 6.
Jess needs 6 cups of rice.

Page No. 492

Question 18.
Mrs. Burnham is making modeling clay for her class. She needs \(\frac{2}{3}\) cup of warm water for each batch.
Part A
Mrs. Burnham has a 1-cup measure that has no other markings. Can she make 6 batches of modeling clay using only the 1-cup measure? Describe two ways you can find the answer.
Type below:
_________

Answer:
Yes. She needs 6 x 2/3 cups of water. 6 x 2/3 = 12/3 = 4 cups.
So, she can use the 1-cup measure 4 times to make 6 batches.

Question 18.
Part B
The modeling clay recipe also calls for \(\frac{1}{2}\) cup of cornstarch. Nikki says Mrs. Burnham will also need 4 cups of cornstarch. Do you agree or disagree? Explain.
Type below:
_________

Answer:
Disagree; 6 x 1/2 = 3 cups of cornstrach.
She doesn’t need 4 cups of cornstarch.

Question 19.
Donna buys some fabric to make place mats. She needs \(\frac{1}{5}\) yard of each type of fabric. She has 9 different types of fabrics to make her design. Use the following equation. Write the number in the box to make the statement true.
\(\frac{9}{5}\) = ______ × \(\frac{1}{5}\)

Answer:
9

Question 20.
Mr. Tuyen uses \(\frac{5}{8}\) of a tank of gas each week to drive to and from his job. How many tanks of gas does Mr. Tuyen use in 5 weeks? Write your answer two different ways.
Mr. Tuyen uses __________ or _________ tanks of gas.
Type below:
_________

Answer:
Mr. Tuyen uses 25/8 or 3\(\frac{1}{8}\) tanks of gas

Explanation:
5 x 5/8 = 25/8 = 3 and the remainder is 1. So, the mixed fraction is 3 1/8.

Question 21.
Rico is making 4 batches of salsa. Each batch needs \(\frac{2}{3}\) cup of corn. He only has a \(\frac{1}{3}\)– cup measure. How many times must Rico measure \(\frac{1}{3}\) cup of corn to have enough for all of the salsa?
______ times

Answer:
8 times

Explanation:
Rico is making 4 batches of salsa. Each batch needs \(\frac{2}{3}\) cup of corn. He only has a \(\frac{1}{3}\)– cup measure.
So, he needs 2x 1/3 cups for one batch. For 4 batches of salsa, 4 x 2 = 8 cups of corn required.

Page No. 497

Question 1.
Write five tenths as a fraction and as a decimal.

Fraction: __________ Decimal: __________
Type below:
_________

Answer:

5/10 = 0.5

Write the fraction or mixed number and the decimal shown by the model.

Question 2.

Type below:
_________

Answer:
3\(\frac{2}{10}\)
three and two-tenths

Question 3.

Type below:
_________

Answer:
\(\frac{8}{10}\)

Write the fraction or mixed number and the decimal shown by the model.

Question 4.

Type below:
_________

Answer:
4/10 = 0.4

Explanation:
4 boxes are shaded out of 10 boxes. So, the fraction is 4/10.

Question 5.

Type below:
_________

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

Question 6.

Type below:
_________

Answer:
2\(\frac{9}{10}\)

Question 7.

Type below:
_________
Answer:
3\(\frac{4}{10}\)

Practice: Copy and Solve Write the fraction or mixed number as a decimal.

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

Answer:
\(\frac{59}{10}\)

Explanation:
Multiply 10 x 5 = 50.
Add 50 + 9 = 59.
The fraction is 59/10

Question 9.
\(\frac{1}{10}\) = _____

Answer:
0.1

Question 10.
\(\frac{7}{10}\) = _____

Answer:
0.7

Question 11.
8 \(\frac{9}{10}\) = _____

Answer:
\(\frac{89}{10}\)

Explanation:
Multiply 10 x 8 = 80.
Add 80 + 9 = 89.
The fraction is 89/10

Question 12.
\(\frac{6}{10}\) = _____

Answer:
0.6

Question 13.
6 \(\frac{3}{10}\) = _____

Answer:
\(\frac{63}{10}\)

Explanation:
Multiply 10 x 6 = 60.
Add 60 + 3 = 63.
The fraction is 63/10

Question 14.
\(\frac{5}{10}\) = _____

Answer:
0.5

Question 15.
9 \(\frac{7}{10}\) = _____

Answer:
\(\frac{97}{10}\)

Explanation:
Multiply 10 x 9 = 90.
Add 90 +7 = 97.
The fraction is 97/10

Page No. 498

Use the table for 16−19.

Question 16.
What part of the rocks listed in the table are igneous? Write your answer as a decimal.
_____

Answer:
0.5

Question 17.
Sedimentary rocks make up what part of Ramon’s collection? Write your answer as a fraction and in word form.
Type below:
_________

Answer:
3/10 and three-tenths

Question 18.
What part of the rocks listed in the table are metamorphic? Write your answer as a fraction and as a decimal.
Type below:
_________

Answer:
2/10 or 0.2

Question 19.
Communicate Niki wrote the following sentence in her report: “Metamorphic rocks make up 2.0 of Ramon’s rock collection.” Describe her error.
Type below:
_________

Answer:
Metamorphic rocks make up 2.0 of Ramon’s rock collection. But from the given table, it is clearly mentioned that the answer is 0.2. So, she made a mistake to make up Ramon’s rock collection.

Question 20.
Josh paid for three books with two $20 bills. He received $1 in change. Each book was the same price. How much did each book cost?
$ _____ each book

Answer:
$19/3 for each book.

Explanation:
Josh paid for three books with two $20 bills. He received $1 in change. So, he paid $19 for three books. As the each book has same price, the answer is $19/3 for each book.

Question 21.
Select a number shown by the model. Mark all that apply.

Type below:
_________

Answer:
1\(\frac{7}{10}\)
1.7

Conclusion:

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Lesson 1: Investigate • Equivalent Fractions

• Equivalent Fractions – Page No. 331
• Equivalent Fractions Lesson Check – Page No. 332

Lesson 2: Generate Equivalent Fractions

• Generate Equivalent Fractions – Page No. 335
• Generate Equivalent Fractions Lesson Check – Page No. 336
• Generate Equivalent Fractions Lesson Check 1 – Page No. 337
• Generate Equivalent Fractions Lesson Check 2 – Page No. 338

Lesson 3: Simplest Form

• Simplest Form – Page No. 341
• Simplest Form Lesson Check – Page No. 342
• Simplest Form Lesson Check 1 – Page No. 343
• Simplest Form Lesson Check 2 – Page No. 344

Lesson 4: Common Denominators

• Common Denominators – Page No. 347
• Common Denominators Lesson Check – Page No. 348
• Common Denominators Lesson Check 1 – Page No. 349
• Common Denominators Lesson Check 2 – Page No. 350
• Common Denominators Lesson Check 3 – Page No. 353
• Common Denominators Lesson Check 4 – Page No. 354

Lesson 5: Problem Solving • Find Equivalent Fractions

• Find Equivalent Fractions – Page No. 355
• Find Equivalent Fractions Lesson Check – Page No. 356

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Page No. 357
• Mid-Chapter Checkpoint Lesson Check – Page No. 358

Lesson 6: Compare Fractions Using Benchmarks

• Compare Fractions Using Benchmarks – Page No. 361
• Compare Fractions Using Benchmarks Lesson Check – Page No. 362
• Compare Fractions Using Benchmarks Lesson Check 1 – Page No. 363
• Compare Fractions Using Benchmarks Lesson Check 2 – Page No. 364

Lesson 7: Compare Fractions

• Compare Fractions – Page No. 367
• Compare Fractions Lesson Check – Page No. 368
• Compare Fractions Lesson Check 1 – Page No. 369
• Compare Fractions Lesson Check 2 – Page No. 370

Lesson 8: Compare and Order Fractions

• Compare and Order Fractions – Page No. 373
• Compare and Order Fractions Lesson Check – Page No. 374
• Compare and Order Fractions Lesson Check 1 – Page No. 375
• Compare and Order Fractions Lesson Check 2- Page No. 376

Review/Test

• Review/Test – Page No. 377
• Review/Test – Page No. 378
• Review/Test – Page No. 379
• Review/Test – Page No. 380
• Review/Test – Page No. 381
• Review/Test – Page No. 382
• Review/Test – Page No. 387
• Review/Test – Page No. 388

Common Core – Equivalent Fractions – Page No. 331

Equivalent Fractions
Use the model to write an equivalent fraction.

Question 1.

\(\frac{4}{6}=\frac{2}{3}\)

Answer:
\(\frac{4}{6}=\frac{2}{3}\)

Explanation:
The first image has 4 parts shaded our of 6 parts. Divide \(\frac{8}{10}\) with 2. You will get \(\frac{2}{3}\). That means 2 parts are shaded out of 3 parts.

Question 2.

\(\frac{3}{4}\) = \(\frac{□}{□}\)

Answer:
\(\frac{3}{4}\) = \(\frac{6}{8}\)

Explanation:
The first image has 3 parts shaded our of 4 parts. Multiply \(\frac{8}{10}\) with 2. You will get \(\frac{6}{8}\). That means 6 parts are shaded out of 8 parts.

Tell whether the fractions are equivalent. Write = or ≠.

Question 3.
\(\frac{8}{10}\) _______ \(\frac{4}{5}\)

Answer:
\(\frac{8}{10}\) = \(\frac{4}{5}\)

Explanation:
Multiply the numerator and denominator of 4 / 5 with 2
8 / 10 = (2 / 2 ) x (4 / 5 )
= 8 / 10
So, 8 / 10 = 4 / 5.

Question 4.
\(\frac{1}{2}\) _______ \(\frac{7}{12}\)

Answer:
\(\frac{1}{2}\) ≠ \(\frac{7}{12}\)

Explanation:
Multiply the numerator and denominator of 1 / 2 with 6
1 / 2 = (6 / 6) x (1 / 2)
= (6 / 12)
So, 1/2 ≠ 7 / 12

My Homework Lesson 6 Answer Key 4th Grade Question 5.
\(\frac{3}{4}\) _______ \(\frac{8}{12}\)

Answer:
\(\frac{3}{4}\) ≠ \(\frac{8}{12}\)

Explanation:
Multiply the numerator and denominator of 3 / 4 with 3
3 / 4 = (3 / 3) x (3 / 4)
= (9 / 12)
So, 3 / 4 ≠ 8 / 12

Question 6.
\(\frac{2}{3}\) _______ \(\frac{4}{6}\)

Answer:
\(\frac{2}{3}\) = \(\frac{4}{6}\)

Explanation:
Multiply the numerator and denominator of 2 / 3 with 2
2 / 3 = (2 / 2) x ( 2 / 3 )
= 4 / 6
So, 2 / 3 = 4 / 6.

Question 7.
\(\frac{5}{8}\) _______ \(\frac{4}{10}\)

Answer:
\(\frac{5}{8}\) ≠ \(\frac{4}{10}\)

Explanation:
Multiply the numerator and denominator of 5 / 8 with 2
5 / 8 =(2 / 2) x (5 / 8)
= (10 / 16)
So, 5 / 8 ≠ 4 / 10

Question 8.
\(\frac{2}{6}\) _______ \(\frac{4}{12}\)

Answer:
\(\frac{2}{6}\) = \(\frac{4}{12}\)

Explanation:
Multiply the numerator and denominator of 2 / 6 with 2
2 / 6 = (2 / 2) x (2 / 6)
= (4 / 12)
So, 2 / 6 = 4 / 12.

Question 9.
\(\frac{20}{100}\) _______ \(\frac{1}{5}\)

Answer:
\(\frac{20}{100}\) = \(\frac{1}{5}\)

Explanation:
Cross Multiply the 20 / 100 with 20 / 20
20 / 100 = (20 / 20) x (20 / 100)
= (1 / 5)
So, 20 / 100 = 1 / 5.

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

Answer:
\(\frac{5}{8}\) ≠ \(\frac{9}{10}\)

Explanation:
Multiply the numerator and denominator of 5 / 8 with 2
5 / 8 = (2 / 2) x (5 / 8)
= 10 / 16
So, 5 / 8 ≠ 9 / 10

Question 11.
Jamal finished \(\frac{5}{6}\) of his homework. Margaret finished \(\frac{3}{4}\) of her homework, and Steve finished \(\frac{10}{12}\) of his homework. Which two students finished the same amount of homework?
_______

Answer:
Jamal and Steve

Explanation:
As per the given data,
Jamal finished work = 5 /6 of his homework
Margaret finished work = 3 / 4th of her homework
Steve finished work = 10 / 12 of his homework
Multiply the numerator and denominator of 5/ 6 with 2
Then, (2 / 2) x (5 / 6) = 10 / 12
Then, Jamal and Steve finished the same amount of homework.

Go Math Grade 4 Chapter 6 Review/Test Answer Key Question 12.
Sophia’s vegetable garden is divided into 12 equal sections. She plants carrots in 8 of the sections. Write two fractions that are equivalent to the part of Sophia’s garden that is planted with carrots.
Type below:
___________

Answer:
\(\frac{2}{3}\) and \(\frac{4}{6}\)

Explanation:
As per the given data,
Sophia’s vegetable garden is divided into 12 equal sections
She plants carrots in 8 of the sections out of 12 sections = 8 / 12
By simplifying the 8 / 12, we will get 4 / 6
Again simplify the 4 /6 by dividing method, you will get 2 /3
2 / 3 = (2 / 2) x (2 / 3)
= 4 / 6
Then, the equivalent fractions are 2 / 3, 4 /6

Common Core – Equivalent Fractions – Page No. 332

Question 1.
A rectangle is divided into 8 equal parts. Two parts are shaded. Which fraction is equivalent to the shaded area of the rectangle?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{2}{6}\)
d. \(\frac{3}{4}\)

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

Explanation:
As per the given data,
A rectangle is divided into 8 equal parts
Two parts are shaded
Then, the shaded area of the rectangle = 2 / 8
By simplifying the 2/ 8, you will get 1/ 4
So, the shaded area of the rectangle = 1 / 4

Question 2.
Jeff uses 3 fifth-size strips to model \(\frac{3}{5}\). He wants to use tenth-size strips to model an equivalent fraction. How many tenth-size strips will he need?
Options:
a. 10
b. 6
c. 5
d. 3

Answer:
b. 6

Explanation:
From the given data,
Jeff uses 3 fifth–size strips to model = 3 / 5 size strips
If he wants to use tenth–size strips to an equivalent fraction = 1 / 10 size strips
The number of strips = x
(1 / 10) x = 3 / 5
x = 30/5
Then, the required number of tenth-size trips = 6

Go Math Grade 4 Chapter 6 Answer Key Pdf Question 3.
Cassidy places 40 stamps on each of the 8 album pages. How many stamps does she place in all?
Options:
a. 300
b. 320
c. 360
d. 380

Answer:
b. 320

Explanation:
As per the given data,
Cassidy places 40 stamps on each of 8 album pages = 8 x 40
= 320
So, the total placed stamps on album pages by Cassidy = 320 stamps

Question 4.
Maria and 3 friends have 1,200 soccer cards. If they share the soccer cards equally, how many will each person receive?
Options:
a. 30
b. 40
c. 300
d. 400

Answer:
c. 300

Explanation:
As per the given data,
Maria and 3 friends have 1200 soccer cards
If soccer cards shared equally by four members = 1200/4
= 300
Then, each person received soccer cards = 300

Question 5.
Six groups of students sell 162 balloons at the school carnival. There are 3 students in each group. If each student sells the same number of balloons, how many balloons does each student sell?
Options:
a. 9
b. 18
c. 27
d. 54

Answer:
a. 9

Explanation:
As per the given, data,
Six groups of students sell 162 balloons at the school carnival
There are 3 students in each group
Then, total number of students in 6 groups = 6 x 3 = 18
If each student sells the same number of balloons = 162 / 18
= 9
Number of balloons sells by each student = 9

Question 6.
Four students each made a list of prime numbers.
Eric: 5, 7, 17, 23
Maya: 3, 5, 13, 17
Bella: 2, 3, 17, 19
Jordan: 7, 11, 13, 21
Who made an error and included a composite number?
Options:
a. Eric
b. Maya
c. Bella
d. Jordan

Answer:
d. Jordan

Explanation:
As per the given data,
Four students each made a list of prime numbers.
Eric: 5, 7, 17, 23
Maya: 3, 5, 13, 17
Bella: 2, 3, 17, 19
Jordan: 7, 11, 13, 21
21 is not a prime number
So, An error made by Jordan

Page No. 335

Question 1.
Complete the table below.

Type below:
___________

Answer:

Write two equivalent fractions.

Question 2.
\(\frac{4}{5}\)
\(\frac{4}{5}\) = \(\frac { 4×□ }{ 5×□ } \) = \(\frac{□}{□}\)
\(\frac{4}{5}\) = \(\frac { 4×□ }{ 5×□ } \) = \(\frac{□}{□}\)
\(\frac{4}{5}\) = \(\frac{□}{□}\) = \(\frac{□}{□}\)
Type below:
___________

Answer:
\(\frac{4}{5}\) = \(\frac{8}{10}\) = \(\frac{80}{100}\)

Explanation:
Two equivalent fractions of 4/5,
(4/5) x (2/2) = 8/10
And
(4/5) x (20/20) = 80/100
8/10 = (8/10) (10/10)
= (80/100)
So, the equivalent fractions of 4/5 = 8/10, 80/100

Question 3.
\(\frac{2}{4}\)
\(\frac{2}{4}\) = \(\frac { 2×□ }{ 4×□ } \) = \(\frac{□}{□}\)
\(\frac{2}{4}\) = \(\frac { 2×□ }{ 4×□ } \) = \(\frac{□}{□}\)
\(\frac{2}{4}\) = \(\frac{□}{□}\) = \(\frac{□}{□}\)
Type below:
___________

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

Explanation:
Two equivalent fractions of 2/4,
(2/4) x (2/2) = 4/8
And
(2/4) x (4/4) = 8/16
4/8 = (4/8) (2/2)
= (8/16)
So, the equivalent fractions of 2/4 = 4/8, 8/16

Write two equivalent fractions.

Question 4.
\(\frac{3}{6}\)
\(\frac{3}{6}\) = \(\frac{□}{□}\) = \(\frac{□}{□}\)
Type below:
___________

Answer:
\(\frac{3}{6}\) = \(\frac{6}{12}\) = \(\frac{12}{24}\)

Explanation:
Two equivalent fractions of 3/6,
(3/ 6) x (2/2) = 6/12
And
(3/6) x (4/ 4) = 12/24
6/12 = (6/12) (2/2)
= (12/24)
So, the equivalent fractions of 3/6 = 6/12, 12/24

Question 5.
\(\frac{3}{10}\)
\(\frac{3}{10}\) = \(\frac{□}{□}\) = \(\frac{□}{□}\)
Type below:
___________

Answer:
\(\frac{3}{10}\) = \(\frac{6}{20}\) = \(\frac{12}{40}\)

Explanation:
Two equivalent fractions of 3/10,
(3/ 10) x (2/2) = 6/20
And
(3/10) x (4/ 4) = 12/40
6/20 = (6/20) (2/2)
= (12/40)
So, the equivalent fractions of 3/10 = 6/20, 12/40

Question 6.
\(\frac{2}{5}\)
\(\frac{2}{5}\) = \(\frac{□}{□}\) = \(\frac{□}{□}\)
Type below:
___________

Answer:
\(\frac{2}{5}\) = \(\frac{4}{10}\) = \(\frac{8}{20}\)

Explanation:
Two equivalent fractions of 2/5,
(2/ 5) x (2/2) = 4/10
And
(2/5) x (4/ 4) = 8/20
4/10 = (4/10) (2/2)
= (8/20)
So, the equivalent fractions of 2/5 = 4/10, 8/20

Tell whether the fractions are equivalent. Write = or ≠.

Question 7.
\(\frac{5}{6}\) ______ \(\frac{10}{18}\)

Answer:
\(\frac{5}{6}\) ≠ \(\frac{10}{18}\)

Explanation:
Multiply the numerator and denominator of 5/6 with 2
5/6 =(2/2) x (5/6)
= (10/12)
So, 5/6 ≠ 10/ 18

Go Math Grade 4 Answer Key Chapter 6 Question 8.
\(\frac{4}{5}\) ______ \(\frac{8}{10}\)

Answer:
\(\frac{4}{5}\) = \(\frac{8}{10}\)

Explanation:
Multiply the numerator and denominator of 4/5 with 2
4/5 =(2/2) x (4/5)
= (8/10)
So, 4/5 = 8/10

Question 9.
\(\frac{1}{5}\) ______ \(\frac{4}{10}\)

Answer:
\(\frac{1}{5}\) ≠ \(\frac{4}{10}\)

Explanation:
Multiply the numerator and denominator of 1/5 with 4
1/5 =(4/4) x (1/5)
= (4/20)
So, 1/5 ≠ 4/10

Question 10.
\(\frac{1}{4}\) ______ \(\frac{2}{8}\)

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

Explanation:
Multiply the numerator and denominator of 1/4 with 2
1/4 =(2/2) x (1/4)
= (2/8)
So, 1/4 = 2/8

Page No. 336

Use the recipe for 11–12.

Question 11.
Kim says the amount of flour in the recipe can be expressed as a fraction. Is she correct? Explain.
______

Answer:
As per the given data, Kim says the amount of flour in the recipe can be expressed as a fraction. But in the recipe, 1 tablespoon flour is added. So, Kim says wrong.

Question 12.
How could you use a \(\frac{1}{8}\) – cup measuring cup to measure the light corn syrup?
Type below:
_________

Answer:
As per the given data,
By using the 1/8 cup measure the 9/12 cup light corn syrup
(9/12)/(1/8) = (9 x 8)/12
= (3 x 8)/4
= (3 x 2)
= 6
So, required 6 cups of 1/8 to measure the light corn syrup of 9/12.

Question 13.
Communicate Explain using words how you know a fraction is equivalent to another fraction.
Type below:
_________

Answer:
If you multiply the numerator and denominator of the first fraction by the same number and the products are the numerator and denominator of the second fraction, then the fractions are equivalent

Question 14.
Kyle drank \(\frac{2}{3}\) cup of apple juice. Fill in each box with a number from the list to generate equivalent fractions for \(\frac{2}{3}\). Not all numbers will be used.
Type below:
_________

Answer:
\(\frac{4}{6}\) and \(\frac{12}{18}\)

Explanation:
As per the given data,
Kyle drank 2/3 cup of apple juice
(2/3) x (2/2) = 4/6
(4/6) x (3/3) = 12/18
Equivalent fractions of 2/3 are 4/6 and 12/18

Common Core – Equivalent Fractions – Page No. 337

Write two equivalent fractions for each.

Question 1.

Answer:
\(\frac{2}{6}\) and \(\frac{4}{12}\)

Explanation:
1/3
(1/3) x (2/2) = 2/6
(1/3) x (4/4) = 4/12
So, the equivalent fractions of 1/3 are 2/6 and 4/12

Question 2.
\(\frac{2}{3}\)
Type below:
_________

Answer:
\(\frac{4}{6}\) and \(\frac{8}{12}\)

Explanation:
2/3
(2/3) x (2/2) = 4/6
(2/3) x (4/4) = 8/12
Then, the equivalent fractions of 2/3 = 4/6 and 8/12

Go Math Grade 4 Lesson 6.2 Answer Key Question 3.
\(\frac{1}{2}\)
Type below:
_________

Answer:
\(\frac{2}{4}\) and \(\frac{4}{8}\)

Explanation:
1/2
(1/2) x (2/2) = 2/4
(1/2) x (4/4) = 4/8
Then, the equivalent fractions of 1/2 = 2/4, 4/8

Question 4.
\(\frac{4}{5}\)
Type below:
_________

Answer:
\(\frac{8}{10}\) and \(\frac{80}{100}\)

Explanation:
4/5
(4/5) x (2/2) = 8/10
(4/5) x (20/20) = 80/100
Then, the equivalent fractions of 4/5 = 8/10 and 80/100

Tell whether the fractions are equivalent. Write # or ≠.

Question 5.
\(\frac{1}{4}\) ______ \(\frac{3}{12}\)

Answer:
\(\frac{1}{4}\) = \(\frac{3}{12}\)

Explanation:
1/4
Multiply the numerator and denominator of 1/4 with 3
Then, (1/4) x (3/3) = 3/12
So, 1/4 = 3/12

Question 6.
\(\frac{4}{5}\) ______ \(\frac{5}{10}\)

Answer:
\(\frac{4}{5}\) ≠ \(\frac{5}{10}\)

Explanation:
4/5
Multiply numerator and denominator of 4/5 with 2
(4/5) x (2/2) = 8/10
Then 4/5 ≠ 5/10

Question 7.
\(\frac{3}{8}\) ______ \(\frac{2}{6}\)

Answer:
\(\frac{3}{8}\) ≠ \(\frac{2}{6}\)

Explanation:
3/8 ≠ 2/6

Question 8.
\(\frac{3}{4}\) ______ \(\frac{6}{8}\)

Answer:
\(\frac{3}{4}\) = \(\frac{6}{8}\)

Explanation:
3/4
Multiply the numerator and denominator of 3/4 with 2
Then, (3/4) x (2/2) = 6/8
So, 3/4 = 6/8

Question 9.
\(\frac{5}{6}\) ______ \(\frac{10}{12}\)

Answer:
\(\frac{5}{6}\) = \(\frac{10}{12}\)

Explanation:
5/6
Multiply the numerator and denominator with 2
(5/6) x (2/2) = 10/12
So, 5/6 = 10/12

Question 10.
\(\frac{6}{12}\) ______ \(\frac{5}{8}\)

Answer:
\(\frac{6}{12}\) ≠ \(\frac{5}{8}\)

Explanation:
6/12 ≠ 5/8

Question 11.
\(\frac{2}{5}\) ______ \(\frac{4}{10}\)

Answer:
\(\frac{2}{5}\) = \(\frac{4}{10}\)

Explanation:
2/5
Multiply the numerator and denominator of 2/5 with 2
(2/5) x (2/2) = 4/10
So, 2/5 = 4/10

Question 12.
\(\frac{2}{4}\) ______ \(\frac{3}{12}\)

Answer:
\(\frac{2}{4}\) ≠ \(\frac{3}{12}\)

Explanation:
2/4
Multiply the numerator and denominator of 2/4 with 3
(2/4) x (3/3) = 6/12
So, 2/4 ≠ 3/ 12

Question 13.
Jan has a 12-ounce milkshake. Four ounces in the milkshake are vanilla, and the rest is chocolate. What are two equivalent fractions that represent the fraction of the milkshake that is vanilla?
Type below:
_________

Answer:
\(\frac{1}{3}\) and \(\frac{2}{6}\)

Explanation:
As per the given data,
Jan has a 12-ounce milkshake
Four ounces in the milkshake are vanilla = 4/12 = 1/3
Then, 8-ounces in milkshake are chocolate = 8/12 = 2/3
4/12 = 1/3
By multiplying 1/3 with 2
(1/3) x (2/2) = 2/6
So, the equivalent fractions of vanilla milkshake are 1/3 and 2/6

Question 14.
Kareem lives \(\frac{4}{10}\) of a mile from the mall. Write two equivalent fractions that show what fraction of a mile Kareem lives from the mall.
Type below:
_________

Answer:
\(\frac{2}{5}\) and \(\frac{8}{20}\)

Explanation:
As per the given data,
Kareem lives 4/10 of a mile from the mall
To find the equivalent fractions of 4/10
Simplify the 4/10 = 2/5
Multiply the numerator and denominator of 2/5 with 4
(2/5) x (4/4) = 8/20
Then, the equivalent fraction of a mile Kareem lives from the mall = 2/5 and 8/20

Common Core – Equivalent Fractions – Page No. 338

Question 1.
Jessie colored a poster. She colored \(\frac{2}{5}\) of the poster red. Which fraction is equivalent to \(\frac{2}{5}\)?
Options:
a. \(\frac{4}{10}\)
b. \(\frac{7}{10}\)
c. \(\frac{4}{5}\)
d. \(\frac{2}{2}\)

Answer:
a. \(\frac{4}{10}\)

Explanation:
As per the given data,
Jessie colored a poster
She colored 2/5th of the poster red
Multiply the numerator and denominator of 2/5 with 2
Then, (2/5) x (2/2) = 4 /10
So, the equivalent fraction of 2/5 is 4/10

Question 2.
Marcus makes a punch that is \(\frac{1}{4}\) cranberry juice. Which two fractions are equivalent to \(\frac{1}{4}\)?
Options:
a. \(\frac{2}{5}, \frac{3}{12}\)
b. \(\frac{2}{8}, \frac{4}{12}\)
c. \(\frac{3}{4}, \frac{6}{8}\)
d. \(\frac{2}{8}, \frac{3}{12}\)

Answer:
d. \(\frac{2}{8}, \frac{3}{12}\)

Explanation:
As per the given data,
Marcus makes a punch that is 1/4th of cranberry juice
Multiply the numerator and denominator of 1/4 with 2
Then, (1/4) x (2/2) = 2/8
Multiply the numerator and denominator of 1/4 with 3
Then, (1/4) x (3/3) = 3/12
Equivalent fractions of 1/4 are 2/8 and 3/12

Question 3.
An electronics store sells a large flat-screen television for $1,699. Last month, the store sold 8 of these television sets. About how much money did the store make on the television sets?
Options:
a. $160,000
b. $16,000
c. $8,000
d. $1,600

Answer:
b. $16,000

Explanation:
As per the given data,
An electronics store sells a large flat-screen television for $1,699
Last month, the store sold 8 of these television sets = 8 x $1,699 = $13,952. The money is about to $16,000.

Question 4.
Matthew has 18 sets of baseball cards. Each set has 12 cards. About how many baseball cards does Matthew have in all?
Options:
a. 300
b. 200
c. 150
d. 100

Answer:
b. 200

Explanation:
From the given data,
Matthew has 18 sets of basketball cards
Each set has 12 cards = 12 x 18
= 216
Total number of basketball cards with Matthew = 216. So, it is near to 200.

Question 5.
Diana had 41 stickers. She put them in 7 equal groups. She put as many as possible in each group. She gave the leftover stickers to her sister. How many stickers did Diana give to her sister?
Options:
a. 3
b. 4
c. 5
d. 6

Answer:
d. 6

Explanation:
As per the given data,
Diana has 41 stickers
She put them in 7 equal groups = 41/7
= 5 (remaining 6)
She gave the leftover stickers to her sister
The number of stickers Diana gives to her sister = 6

Question 6.
Christopher wrote the number pattern below. The first term is 8.
8, 6, 9, 7, 10, …
Which is a rule for the pattern?
Options:
a. Add 2, add 3.
b. Add 6, subtract 3.
c. Subtract 6, add 3.
d. Subtract 2, add 3

Answer:
d. Subtract 2, add 3

Explanation:
From the given data,
Christopher wrote the number pattern = 8, 6, 9, 7, 10, …..
The first number in the pattern = 8
8 – 2 = 6 + 3 = 9 – 2 = 7 +3 = 10 ….
So, the rule for the above pattern is to subtract 2, add 3

Page No. 341

Question 1.
Write \(\frac{8}{10}\) in simplest form.
\(\frac{8}{10}\) = \(\frac { 8÷□ }{ 10÷□ } \) = \(\frac{□}{□}\)
\(\frac{□}{□}\)

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

Explanation:
8/10 in simplest form
Divide the 8/10 with 2
(8/2)/(10/2) = 4/5
So, the simplest form of 8/10 is 4/5

Write the fraction in simplest form.

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

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

Explanation:
6/12 in simplest form
Divide the 6/12 with 6
(6/6)/(12/6) = 1/2
So, the simplest form of 6/12 is 1/2

Question 3.
\(\frac{2}{10}\)
\(\frac{□}{□}\)

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

Explanation:
2/10 in simplest form
Divide the 2/10 with 2
(2/2)/(10/2) = 1/5
So, the simplest form of 2/10 is 1/5

Question 4.
\(\frac{6}{8}\)
\(\frac{□}{□}\)

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

Explanation:
6/8 in simplest form
Divide the 6/8 with 2
(6/2)/(8/2) = 3/4
So, the simplest form of 6/8 is 3/4

Question 5.
\(\frac{4}{6}\)
\(\frac{□}{□}\)

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

Explanation:
4/6 in simplest form
Divide the 4/6 with 2
(4/2)/(6/2) = 2/3
So, the simplest form of 4/6 is 2/3

Write the fraction in simplest form.

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

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

Explanation:
9/12in simplest form
Divide the 9/12 with 3
(9/3)/(12/3) = 3/4
So, the simplest form of 9/12 is 3/4

Lesson 6.3 Answer Key 4th Grade Question 7.
\(\frac{4}{8}\)
\(\frac{□}{□}\)

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

Explanation:
4/8in simplest form
Divide the 4/8 with 4
(4/4)/(8/4) = 1/2
So, the simplest form of 4/8 is 1/2

Question 8.
\(\frac{10}{12}\)
\(\frac{□}{□}\)

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

Explanation:
10/12 in simplest form
Divide the 10/12 with 2
(10/2)/(12/2) = 5/6
So, the simplest form of 10/12 is 5/6

Question 9.
\(\frac{20}{100}\)
\(\frac{□}{□}\)

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

Explanation:
20 /100 in simplest form
Divide the 20/100 with 20
(20/20)/(100/20) = 1/5
So, the simplest form of 20/100 is 1/5

Tell whether the fraction is in simplest form. Write yes or no.

Question 10.
\(\frac{2}{8}\)
______

Answer:
No

Explanation:
2/8 in simplest form
Divide the 2/8 with 2
(2/2)/(8/2) = 1/4
The simplest form of 2/8 is 1/4
So, 2/8 is not the simplest form

Question 11.
\(\frac{9}{12}\)
______

Answer:
No

Explanation:
9/12 in simplest form
Divide the 9/12 with 3
(9/3)/(12/3) = 3/4
The simplest form of 9/12 is 3/4
So, 9/12 is not the simplest form

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

Answer:
Yes

Explanation:
5/6 is not divided by any number
Yes, 5/6 is the simplest form

Question 13.
\(\frac{4}{10}\)
______

Answer:
No

Explanation:
4/10 in simplest form
Divide the 4/10 with 2
(4/2)/(10/2) = 2/5
So, 4/10 is not the simplest form

Question 14.
There are 18 students in Jacob’s homeroom. Six students bring their lunch to school. The rest eat lunch in the cafeteria. In the simplest form, what fraction of students eat lunch in the cafeteria?
\(\frac{□}{□}\) of students

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

Explanation:
As per the given data,
There are 18 students in Jacob’s homeroom
6 students bring their lunch to school = 6/18 = 1/3
The rest eat lunch in the cafeteria = 18 – 6 = 12/18
Divide the numerator and denominator of 12/18 with 6
(12/6) x (18/6) = 2/3
So, 2/3 of students eat lunch in the cafeteria

Page No. 342

Use the map for 15−16.

Question 15.
Identify Relationships What fraction of the states in the southwest region share a border with Mexico? Is this fraction in simplest form?
\(\frac{□}{□}\)

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

Explanation:
As per the given data,
Southwest region states = 4
Number of states in the southwest region shares a border with Mexico out of total southwest region states = 3/4
Yes, 3/4 is the simplest form

Question 16.
What’s the Question? \(\frac{1}{3}\) of the states in this region are on the Gulf of Mexico.
Type below:
_________

Answer:
In the simplest form, what fraction of the states in the southeast area on the Gulf of Mexico?

Common Denominators Lesson 6.4 Question 17.
Pete says that to write \(\frac{4}{6}\) as \(\frac{2}{3}\), you combine pieces, but to write \(\frac{4}{6}\) as \(\frac{8}{12}\), you break apart pieces. Does this make sense? Explain.
______

Answer:
As per the given data,
Yes, it makes sense,
To write 4/6 as 2/3 combine sixth-size pieces into equal groups of 2
Then (4/2)/(6/2) = 2/3
To write 4/6 as 8/12, break each sixth piece into 2 pieces
Then, 4/6 = (4 x 2)/(6 x 2) = 8/12

Question 18.
In Michelle’s homeroom, \(\frac{9}{15}\) of the students ride the bus to school, \(\frac{4}{12}\) get a car ride, and \(\frac{2}{30}\) walk to school.
For numbers 18a–18c, select True or False for each statement.
a. In simplest form, \(\frac{3}{5}\) of the students ride the bus to school.
i. True
ii. False

Answer:
i. True

Explanation:
9/15 of the students ride the bus to school
By dividing the numerator and denominator of 9/15 with 3
(9/3)/(15/3) =3/5
So, 3/5 of the students ride the bus to school
True

Question 18.
b. In simplest form, \(\frac{1}{4}\) of the students get a car ride to school.
i. True
ii. False

Answer:
ii. False

Explanation:
a. 4/12 of the students get a car ride
The simplest form of 4/12 = 1/3
So, 1/4 of the students get a car ride to school is a False statement

Question 18.
c. In simplest form, \(\frac{1}{15}\) of the students walk to school.
i. True
ii. False

Answer:
i. True

Explanation:
a. 2/30 of the students walk to school
By dividing the 2/30 with 2
(2/2)/(30/2) = 1/15
So, 1/15 of the students walk to school is a true statement

Common Core – Simplest Form – Page No. 343

Write the fraction in simplest form.

Question 1.

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

Explanation:
To write the 6/10 in the simplest form
Divide the numerator and denominator of 6/10 with 2
(6 ÷2)/(10 ÷2) = 3/5
So, the simplest form of 6/10 = 3/5

Question 2.
\(\frac{6}{8}\) = \(\frac{□}{□}\)

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

Explanation:
To write the 6/8in a simplest form
Divide the numerator and denominator of 6/8 with 2
(6 ÷2)/(8 ÷2) = 3/4
So, the simplest form of 6/8 = 3/4

Question 3.
\(\frac{5}{5}\) = \(\frac{□}{□}\)

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

Explanation:
To write the 5/5in a simplest form
Divide the numerator and denominator of 5/5 with 5
(5 ÷5)/(5 ÷5) = 1/1
So, the simplest form of 5/5 = 1

Question 4.
\(\frac{8}{12}\) = \(\frac{□}{□}\)

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

Explanation:
To write the 8/12in a simplest form
Divide the numerator and denominator of 8/12 with 4
(8 ÷4)/(12 ÷4) = 2/3
So, the simplest form of 8/12 = 2/3

Question 5.
\(\frac{100}{100}\) = \(\frac{□}{□}\)

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

Explanation:
The simplest form of 100/100 = 1

Question 6.
\(\frac{2}{6}\) = \(\frac{□}{□}\)

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

Explanation:
To write the 2/6in a simplest form
Divide the numerator and denominator of 2/6 with 2
(2 ÷2)/(6 ÷2) = 1/3
So, the simplest form of 2/6 = 1/3

Question 7.
\(\frac{2}{8}\) = \(\frac{□}{□}\)

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

Explanation:
To write the 2/8in a simplest form
Divide the numerator and denominator of 2/8 with 2
(2 ÷2)/(8 ÷2) = 1/4
So, the simplest form of 2/8 = 1/4

Question 8.
\(\frac{4}{10}\) = \(\frac{□}{□}\)

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

Explanation:
To write the 4/10 in a simplest form
Divide the numerator and denominator of 4 /10 with 2
(4 ÷2)/(10 ÷2) = 2/5
So, the simplest form of 4/10 = 2/5

Tell whether the fractions are equivalent. Write = or ≠. (if you do not have ≠on your keyboard, copy and paste this one: ≠ )

Question 9.
\(\frac{6}{12}\) _______ \(\frac{1}{12}\)

Answer:
\(\frac{6}{12}\) ≠ \(\frac{1}{12}\)

Explanation:
6/12 ≠ 1/12

Question 10.
\(\frac{3}{4}\) _______ \(\frac{5}{6}\)

Answer:
\(\frac{3}{4}\) ≠ \(\frac{5}{6}\)

Explanation:
3/4 ≠ 5/6

Question 11.
\(\frac{6}{10}\) _______ \(\frac{3}{5}\)

Answer:
\(\frac{6}{10}\) = \(\frac{3}{5}\)

Explanation:
6/10
Divide the numerator and denominator of 6/10 with 2
(6 ÷ 2)/( 10 ÷ 2) = 3/5
So, 6/10 = 3/5

Question 12.
\(\frac{3}{12}\) _______ \(\frac{1}{3}\)

Answer:
\(\frac{3}{12}\) ≠ \(\frac{1}{3}\)

Explanation:
3/12 ≠ 1/3

Question 13.
\(\frac{6}{10}\) _______ \(\frac{60}{100}\)

Answer:
\(\frac{6}{10}\) = \(\frac{60}{100}\)

Explanation:
6/10
Multiply the numerator and denominator of 6/10 with 10
(6 x 10)/(10 x 10) = 60/100
So, 6/10 = 60/100

Lesson 6.4 Go Math 4th Grade Question 14.
\(\frac{11}{12}\) _______ \(\frac{9}{10}\)

Answer:
\(\frac{11}{12}\) ≠ \(\frac{9}{10}\)

Explanation:
11/12 ≠ 9/10

Question 15.
\(\frac{2}{5}\) _______ \(\frac{8}{20}\)

Answer:
\(\frac{2}{5}\) = \(\frac{8}{20}\)

Explanation:
2/5
Multiply the numerator and denominator of 2/5 with 4
(2 x 4)/(5 x 4) = 8/20
So, 2/5 = 8/20

Question 16.
\(\frac{4}{8}\) _______ \(\frac{1}{2}\)

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

Explanation:
4/8
Divide the numerator and denominator of 4/8 with 4
(4 x 4)/(8 x 4) = 1/2
So, 4/8 = 1/2

Question 17.
At Memorial Hospital, 9 of the 12 babies born on Tuesday were boys. In the simplest form, what fraction of the babies born on Tuesday were boys?
_______

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

Explanation:
As per the given data,
At Memorial Hospital, 9 of the 12 babies born on Tuesday were boys = 9/12
Divide the numerator and denominator of 9/12 with 3
(9 ÷ 3)/(12 ÷ 3) = 3/4
So, in the simplest form
3/4 of the babies born on Tuesday were boys

Question 18.
Cristina uses a ruler to measure the length of her math textbook. She says that the book is \(\frac{4}{10}\) meter long. Is her measurement in simplest form? If not, what is the length of the book in simplest form?
\(\frac{□}{□}\)

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

Explanation:
As per the given data,
Cristiana uses a ruler to measure the length of her math textbook
She says that the book is 4/10meter long
It is not in the simplest form
Divide the numerator and denominator of 4/10 with 2
(4÷ 2)/( 10 ÷ 2) = 2/5
The length of the book in the simplest form = 2/5

Common Core – Simplest Form – Page No. 344

Question 1.
Six out of the 12 members of the school choir are boys. In the simplest form, what fraction of the choir is boys?
Options:
a. \(\frac{1}{6}\)
b. \(\frac{6}{12}\)
c. \(\frac{1}{2}\)
d. \(\frac{12}{6}\)

Answer:
c. \(\frac{1}{2}\)

Explanation:
As per the given data,
Six out of the 12 members of the school choir are boys = 6/12
To write the simplest form of 6/12, divide the numerator and denominator with 6
Then, (6 ÷ 6)/(12 ÷ 6) = 1/2
In the simplest form, 1/2 of the choir is boys

Question 2.
Which of the following fractions is in simplest form?
Options:
a. \(\frac{5}{6}\)
b. \(\frac{6}{8}\)
c. \(\frac{8}{10}\)
d. \(\frac{2}{12}\)

Answer:
a. \(\frac{5}{6}\)

Explanation:
5/6 is in the simplest form
6/8 simplest form = 3/4
8/10 simplest form = 4/5
2/12 simplest form = 1/6

Question 3.
Each of the 23 students in Ms. Evans’ class raised $45 for the school by selling coupon books. How much money did the class raise in all?
Options:
a. $207
b. $225
c. $1,025
d. $1,035

Answer:
d. $1,035

Explanation:
As per the given data,
Each of the 23 students in Ms. Evan’s class raised $45 for the school by selling coupon books
= 23 x $45
= $1,035

Question 4.
Which pair of numbers below have 4 and 6 as common factors?
Options:
a. 12, 18
b. 20, 24
c. 28, 30
d. 36, 48

Answer:
d. 36, 48

Explanation:
36, 48
Here, 36 = 4 x 9
= 2 x 2 x 3 x 3
48 = 6 x 8
= 2 x 3 x 4 x 2

Question 5.
Bart uses \(\frac{3}{12}\) cup milk to make muffins. Which fraction is equivalent to \(\frac{3}{12}\)?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{1}{2}\)
d. \(\frac{2}{3}\)

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

Explanation:
As per the given data,
Bart uses 3/12 cup of milk to make muffins
Divide the fraction with 3
(3 ÷ 3)/(12 ÷ 3) = 1/4
So, the equivalent fraction for 3/12 = 1/4

Go Math Lesson 6.4 Answer Key Homework 4th Grade Question 6.
Ashley bought 4 packages of juice boxes. There are 6 juice boxes in each package. She gave 2 juice boxes to each of 3 friends. How many juice boxes does Ashley have left?
Options:
a. 24
b. 22
c. 18
d. 12

Answer:
c. 18

Explanation:
As per the given data,
Ashley bought 4 packages of juice boxes
There are 6 juice boxes in each package = 6 x 4 = 24
She gave 2 juice boxes to each of 3 friends = 2 x 3 = 6 juice boxes
So, 24 – 6 = 18
Total number of juice boxes left with Ashley = 18

Page No. 347

Question 1.
Find a common denominator for \(\frac{1}{3}\) and \(\frac{1}{12}\) by dividing each whole into the same number of equal parts. Use the models to help.

common denominator:

Answer:
common denominator: 12

Explanation:
List the multiples of 3 = 3, 6, 9, 12, 15, 18, 21, ….
List the multiples of 12 = 12, 24, 36, 48, ….
So, the common denominators of 1/3 and 1/ 12 are 12

Write the pair of fractions as a pair of fractions with a common denominator.

Question 2.
\(\frac{1}{2}\) and \(\frac{1}{4}\)
Type below:
_________

Answer:
\(\frac{4}{8}\) and \(\frac{2}{8}\)

Explanation:
Common denominator of 1/2 and 1/4
List the multiples of 2 = 2, 4, 6, 8, 10, …
List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . .
Then, the common denominator of 1/2 and 1/4 is 4
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 4) ÷( 2 x 4) and ( 1 x 4 ) ÷ ( 4 x 4)
So, the common pair of fractions = 4/8 and 2/8

Question 3.
\(\frac{3}{4}\) and \(\frac{5}{8}\)
Type below:
_________

Answer:
\(\frac{6}{8}\) and \(\frac{5}{8}\)

Explanation:
Common denominator of 3/4 and 5/8
List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . .
List the multiples of 8 = 8, 16, 24, 32, . . . .
Then, the common denominator of 3/4 and 5/8 is 8
For the Common pair of fractions, multiply the common denominator with fractions
That is, (3 x 8) ÷( 4 x 8) and ( 5 x 8 ) ÷ ( 8 x 8)
So, the common pair of fractions = 6/8 and 5/8

Question 4.
\(\frac{1}{3}\) and \(\frac{1}{4}\)
Type below:
_________

Answer:
\(\frac{4}{12}\) and \(\frac{3}{12}\)

Explanation:
The common denominator of 1/3 and 1/4
List the multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, ….
List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . .
Then, the common denominator of 1 /3 and 1/4 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 12) ÷( 3 x 12) and ( 1 x 12 ) ÷ ( 4 x 12)
So, the common pair of fractions = 4/12 and 3/12

Question 5.
\(\frac{4}{12}\) and \(\frac{5}{8}\)
Type below:
_________

Answer:
\(\frac{8}{24}\) and \(\frac{15}{24}\)

Explanation:
Common denominator of 4/12 and 5/8
List the multiples of 12 = 12, 24, 36, 48, 60, …..
List the multiples of 8 = 8, 16, 24, 32, 40, 48, …
Then, the common denominator of 4/12 and 5/8 is 24
For the Common pair of fractions, multiply the common denominator with fractions
That is, (4 x 24) ÷( 12 x 24) and ( 5 x 24 ) ÷ ( 8 x 24)
So, the common pair of fractions = 8/24 and 15/24

Write the pair of fractions as a pair of fractions with a common denominator.

Question 6.
\(\frac{1}{4}\) and \(\frac{5}{6}\)
Type below:
_________

Answer:
\(\frac{3}{12}\) and \(\frac{10}{12}\)

Explanation:
The common denominator of 1/4 and 5/6
List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . .
List the multiples of 6 = 6, 12, 18, 24, 30, 36, ….
Then, the common denominator of 1/4 and 5/6 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 12) ÷( 4 x 12) and ( 5 x 12 ) ÷ ( 6 x 12)
So, common pair of fractions = 3/12 and 10/12

Lesson 6.4 Common Denominators Answer Key Question 7.
\(\frac{3}{5}\) and \(\frac{4}{10}\)
Type below:
_________

Answer:
\(\frac{6}{10}\) and \(\frac{4}{10}\)

Explanation:
The common denominator of 3/5 and 4/10
List the multiples of 5 = 5, 10, 15, 20, 25, 30, …..
List the multiples of 10 = 10, 20, 30, 40, 50 ….
Then, the common denominator of 3/5 and 4/10 is 10
For the Common pair of fractions, multiply the common denominator with fractions
That is, (3 x 10) ÷( 5 x 10) and ( 4 x 10 ) ÷ ( 10 x 10)
So, the common pair of fractions = 6/10 and 4/10

Tell whether the fractions are equivalent. Write = or ≠.

Question 8.
\(\frac{3}{4}\) ______ \(\frac{1}{2}\)

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

Explanation:
3/4 ≠ 1/2

Question 9.
\(\frac{3}{4}\) ______ \(\frac{6}{8}\)

Answer:
\(\frac{3}{4}\) = \(\frac{6}{8}\)

Explanation:
3/4
Multiply the numerator and denominator of 3/4 with 2
(3 x 2) ÷ ( 4 x 2 ) = 6/8
So, 3/4 = 6/8

Question 10.
\(\frac{1}{2}\) ______ \(\frac{4}{8}\)

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

Explanation:
1/2
Multiply the numerator and denominator of 1/2 with 4
(1 x 4) ÷ ( 2 x 4 ) = 4/8
So, 1/2 = 4/8

Question 11.
\(\frac{6}{8}\) ______ \(\frac{4}{8}\)

Answer:
\(\frac{6}{8}\) ≠ \(\frac{4}{8}\)

Explanation:
6/8 ≠ 4/8

Question 12.
Jerry has two same-size circles divided into the same number of equal parts. One circle has \(\frac{3}{4}\) of the parts shaded, and the other has \(\frac{2}{3}\) of the parts shaded. His sister says the least number of pieces each circle could be divided into is 7. Is his sister correct? Explain.
______

Answer:
As per the given data,
Jerry has two same size circles divided into the same number of equal parts
One circle has 3/4 of the parts shaded
So, non-shaded parts of one circle = 1 – 3/4 = 1/4
Another circle has 2/3 of the parts shaded
Non – shaded parts = 1 – 2/3 = 1/3
We can’t draw a conclusion about how many parts or pieces a circle can be divided
So, his sister is incorrect

Page No. 348

Question 13.
Carrie has a red streamer that is \(\frac{3}{4}\) yard long and a blue streamer that is \(\frac{5}{6}\) yard long. She says the streamers are the same length. Does this make sense? Explain.

______

Answer:
Carrie has a red streamer that is 3/4 yard long
The blue streamer that is 5/6 yard long
3/4 ≠ 5/6
She says the streamers are the same length, it doesn’t make any sense.

Question 14.
Leah has two same-size rectangles divided into the same number of equal parts. One rectangle has \(\frac{1}{3}\) of the parts shaded, and the other has \(\frac{2}{5}\) of the parts shaded. What is the least number of parts into which both rectangles could be divided?
______ parts

Answer:
15 parts

Explanation:
As per the given data,
Leah has two same size rectangles divided into the same number of equal parts
One rectangle has 1/3 of the parts shaded
Other rectangle has 2/5 of the parts shaded
15 parts

Question 15.
Julian says a common denominator for \(\frac{3}{4}\) and \(\frac{2}{5}\) is 9. What is Julian’s error? Explain.
Type below:
___________

Answer:
As per the given data,
Julian says a common denominator for 3/4 and 2/5 is 9
To find the common denominator for 3/4 and 2/5
List the multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, …..
List the multiples of 5 = 5, 10, 15, 20, 25, 30, ….
So, the common denominator for 3/4 and 2/5 is 20
Julian says 9 in place of 20 and it is wrong.

Go Math 4th Grade Chapter 6 Answer Key Question 16.
Miguel has two same-size rectangles divided into the same number of equal parts. One rectangle has \(\frac{3}{4}\) of the parts shaded, and the other has \(\frac{5}{8}\) of the parts shaded.
Into how many parts could each rectangle be divided? Show your work by sketching the rectangles.

______ parts

Answer:

8 parts

Explanation:
As per the given data,
Miguel has two same–size rectangles divided into the same number of equal parts.
One rectangle has 3/4 of the parts shaded.
Another has 5/8 of the parts shaded.
The possible parts are 8.

Common Core – Common Denominators – Page No. 349

Write the pair of fractions as a pair of fractions with a common denominator.

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

Answer:
\(\frac{8}{12} \text { and } \frac{9}{12}\)

Explanation:
2/3 and 3/4
List the multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, …
List the multiples of 4 = 4, 8, 12, 16, 20, …
Common multiple of 3 and 4 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (2 x 12) ÷( 3 x 12) and ( 3 x 12 ) ÷ ( 4 x 12)
So, common pair of fractions = 8/12 and 9/12

Question 2.
\(\frac{1}{4} \text { and } \frac{2}{3}\)
Type below:
_________

Answer:
\(\frac{3}{12} \text { and } \frac{8}{12}\)

Explanation:
1/4 and 2/3
List the multiples of 4 = 4, 8, 12, 16, 20, …
List the multiples of 3 = 3, 6, 9, 12, 15, 18, …
Common multiple of 4 and 3 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 12) ÷( 4 x 12) and ( 2 x 12 ) ÷ ( 3 x 12)
So, common pair of fractions = 3/12 and 8/12

Question 3.
\(\frac{3}{10} \text { and } \frac{1}{2}\)
Type below:
_________

Answer:
\(\frac{3}{10} \text { and } \frac{5}{10}\)

Explanation:
3/10 and 1/2
List the multiples of 10 = 10, 20, 30, 40, 50, ….
List the multiples of 2 = 2, 4, 6, 8, 10, 12, 14, ….
Common multiple of 10 and 2 is 10
For the Common pair of fractions, multiply the common denominator with fractions
That is, (3 x 10) ÷( 10 x 10) and ( 1 x 10 ) ÷ ( 2 x 10)
So, common pair of fractions = 3/10 and 5/10

Question 4.
\(\frac{3}{5} \text { and } \frac{3}{4}\)
Type below:
_________

Answer:
\(\frac{12}{20} \text { and } \frac{15}{20}\)

Explanation:
3/5 and 3/4
List the multiples of 5 = 5, 10, 15, 20, 25, 30, ….
List the multiples of 4 = 4, 8, 12, 16, 20, 24, …
Common multiple of 5 and 4 is 20
For the Common pair of fractions, multiply the common denominator with fractions
That is, (3 x 20) ÷( 5 x 20) and ( 3 x 20 ) ÷ ( 4 x 20)
So, common pair of fractions = 12/20 and 15/20

Question 5.
\(\frac{2}{4} \text { and } \frac{7}{8}\)
Type below:
_________

Answer:
\(\frac{4}{8} \text { and } \frac{7}{8}\)

Explanation:
2/4 and 7/8
List the multiples of 4 = 4, 8, 12, 16, 20, 24, …
List the multiples of 8 = 8, 16, 24, 32, 40, ….
Common multiple of 4 and 8 is 8
For the Common pair of fractions, multiply the common denominator with fractions
That is, (2 x 8) ÷( 4 x 8) and ( 7 x 8 ) ÷ ( 8 x 8)
So, common pair of fractions = 4/8 and 7/8

Question 6.
\(\frac{2}{3} \text { and } \frac{5}{12}\)
Type below:
_________

Answer:
\(\frac{8}{12} \text { and } \frac{5}{12}\)

Explanation:
2/3 and 5/12
List the multiples of 3 = 3, 6, 9, 12, 15, 18, …
List the multiples of 12 = 12, 24, 36, 48, 60, …
Common multiple of 3 and 12 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (2 x 12) ÷( 3 x 12) and ( 5 x 12 ) ÷ ( 12 x 12)
So, common pair of fractions = 8/12 and 5/12

Question 7.
\(\frac{1}{4} \text { and } \frac{1}{6}\)
Type below:
_________

Answer:
\(\frac{3}{12} \text { and } \frac{2}{12}\)

Explanation:
1/4 and 1/6
List the multiples of 4 = 4, 8, 12, 16, 20, 24, …
List the multiples of 6 = 6, 12, 18, 24, 30, …
Common multiple of 4 and 6 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 12) ÷( 4 x 12) and ( 1 x 12 ) ÷ ( 6 x 12)
So, common pair of fractions = 3/12 and 2/12

Tell whether the fractions are equivalent. Write = or ≠.

Question 8.
\(\frac{1}{2}\) ______ \(\frac{2}{5}\)

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

Explanation:
Multiply the numerator and denominator of 1/2 with 2
(1 x 2) ÷ (2 x 2) = 2/4
So, 1/2 ≠ 2/5

Question 9.
\(\frac{1}{2}\) ______ \(\frac{3}{6}\)

Answer:
\(\frac{1}{2}\) = \(\frac{3}{6}\)

Explanation:
1/2
Multiply the numerator and denominator of 1/2 with 3
(1 x 3) ÷ (2 x 3) = 3/6
So, 1/2 = 3/6

Question 10.
\(\frac{3}{4}\) ______ \(\frac{5}{6}\)

Answer:
\(\frac{3}{4}\) ≠ \(\frac{5}{6}\)

Explanation:
3/4 ≠ 5/6

Question 11.
\(\frac{6}{10}\) ______ \(\frac{3}{5}\)

Answer:
\(\frac{6}{10}\) = \(\frac{3}{5}\)

Explanation:
6/10
Divide the numerator and denominator of 6/10 with 2
(6 ÷ 2)/(10 ÷2) = 3/5
So, 6/10 = 3/5

Question 12.
\(\frac{6}{8}\) ______ \(\frac{3}{4}\)

Answer:
\(\frac{6}{8}\) = \(\frac{3}{4}\)

Explanation:
6/8
Divide the numerator and denominator of 6/8 with 2
(6 ÷2)/(8 ÷2) = 3/4
So, 6/8 = 3/4

Question 13.
\(\frac{3}{4}\) ______ \(\frac{2}{3}\)

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

Explanation:
3/4 ≠ 2/3

Question 14.
\(\frac{2}{10}\) ______ \(\frac{4}{5}\)

Answer:
\(\frac{2}{10}\) ≠ \(\frac{4}{5}\)

Explanation:
2/10
Divide the numerator and denominator of 2/10 with 2
(2 ÷ 2)/(10 ÷ 2) = 1/5
So, 2/10 ≠ 1/5

Question 15.
\(\frac{1}{4}\) ______ \(\frac{3}{12}\)

Answer:
\(\frac{1}{4}\) = \(\frac{3}{12}\)

Explanation:
1/4
Multiply the numerator and denominator of 1/4 with 3
(1 x 3)/(4 x 3) = 3/12
So, 1/4 = 3/12

Go Math Grade 4 Chapter 6 Review Test Answer Key Question 16.
Adam drew two same-sized rectangles and divided them into the same number of equal parts. He shaded \(\frac{1}{3}\) of one rectangle and \(\frac{1}{4}\) of other rectangle. What is the least number of parts into which both rectangles could be divided?
_________

Answer:
12 parts

Explanation:
As per the given data,
Adam drew two same size rectangles and divided them into the same number of equal parts
He shaded 1/3 of one rectangle
1/4 of another rectangle
List the multiples of 3 = 3, 6, 9, 12, 15, 18, …
List the multiples of 4 = 4, 8, 12, 16, 20, …
A common multiple of 3 and 4 is 12
So, the least number of parts which rectangles could be divided = 12 parts

Question 17.
Mera painted equal sections of her bedroom wall to make a pattern. She painted \(\frac{2}{5}\) of the wall white and \(\frac{1}{2}\) of the wall lavender. Write an equivalent fraction for each using a common denominator.
Type below:
_________

Answer:
1/2 are 4/10 and 5/10

Explanation:
As per the given data,
Mera painted equal sections of her bedroom wall to make a pattern
She painted 2/5 of the wall white and 1/2 of the wall lavender
List the multiples of 5 = 5, 10, 15, 20, 25, 30, …
List the multiples of 2 = 2 ,4, 6, 8, 10, 12, 14, …
The common denominator of 2/5 and 1/2 = 10
Multiply the 2/5 and 1/2 with 10
(2 x 10)/(5 x 10) and (1 x 10)/(2 x 10)
4/10 and 5/10
So, common fractions of 2/5 and 1/2 are 4/10 and 5/10

Common Core – Common Denominators – Page No. 350

Question 1.
Which of the following is a common denominator of \(\frac{1}{4}\) and \(\frac{5}{6}\)?
Options:
a. 8
b. 9
c. 12
d. 15

Answer:
c. 12

Explanation:
The common denominator of 1/4 and 5/6
List the multiples of 4 = 4, 8, 12, 16, 20, 24, …
List the multiples of 6 = 6, 12, 18, 24, 30, ….
So, the common denominator of 1/4 and 5/6 is 12

Question 2.
Two fractions have a common denominator of 8. Which of the following could be the two fractions?
Options:
a. \(\frac{1}{2} \text { and } \frac{2}{3}\)
b. \(\frac{1}{4} \text { and } \frac{1}{2}\)
c. \(\frac{3}{4} \text { and } \frac{1}{6}\)
d. \(\frac{1}{2} \text { and } \frac{4}{5}\)

Answer:
b. \(\frac{1}{4} \text { and } \frac{1}{2}\)

Explanation:
As per the given data,
Two fractions have a common denominator of 8
a. 1/2 and 2/3
List the multiples of 2 = 2, 4, 6, 8,10, ….
List the multiples of 3 = 3, 6, 9, 12, …
There is no common denominator of 8 for 1/2 and 2/3
b. 1/4 and 1 /2
List the multiples of 2 = 2, 4, 6, 8,10, ….
List the multiples of 4 = 4, 8, 12, 16, …
Here, the common denominator of 1 /4 and 1 /2 is 8
So, the answer is 1/4 and 1/2

Question 3.
Which number is 100,000 more than seven hundred two thousand, eighty-three?
Options:
a. 703,083
b. 712,083
c. 730,083
d. 802,083

Answer:
d. 802,083

Explanation:
802,083

Question 4.
Aiden baked 8 dozen muffins. How many total muffins did he bake?
Options:
a. 64
b. 80
c. 96
d. 104

Answer:
c. 96

Explanation:
As per the given data,
Aiden baked 8 dozen muffins
1 dozen = 12
then, 8 dozens = 12 x 8 = 96
So, Aiden baked total 96 muffins

Question 5.
On a bulletin board, the principal, Ms. Gomez, put 115 photos of the fourth grade students in her school. She put the photos in 5 equal rows. How many photos did she put in each row?
Options:
a. 21
b. 23
c. 25
d. 32

Answer:
b. 23

Explanation:
As per the given data,
On a bulletin board, the principal, Ms. Gomez, put 115 photos of the fourth-grade students in her school
She put the photos in 5 equal rows
Then, number of photos in each row = 115/5 = 23
So, Ms. Gomez put photos in each row = 23

Question 6.
Judy uses 12 tiles to make a mosaic. Eight of the tiles are blue. What fraction, in simplest form, represents the tiles that are blue?
Options:
a. \(\frac{2}{3}\)
b. \(\frac{2}{5}\)
c. \(\frac{3}{4}\)
d. \(\frac{12}{18}\)

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

Explanation:
As per the given data,
Judy uses 12 tiles to make a mosaic
Eight of the tiles are blue = 8/12
Divide the numerator and denominator of 8/12 with 4
(8 ÷ 4)/(12 ÷ 4) = 2/3
The simplest form of 8/12 is 2/3

Page No. 353

Question 1.
Keisha is helping plan a race route for a 10-kilometer charity run. The committee wants to set up the following things along the course.
Viewing areas: At the end of each half of the course
Water stations: At the end of each fifth of the course
Distance markers: At the end of each tenth of the course
Which locations have more than one thing located there?
First, make a table to organize the information.

Next, identify a relationship. Use a common denominator, and find equivalent fractions.
Finally, identify the locations at which more than one thing will be set up. Circle the locations.
Type below:
___________

Answer:
Keisha is helping plan a race route for a 10-kilometer charity run.

Question 2.
What if distance markers will also be placed at the end of every fourth of the course? Will any of those markers be set up at the same location as another distance marker, a water station, or a viewing area? Explain.
Type below:
___________

Answer:
It really depends on where you place the other markers.

Question 3.
Fifty-six students signed up to volunteer for the race. There were 4 equal groups of students, and each group had a different task.
How many students were in each group?
_____ students

Answer:
14 students

Explanation:
As per the given data,
Fifty-six students signed up to volunteer for the race
There are four groups of students
Number of students in each group = 56/4 = 14
Total number of students in each group = 14

Page No. 354

Question 4.
A baker cut a pie in half. He cut each half into 3 equal pieces and each piece into 2 equal slices. He sold 6 slices. What fraction of the pie did the baker sell?
\(\frac{□}{□}\)

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

Explanation:
A baker cut a pie in half. He cut each half into 3 equal pieces and each piece into 2 equal slices. He sold 6 slices. So, the remaining part is 1/2 of the pie.

Question 5.
Andy cut a tuna sandwich and a chicken sandwich into a total of 15 same-size pieces. He cut the tuna sandwich into 9 more pieces than the chicken sandwich. Andy ate 8 pieces of the tuna sandwich. What fraction of the tuna sandwich did he eat?
\(\frac{□}{□}\)

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

Explanation:
Let x be the number of pieces of the chicken sandwich so that x + 9 is the number of pieces of a tuna sandwich.
There is a total of 15 same-size pieces. So, we can write as
x + (x + 9) = 15
2x + 9 = 15
2x = 6
x = 3.
This means that there ate 3 + 9 = 12 pieces of a tuna sandwich. Since Andy ate 8, then this corresponds to a fraction of 8/12 = 2/3.

Question 6.
Luke threw balls into these buckets at a carnival. The number on the bucket gives the number of points for each throw. What is the least number of throws needed to score exactly 100 points? Explain.

_____ throws

Answer:
13 throws

Explanation:
Take the maximum number to get the minimum throws = 9 X 10 = 90.
6 X 1 = 6; 2 X 2 = 4.
Add 90 + 6 + 4 = 100;
So, the least number of throws needed to score exactly 100 points = 10 + 1 + 2 = 13.

Question 7.
Victoria arranges flowers in vases at her restaurant. In each arrangement, \(\frac{2}{3}\) of the flowers are yellow. What other fractions can represent the part of the flowers that are yellow? Shade the models to show your work.

\(\frac{□}{□}\)

Answer:

\(\frac{2}{3}\), \(\frac{8}{12}\), \(\frac{40}{60}\)

Explanation:
Basically, any fraction obtained by multiplying both the numerator and denominator by the same value would be an equivalent fraction:
2/3 = 2/3 * 4/4 = 8/12
8/12 = 8/12 * 5/5 = 40/60
etc.

Common Core – Find Equivalent Fractions – Page No. 355

Question 1.
Miranda is braiding her hair. Then she will attach beads to the braid. She wants \(\frac{1}{3}\) of the beads to be red. If the greatest number of beads that will fit on the braid is 12, what other fractions could represent the part of the beads that are red?

Answer:
\(\frac{2}{6}\), \(\frac{3}{9}\), \(\frac{4}{12}\)

Explanation:
Miranda is braiding her hair. Then she will attach beads to the braid. She wants \(\frac{1}{3}\) of the beads to be red. If the greatest number of beads that will fit on the braid is 12.
\(\frac{1}{3}\) X \(\frac{2}{2}\) = \(\frac{2}{6}\)
\(\frac{1}{3}\) X \(\frac{3}{3}\) = \(\frac{3}{9}\)
\(\frac{1}{3}\) X \(\frac{4}{4}\) = \(\frac{4}{12}\)

Question 2.
Ms. Groves has trays of paints for students in her art class. Each tray has 5 colors. One of the colors is purple. What fraction of the colors in 20 trays is purple?
\(\frac{□}{□}\)

Answer:
\(\frac{20}{100}\) or \(\frac{1}{5}\)

Explanation:
If you have 20 trays that are 100 colors with 20 being purple. 20/ 100 is 1/5

Question 3.
Miguel is making an obstacle course for field day. At the end of every sixth of the course, there is a tire. At the end of every third of the course, there is a cone. At the end of every half of the course, there is a hurdle. At which locations of the course will people need to go through more than one obstacle?
Type below:
_________

Answer:
\(\frac{1}{3}\), \(\frac{1}{2}\), \(\frac{2}{3}\) and final locations

Explanation:
We have three fractions with different denominators: sixths, thirds, and halves.
The first step is to make all the denominators equal for 1/6, 1/3, 1/2.
In this case, we want sixths since LCM(2, 3, 6) = 6
since 1/3 = 2/6, and 1/2 = 3/6. Now we can start solving.
1. There are six tires at the following: 1/6, 2/6, 3/6, 4/6, 5/6, and 6/6.
2. There are three cones at the following (G.C.F.): 2/6 (or 1/3), 4/6 (or 2/3), and 6/6 (or 3/3).
3. There are two hurdles at the following (G.C.F.): 3/6 (or 1/2) and 6/6 (or 2/2).
We look for common numbers.
1. On 2/6, there are two obstacles: a tire and a cone.
2. On 3/6, there are two obstacles: a tire and a hurdle.
3. On 4/6, there are two obstacles: a tire and a cone.
4. At 6/6, there are three obstacles: a tire, cone, and a hurdle.
2/6 = 1/3
3/6 = 1/2
4/6 = 2/3
6/6 = 1
The answers are 1/3, 1/2, 2/3, and 1.

Question 4.
Preston works in a bakery where he puts muffins in boxes. He makes the following table to remind himself how many blueberry muffins should go in each box.

How many blueberry muffins should Preston put in a box with 36 muffins?
_________

Answer:
12 blueberry muffins

Explanation:
Preston works in a bakery where he puts muffins in boxes. He makes the following table to remind himself how many blueberry muffins should go in each box.
So, he had 2 blueberry muffins out of 6 muffins.
2/6 X 2/2 = 4/12. 4 blueberry muffins out of 12 muffins.
2/6 X 4/4 = 8/24. 8 blueberry muffins out of 24 muffins.
2/6 X 6/6 = 12/36. 12 blueberry muffins out of 36 muffins.

Common Core – Find Equivalent Fractions – Page No. 356

Question 1.
A used bookstore will trade 2 of its books for 3 of yours. If Val brings in 18 books to trade, how many books can she get from the store?
Options:
a. 9
b. 12
c. 18
d. 27

Answer:
b. 12

Explanation:
A used bookstore will trade 2 of its books for 3 of yours. If Val brings in 18 books to trade 2/3 X 6/6 = 12/18, she get 12 books

Question 2.
Every \(\frac{1}{2}\) hour Naomi stretches her neck; every \(\frac{1}{3}\) hour she stretches her legs; and every \(\frac{1}{6}\) hour she stretches her arms. Which parts of her body will Naomi stretch when \(\frac{2}{3}\) of an hour has passed?
Options:
a. neck and legs
b. neck and arms
c. legs and arms
d. none

Answer:
c. legs and arms

Explanation:
Summing \(\frac{1}{2}\)‘s only gives integer values giving 1, 2, 3, 4…or
integer values +\(\frac{1}{2}\) and 0 + \(\frac{1}{2}\) = \(\frac{1}{2}\), 1 \(\frac{1}{2}\), 2 \(\frac{1}{2}\)…
So neck is excluded
Every \(\frac{1}{3}\): \(\frac{1}{3}\) + \(\frac{1}{2}\) = \(\frac{2}{3}\)
Legs will be stretched at \(\frac{2}{3}\) hour
Every \(\frac{1}{6}\): \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) = \(\frac{4}{6}\)
Divide top and bottom by 2 giving:
(4 ÷ 2)/(6 ÷ 2) = \(\frac{2}{3}\)
Arms will be stretched at latex]\frac{2}{3}[/latex] hour

Question 3.
At the beginning of the year, the Wong family car had been driven 14,539 miles. At the end of the year, their car had been driven 21,844 miles. How many miles did the Wong family drive their car during that year?
Options:
a. 6,315 miles
b. 7,295 miles
c. 7,305 miles
d. 36,383 miles

Answer:
c. 7,305 miles

Explanation:
If at the beginning of the year, the Wong family’s car had driven 14539 miles and at the end of the year, it had driven 21844 miles, then subtract 14539 from 21844 to determine the difference between the two values, which will tell you how many miles the Wong family drove their car for during the year.
21844 – 14539 = 7305 miles

Question 4.
Widget Company made 3,600 widgets in 4 hours. They made the same number of widgets each hour. How many widgets did the company make in one hour?
Options:
a. 80
b. 90
c. 800
d. 900

Answer:
d. 900

Explanation:

3,600 widgets in 4 hours therefore 3,600 / 4 for one hour = 900 widgets 900 widgets in one hour.

Question 5.
Tyler is thinking of a number that is divisible by 2 and by 3. By which of the following numbers must Tyler’s number also be divisible?
Options:
a. 6
b. 8
c. 9
d. 12

Answer:
a. 6

Explanation:
The number 6 is divisible by 2 and by 3.

Question 6.
Jessica drew a circle divided into 8 equal parts. She shaded 6 of the parts. Which fraction is equivalent to the part of the circle that is shaded?
Options:
a. \(\frac{2}{3}\)
b. \(\frac{3}{4}\)
c. \(\frac{10}{16}\)
d. \(\frac{12}{18}\)

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

Explanation:
Jessica drew a circle divided into 8 equal parts. She shaded 6 of the parts.
6/8 = 3/4

Page No. 357

Choose the best term from the box.

Question 1.
________ name the same amount.
________

Answer:
Equivalent Fractions

Question 2.
A _________ is a common multiple of two or more denominators
________

Answer:
Common Denominator

Write two equivalent fractions.

Question 3.
\(\frac{2}{5}\)
Type below:
________

Answer:
\(\frac{4}{10}\) and \(\frac{6}{15}\)

Explanation:
Two equivalent fractions of 2/5
Multiply the 2/5 with 2
(2 x 2)/(5 x 2) = 4/10
Multiply the 2/5 with 3
(2 x 3)/(5 x 3) = 6/15
So, the equivalent fractions of 2/5 are 4/10 and 6/15

Question 4.
\(\frac{1}{3}\)
Type below:
________

Answer:
\(\frac{2}{6}\) and \(\frac{3}{9}\)

Explanation:
Two equivalent fractions of 1/3
Multiply the 1/3 with 2
(1 x 2)/(3 x 2) = 2/6
Multiply the 1/3 with 3
(1 x 3)/(3 x 3) = 3/9
So, the equivalent fractions of 1/3 are 2/6 and 3/9

Question 5.
\(\frac{3}{4}\)
Type below:
________

Answer:
\(\frac{6}{8}\) and \(\frac{9}{12}\)

Explanation:
Two equivalent fractions of 3/4
Multiply the 3/4 with 2
(3 x 2)/(4 x 2) = 6/8
Multiply the 3/4 with 3
(3 x 3)/(4 x 3) = 9/12
So, the equivalent fractions of 3/4 are 6/8 and 9/12

Tell whether the fractions are equivalent. Write = or ≠.

Question 6.
\(\frac{2}{3}\) ______ \(\frac{4}{12}\)

Answer:
\(\frac{2}{3}\) ≠ \(\frac{4}{12}\)

Explanation:
2/ 3
Multiply the numerator and denominator of 2/3 with 2
(2 x 2)/(3 x 2) = 4/6
So, 2/3 ≠ 4/12

Question 7.
\(\frac{5}{6}\) ______ \(\frac{10}{12}\)

Answer:
\(\frac{5}{6}\) =_ \(\frac{10}{12}\)

Explanation:
5/6
Multiply the 5/6 with 2
(5 x 2)/(6 x 2) = 10/12
So, 5/6 = 10/12

Question 8.
\(\frac{1}{4}\) ______ \(\frac{4}{8}\)

Answer:
\(\frac{1}{4}\) ≠ \(\frac{4}{8}\)

Explanation:
1/4
Multiply the numerator and denominator of 1/4 with 4
(1 x 4)/(4 x 4) = 4/16
So, 1/4 ≠ 4/8

Write the fraction in simplest form.

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

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

Explanation:
6/8
Divide the numerator and denominator of 6/8 with 2
(6 ÷ 2)/( 8 ÷ 2) = 3/4
The simplest form of 6/8 is 3/4

Question 10.
\(\frac{25}{100}\)
\(\frac{□}{□}\)

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

Explanation:
25/100
Divide the numerator and denominator of 25/100 with 25
(25 ÷ 25)/( 100 ÷ 25) = 1/4
The simplest form of 25/100 is 1/4

Question 11.
\(\frac{8}{10}\)
\(\frac{□}{□}\)

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

Explanation:
8/10
Divide the numerator and denominator of 8/10 with 2
(8 ÷ 2)/( 10 ÷ 2) = 4/5
The simplest form of 8/10 is 4/5

Write the pair of fractions as a pair of fractions with a common denominator.

Question 12.
\(\frac{3}{10} \text { and } \frac{2}{5}\)
Type below:
_________

Answer:
\(\frac{3}{10} \text { and } \frac{4}{10}\)

Explanation:
3/ 10 and 2/5
List the multiples of 10 = 10, 20, 30, 40, 50, …
List the multiples of 5 = 5, 10, 15, 20, 25, 30, …
Common denominator of 3/10 and 2/5 = 10
Multiply the 3/10 and 2/5 with 10
(3 x 10)/(10 x 10) and (2 x 10)/(5 x 10)
3/ 10 and 4/10
Pair of fractions of 3/10 and 2/5 are 3/10 and 4/10

My Homework Lesson 6 Compare and Order Fractions Answer Key Question 13.
\(\frac{1}{3} \text { and } \frac{3}{4}\)
Type below:
_________

Answer:
\(\frac{3}{12} \text { and } \frac{9}{12}\)

Explanation:
1/3 and 3/4
List the multiples of 3 = 3, 6, 9, 12, 15, 18, …
List the multiples of 4 = 4, 8, 12, 16, 20, ….
The common denominator of 1/3 and 3/4 are 12
Multiply the 1/3 and 3/4 with 12
(1 x 12)/(3 x 12) and (3 x 12)/(4 x 12)
3/ 12 and 9/12.
Pair of fractions of 1/3 and 3/4 are 3/12 and 9/12

Page No. 358

Question 14.
Sam needs \(\frac{5}{6}\) cup mashed bananas and \(\frac{3}{4}\) cup mashed strawberries for a recipe. He wants to find out whether he needs more bananas or more strawberries. How can he write \(\frac{5}{6}\) and \(\frac{3}{4}\) as a pair of fractions with a common denominator?
Type below:
_________

Answer:
\(\frac{10}{12}\) and \(\frac{9}{12}\)

Explanation:
Sam needs 5/6 cup mashed bananas and 3/4 cup mashed strawberries for a recipe
He wants to find out whether he needs more bananas or strawberries
List the multiples of 6 = 6, 12, 18, 24, 30, 36, 42,…..
List the multiples of 4 = 4, 8, 12, 16, 20, 24, ….
The common denominator of 6 and 4 is 12
Multiply the numerator and denominator of 5/6 and 3/4 with 12
(5 x 12)/(6 x 12) and (3 x 12)/(4 x 12)
10/12 and 9/12
Pair of fractions with a common denominator for 5/6 and 3/4 are 10/12 and 9/12

Question 15.
Karen will divide her garden into equal parts. She will plant corn in \(\frac{8}{12}\) of the garden. What is the fewest number of parts she can divide her garden into?
______ parts

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

Explanation:
As per the given data,
Keren will divide her garden into equal parts
She will plant corn in 8/12 of the garden
To get the least number of parts she can divide her garden, simplify the 8/12
Divide the numerator and denominator of 8/12 with 4
(8 ÷ 4)/(12 ÷ 4) = 2/3
So, Karen can divide her garden into 2/3 of parts

Question 16.
Olivia is making scarves. Each scarf will have 5 rectangles, and \(\frac{2}{5}\) of the rectangles will be purple. How many purple rectangles does she need for 3 scarves?
______ purple rectangles

Answer:
6 purple rectangles

Explanation:
As per the given data,
Olivia is making scarves
Each scarf will have 5 rectangles and 2/5 of the rectangles will be purple = 5 x 2/5 = 2
That means each scarf will have 2 purple rectangles
For 3 scarves = 3 x 2 = 6
So, she needs 6 purple rectangles.

Question 17.
Paul needs to buy \(\frac{5}{8}\) pound of peanuts. The scale at the store measures parts of a pound in sixteenths. What measure is equivalent to \(\frac{5}{8}\) pound?
\(\frac{□}{□}\) pound of peanuts

Answer:
\(\frac{10}{16}\) pound of peanuts

Explanation:
As per the given data,
Paul needs to buy 5/8 pounds of peanuts
The scale at the store measures parts of a pound in sixteenths = 16 x 5/8 = 10
To find an Equivalent fraction of 5/8
Multiply the numerator and denominator of 5/8 with 2
(5 x 2)/( 8 x 2) = 10/16
So, the equivalent fraction of 5/8 is 10/16

Page No. 361

Question 1.
Compare \(\frac{2}{5}\) and \(\frac{1}{8}\). Write < or >.

\(\frac{2}{5}\) _____ \(\frac{1}{8}\)

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

Explanation:
Least common denominator of 5 and 8 = 40
Multiply the numerator and denominator of 2/5 and 1/8 with 40
2/ 5 = (2 x 8)/(5 x 8) = 16/40
1/8 = (1 x 5)/(8 x 5) = 5/40
The denominators are the same now
So, compare the numerator to find the greater number
16/40 > 5/40
So, 2/5 > 1/8

Compare. Write < or >.

Question 2.
\(\frac{1}{2}\) _____ \(\frac{4}{6}\)

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

Explanation:
1/2 and 4/6
Least common denominator of 2 and 6 = 6
Multiply the numerator and denominator of 1/2 and 4/6 with 6
1/ 2 = (1 x 6)/(2 x 6) = 6/12
4/ 6 = (4x 2)/(6 x 2) = 8/12
The denominators are the same now
So, compare the numerator to find the greater number.
6/12 < 8/12
So, 1/2 < 4/6

Question 3.
\(\frac{3}{10}\) _____ \(\frac{1}{2}\)

Answer:
\(\frac{3}{10}\) > \(\frac{1}{2}\)

Explanation:
1 / 10 and 1/2
The least common denominator of 10 and 2 = 10
Multiply the numerator and denominator of 3/10 and 1/2 by 10
3/ 10 = (3 x 2)/(10 x 2) = 6/20
1/2 = (1 x 10)/(2 x 10) = 10/20
The denominators are the same now
So, compare the numerator to find the greater number.
6/20 < 10/20
So, 3/10 > 1/2

Question 4.
\(\frac{11}{12}\) _____ \(\frac{4}{8}\)

Answer:
\(\frac{11}{12}\) > \(\frac{4}{8}\)

Explanation:
11/12 and 4/8
Least common denominator of 12 and 8 = 24
Multiply the numerator and denominator of 11/12 and 4/8 with 24
11/ 12 = (11 x 8)/(12 x 8) = 88/96
4/8 = (4 x 12)/(8 x 12) = 48/96
The denominators are the same now
So, compare the numerator to find the greater number
88/96 > 48/96
So, 11/12 > 4/8

Practice and Homework Lesson 6.6 Answer Key Question 5.
\(\frac{5}{8}\) _____ \(\frac{2}{5}\)

Answer:
\(\frac{5}{8}\) > \(\frac{2}{5}\)

Explanation:
5/ 8 and 2/5
Least common denominator of 5 and 8 = 40
Multiply the numerator and denominator of 5/8 and 2/8 with 40
5/ 8 = (5 x 5)/(8 x 5) = 25/40
2/5 = (2 x 8)/(5 x 8) = 16/40
The denominators are same now
So, compare the numerator to find the greater number
25/ 40 > 16/40
So, 5/8 > 2/5

Question 6.
\(\frac{8}{10}\) _____ \(\frac{3}{8}\)

Answer:
\(\frac{8}{10}\) > \(\frac{3}{8}\)

Explanation:
8/10 and 3/8
Least common denominator of 10 and 8 = 40
Multiply the numerator and denominator of 8/10 and 3/8 with 40
8/ 10 = (8 x 8)/(10 x 8) = 64/80
3/8 = (3 x 10)/(8 x 10) = 30/80
The denominators are same now
So, compare the numerator to find the greater number
64/80 > 30/80
So, 8/10 > 3/8

Question 7.
\(\frac{1}{3}\) _____ \(\frac{7}{12}\)

Answer:
\(\frac{1}{3}\) < \(\frac{7}{12}\)

Explanation:
1/3 and 7/12
Least common denominator of 3 and 12 = 12
Multiply the numerator and denominator of 1/3 and 7/12 with 40.
1/ 3 = (1 x 12)/(3 x 12) = 12/36
7/12 = (7 x 3)/(12 x 3) = 21/36
The denominators are same now
So, compare the numerator to find the greater number
12/36 < 21/36
So, 1/3 < 7/12

Question 8.
\(\frac{2}{6}\) _____ \(\frac{7}{8}\)

Answer:
\(\frac{2}{6}\) < \(\frac{7}{8}\)

Explanation:
2/6 and 7/8
Least common denominator of 6 and 8 = 24
Multiply the numerator and denominator of 2/6 and 7/8 with 40
2/ 6 = (2 x 8)/(6 x 8) = 16/48
7/8 = (7 x 6)/(8 x 6) = 42/48
The denominators are same now
So, compare the numerator to find the greater number
16/48<42/48
So, 2/6 < 7/8

Question 9.
\(\frac{4}{8}\) _____ \(\frac{2}{10}\)

Answer:
\(\frac{4}{8}\) > \(\frac{2}{10}\)

Explanation:
4/8 and 2/10
Least common denominator of 8 and 10 = 40
Multiply the numerator and denominator of 4/8 and 2/10 with 40
4/ 8 = (4 x 10)/(8 x 10) = 40/80
2/10 = (2 x 8)/(10 x 8) = 16/80
The denominators are same now
So, compare the numerator to find the greater number
40/80 > 16/80
So, 4/8 > 2/10

Reason Quantitatively Algebra Find a numerator that makes the statement true.

Question 10.
\(\frac{2}{4}<\frac { □ }{ 6 } \)
□ = _____

Answer:
4

Explanation:
2/4 < x/6
Least common denominator of 4 and 6 = 12
Multiply the numerator and denominator of 2/4 < x/6 with 40
2/4 = (2 x 6)/(4 x 6) = 12/24
x/6 = (x x 4)/(6 x 4) = 4 x/24
The denominators are same now
So, compare the numerator to find the greater number
12/24 < 4 X 4/24

Question 11.
\(\frac{8}{10}>\frac { □ }{ 8 } \)
□ = _____

Answer:
1

Explanation:
8/10 < x/8
Least common denominator of 10 and 8 = 40
8/10 = (8 x 4)/(10 x 4) = 32/40
x/8 = (x X 5)/(8 x 5) = 5x/40
The denominators are same now
So, compare the numerator to find the greater number
8/10 < 5x/40. X will be 1

Question 12.
\(\frac{10}{12}>\frac { □ }{ 4 } \)
□ = _____

Answer:
1

Explanation:
10/12 < x/4
Least common denominator of 12 and 4 = 12
10/12 = (10 x 1)/(12 x 1) = 10/12
x/4 = (x X 3)/(4 x 3) = 3x/12
The denominators are same now
So, compare the numerator to find the greater number
10/12 < 3/12. X will be 1.

Question 13.
\(\frac{2}{5}<\frac { □ }{ 10 } \)
□ = _____

Answer:
5

Explanation:
2/5 < x/10
Least common denominator of 5 and 10 = 10
2/5 = (2x 2)/(5 x 2) = 4/10
x/10 = (x X 1)/(10 x 1) = x/10
The denominators are same now
So, compare the numerator to find the greater number
2/5 < 5/10. X will be 5.

Question 14.
When two fractions are between 0 and \(\frac{1}{2}\), how do you know which fraction is greater? Explain.
Type below:
_______

Answer:
When two fractions are between 0 and \(\frac{1}{2}\). \(\frac{1}{2}\) is greater. As the tenths place of 5 is greater than 0. \(\frac{1}{2}\) is greater.

Question 15.
If you know that \(\frac{2}{6}<\frac{1}{2}\) and \(\frac{3}{4}<\frac{1}{2}\), what do you know about \(\frac{2}{6} \text { and } \frac{3}{4}\)?
Type below:
_______

Answer:

Explanation:
As per the given data,
2/6 < 1/2 and 3/4 < 1/2
Then, 2/6 and 3/4 is
The least common denominator of 6 and 4 is 12
(2 x 4)/(6 x 4) and (3 x 6)/(4 x 6)
8/24 and 18/24
Now, the denominators are same, then compare the numerators
8/24 > 18/24
So, 2/6 > 3/4

Question 16.
Sandra has ribbons that are \(\frac{3}{4}\) yard, \(\frac{2}{6}\) yard, \(\frac{1}{5}\) yard, and \(\frac{4}{7}\) yard long. She needs to use the ribbon longer than \(\frac{2}{3}\) yard to make a bow. Which length of ribbon could she use for the bow?
\(\frac{□}{□}\) yard

Answer:

Explanation:

Page No. 362

Question 17.
Saundra ran \(\frac{7}{12}\) of a mile. Lamar ran \(\frac{3}{4}\) of a mile. Who ran farther? Explain.
_______

Answer:
As per the given data,
Saundra ran 7/12 of a mile
Lamar ran 3/4 of a mile
The least common denominator of 7/12 and 3/4 is 12
(7x 1)/( 12 x 1) and ( 3 x 3 )/( 4 x 3)
7/12 and 9/12
So, 7/12 < 9/12
So, 7/12 < 3/4
Lamar ran greater distance than Saundra

Question 18.
What’s the Question? Selena ran farther than Manny.
Type below:
_______

Answer:
Who ran farther? Selena or Manny

Go Math Grade 4 Practice Book Pdf Lesson 6.6 Question 19.
Chloe made a small pan of ziti and a small pan of lasagna. She cut the ziti into 8 equal parts and the lasagna into 9 equal parts. Her family ate \(\frac{2}{3}\) of the lasagna. If her family ate more lasagna than ziti, what fraction of the ziti could have been eaten?
Type below:
_______

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

Explanation:
As per the given data,
Chloe made a small pan of ziti and a small pan of lasagna
She cut the ziti into 8 equal parts and the lasagna into 9 equal parts
Her family ate 2/3 of the lasagna = (2/3) x 9 = 6 parts
If her family ate more lasagna than ziti, then that is less than 6 parts
So, 1/4 of the ziti = (1/4) x 8 = 2 parts
So, 1/4 of the ziti eaten by Chloe’s family

Question 20.
James, Ella, and Ryan biked around Eagle Lake. James biked \(\frac{2}{10}\) of the distance in an hour. Ella biked \(\frac{4}{8}\) of the distance in an hour. Ryan biked \(\frac{2}{5}\) of the distance in an hour. Compare the distances biked by each person by matching the statements to the correct symbol. Each symbol may be used more than once or not at all.

Type below:
_______

Answer:
2/10 < 4/8
1 / 8 > 2/5
2/10 < 2/5

Explanation:
As per the given data,
James, Ella, and Ryan biked around eagle lake
James biked 2/10 of the distance in an hour
Ella biked 4/8 of the distance in an hour
Ryan biked 2/5 of the distance in an hour
Least common denominator of 2 /10, 4/8, and 2/5 is 40
(2x 4)/(10 x 4), (4 x 5)/(8 x 5), and (2 x 8)/(5 x 8)
8/40, 20/ 40, and 16/ 40
8/40 < 16/40 < 20/40
2/10 < 2/5 < 4/8
So, 2/10 < 4/8
1 / 8 > 2/5
2/10 < 2/5

Common Core – Compare Fractions Using Benchmarks – Page No. 363

Compare. Write < or > .

Question 1.

Answer:
\(\frac{1}{8}\) < \(\frac{6}{10}\)

Explanation:

Question 2.
\(\frac{4}{12}\) _______ \(\frac{4}{6}\)

Answer:
\(\frac{4}{12}\) < \(\frac{4}{6}\)

Explanation:
4/12 and 4/6
4/12 is less than 1/2
4/6 is greater than 1/2
So, 4/12 < 4/6

Question 3.
\(\frac{2}{8}\) _______ \(\frac{1}{2}\)

Answer:
\(\frac{2}{8}\) < \(\frac{1}{2}\)

Explanation:
2/8 and 1/2
2/8 is less than 1/2
1/2 is equal to 1/2
So, 2/8 < 1/2

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

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

Explanation:
3/5 and 3/3
3/5 is greater than 1/2
3/3 is equal to 1
So, 3/5 < 3/3

Question 5.
\(\frac{7}{8}\) _______ \(\frac{5}{10}\)

Answer:
\(\frac{7}{8}\) > \(\frac{5}{10}\)

Explanation:
7/8 and 5/10
7/8 is greater than 1/2
5/10 is equal to 1/2
So, 5/10 < 7/8

Question 6.
\(\frac{9}{12}\) _______ \(\frac{1}{3}\)

Answer:
\(\frac{9}{12}\) > \(\frac{1}{3}\)

Explanation:
9/12 and 1/3
9/ 12 is greater than 1/2
1/3 is less than 1/2
1/3 < 9/12

Question 7.
\(\frac{4}{6}\) _______ \(\frac{7}{8}\)

Answer:
\(\frac{4}{6}\) < \(\frac{7}{8}\)

Explanation:
4/6 and 7/8
4/6 is greater than 1/2
7/8 is closer to 1
So, 4/6 < 7/8

Question 8.
\(\frac{2}{4}\) _______ \(\frac{2}{3}\)

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

Explanation:
2/4 and 2/3
2/4 is equal to 1/2
2/3 is greater than 1/2
So, 2/4 < 2/3

Question 9.
\(\frac{3}{5}\) _______ \(\frac{1}{4}\)

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

Explanation:
3/5 and 1/4
3/5 is greater than 1/2
1/4 is less than 1/2
So, 1/4 < 3/5

Question 10.
\(\frac{6}{10}\) _______ \(\frac{2}{5}\)

Answer:
\(\frac{6}{10}\) > \(\frac{2}{5}\)

Explanation:
6/10 and 2/5
6/10 is greater than 1/2
2/5 is less than 1/2
So, 2/5 < 6/10

Question 11.
\(\frac{1}{8}\) _______ \(\frac{2}{10}\)

Answer:
\(\frac{1}{8}\) < \(\frac{2}{10}\)

Explanation:
1/8 and 2/10
1/8 is less than 1/2
2/10 is less than 1/2 but greater than 1/8
So, 1/8 < 2/10

Question 12.
\(\frac{2}{3}\) _______ \(\frac{5}{12}\)

Answer:
\(\frac{2}{3}\) > \(\frac{5}{12}\)

Explanation:
2/3 and 5/12
2/3 is greater than 1/2
5/12 is less than 1/2
So, 5/12 < 2/3

Question 13.
\(\frac{4}{5}\) _______ \(\frac{5}{6}\)

Answer:
\(\frac{4}{5}\)< \(\frac{5}{6}\)

Explanation:
4/5 and 5/6
4/5 is greater than 1/2
5/6 is greater than 1/2
Common denominator is 30
(4×6)/(5×6) and (5×5)/(6×5)
24/30 and 25/30
24/30 < 25/30
So, 4/5 < 5/6

Question 14.
\(\frac{3}{5}\) _______ \(\frac{5}{8}\)

Answer:
\(\frac{3}{5}\) < \(\frac{5}{8}\)

Explanation:
3/5 and 5/8
3/5 is greater than 1/2
5/8 is greater than 1/2
Common denominator is 40
(3×8)/(5×8) and (5×5)/(8×5)
24/40 and 25/ 40
24/40 < 25/40
3/5 < 5/8

Question 15.
\(\frac{8}{8}\) _______ \(\frac{3}{4}\)

Answer:
\(\frac{8}{8}\) > \(\frac{3}{4}\)

Explanation:
8/8 and 3/4
8/8 is equal to 1
3/4 is less than 1
3/4 < 8/8

Question 16.
Erika ran \(\frac{3}{8}\) mile. Maria ran \(\frac{3}{4}\) mile. Who ran farther?
_________

Answer:
Maria

Explanation:
As per the data,
Erika ran 3/8 mile
Maria ran 3/4 mile
Multiply the numerator and denominator of 3/4 with 2
(3×2)/(4×2) = 6/8
3/8 < 6/8
So, 3/8 < 3/4
So, Maria ran faster than Erika

Lesson 6.8 Compare and Order Fractions Question 17.
Carlos finished \(\frac{1}{3}\) of his art project on Monday. Tyler finished \(\frac{1}{2}\) of his art project on Monday. Who finished more of his art project on Monday?
_________

Answer:
Tyler

Explanation:
From the given data,
Carlos finished 1/3 of his art project on Monday
Tyler finished ½ of his art project on Monday
1/3 is less than 1/2
1/2 is equal to 1/2
So, 1/3 < 1/2
Then, Tyler finished more of his work on Monday

Common Core – Compare Fractions Using Benchmarks – Page No. 364

Question 1.
Which symbol makes the statement true?

Options:
a. >
b.<
c. =
d. none

Answer:
a. >

Explanation:
4/6 ? 3/8
By comparing 4/6 with 1/2, 4/6 > 1/2
By comparing 3/8 with 1/2, 3/8 < 1/2
So, 4/6 > 3/8

Question 2.
Which of the following fractions is greater than \(\frac{3}{4}\)?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{5}{6}\)
c. \(\frac{3}{8}\)
d. \(\frac{2}{3}\)

Answer:
b. \(\frac{5}{6}\)

Explanation:
From the given data,
By comparing the 3/4 with 1/2, 3/4 > 1/2
Same as above, compare the options with ½
a. 1/4 < 1/2
b. 5/6 > 1/2
c. 3/8 < 1/2
d. 2/3 > 1/2
5/6 and 2/3 are greater than the 1/2
So, compare the 5/6 with 2/3
Then, 5/6 > 2/3
So, 5/6 > 3/4

Question 3.
Abigail is putting tiles on a tabletop. She needs 48 tiles for each of the 8 rows. Each row will have 6 white tiles. The rest of the tiles will be purple. How many purple tiles will she need?
Options:
a. 432
b. 384
c. 336
d. 48

Answer:
c. 336

Explanation:
As per the given data
Abigail is putting tiles on a tabletop
Number of rows = 8
She needs 48 tiles for each row = 48×8 = 384
Number of white tiles per row = 6×8 = 48
Rest of the tiles will be purple = 384 – 48 =336
So, the total number of purple color tiles = 336

Question 4.
Each school bus going on the field trip holds 36 students and 4 adults. There are 6 filled buses on the field trip. How many people are going on the field trip?
Options:
a. 216
b. 240
c. 256
d. 360

Answer:
b. 240

Explanation:
From the given data,
Each school bus going on the field trip holds 36 students and 4 adults
There are 6 filled buses on the field trip
6 x (36 + 4) = 6 x 40 = 240
So, the total number of people on the field trip = 240

Question 5.
Noah wants to display his 72 collector’s flags. He is going to put 6 flags in each row. How many rows of flags will he have in his display?
Options:
a. 12
b. 15
c. 18
d. 21

Answer:
a. 12

Explanation:
As mentioned in the data,
Noah wants to display his 72 collector’s flag
He is going to put 6 flags in each row = 6x = 72
X = 12
So, a total 12 number of rows of flags will have on his display

Question 6.
Julian wrote this number pattern on the board:
3, 10, 17, 24, 31, 38.
Which of the numbers in Julian’s pattern are composite numbers?
Options:
a. 3, 17, 31
b. 10, 24, 38
c. 10, 17, 38
d. 17, 24, 38

Answer:
b. 10, 24, 38

Explanation:
As per the given information
Julian wrote his number pattern on the board =3, 10, 17, 24, 31, 38
Factors of 3 = 1,3
Factors of 10 = 1,2,5,10
Factors of 17 = 1, 17
Factors of 24 = 1, 2, 3, 4, 6
Factors of 31 = 1, 31
Factors of 38 = 1, 2, 19, 38
So, the composite number is 10, 24, and 38, which numbers have more than 2 factors

Page No. 367

Question 1.
Compare \(\frac{2}{5}\) and \(\frac{1}{10}\).
Think: Use ______ as a common denominator.
\(\frac{2}{5}=\frac { □×□ }{ □×□ } \) = \(\frac{□}{□}\)
\(\frac{1}{10}\)
Think: 4 tenth-size parts 1 tenth-size part.
\(\frac{2}{5}\) _____ \(\frac{1}{10}\)

Answer:
\(\frac{2}{5}\) > \(\frac{1}{10}\)

Explanation:
Compare 2/5 and 1/10
Think: 10 as common denominator
Multiply the numerator and denominator of 2/5 with 2
Then, (2×2) ÷ (5×2) = 4/10
Now, compare the 4/10 with 1/10
4/10 > 1/10
So, 2/5 > 1/10

Question 2.
Compare \(\frac{6}{10}\) and \(\frac{3}{4}\).
Think: Use ______ as a common denominator.
\(\frac{6}{10}\)
\(\frac{3}{4}=\frac { □×□ }{ □×□ } \) = \(\frac{□}{□}\)
Think: A tenth-size part an eighth-size part.
\(\frac{6}{10}\) _____ \(\frac{3}{4}\)

Answer:
\(\frac{6}{10}\) < \(\frac{3}{4}\)

Explanation:
Compare 6/10 and 3/4
Think: Use 40 as a common denominator
So, multiply the denominator and numerator of 3/4 with 10
That is, (3×10) ÷ (4×10) = 30/40
Multiply the numerator and denominator of 6/10 with 4
That is, (6×4) ÷ (10×4) = 24/40
Denominators are same, compare the numerator values of 24/40 and 30/40
So, 24/40 < 30/40
Then, 6/10 < 3/4

Compare. Write <, >, or =.

Question 3.
\(\frac{7}{8}\) _____ \(\frac{2}{8}\)

Answer:
\(\frac{7}{8}\) > \(\frac{2}{8}\)

Explanation:
Compare 7/8 and 2/8
Denominator values are same but numerator values are different
Now, compare the numerator values of 7/8 and 2/8
Then, 7/8 > 2/8

Question 4.
\(\frac{5}{12}\) _____ \(\frac{3}{6}\)

Answer:
\(\frac{5}{12}\) < \(\frac{3}{6}\)

Explanation:
Compare 5/12 and 3/6
Multiply the numerator and denominator of 3/6 with 2
(3×2) ÷ (6×2) = 6/12
So, 5/12 < 6/12

Question 5.
\(\frac{4}{10}\) _____ \(\frac{4}{6}\)

Answer:
\(\frac{4}{10}\) < \(\frac{4}{6}\)

Explanation:
Compare 4/10 and 4/6
Multiply the numerator and denominator of 4/6 with 10
(4×10) ÷ (6×10) = 40/60
Multiply the numerator and denominator of 4/10 with 6
(4×6) ÷ (10×6) = 24/60
So, 24/60 < 40/60
Then, 4/10 < 4/6

Question 6.
\(\frac{6}{12}\) _____ \(\frac{2}{4}\)

Answer:
\(\frac{6}{12}\) = \(\frac{2}{4}\)

Explanation:
Compare 6/12 and 2/4
Multiply the numerator and denominator of 2/4 with 3
(2×3) ÷ (4×3) = 6/12
So, 6/12 = 6/12
Then, 6/12 = 2/4

Question 7.
\(\frac{1}{3}\) _____ \(\frac{1}{4}\)

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

Explanation:
Compare 1/3 and 1/4
Multiply the numerator and denominator of 1/3 with 4
(1×4) ÷ (3×4) = 4/12
Multiply the numerator and denominator of 1/4 with 3
(1×3) ÷ (4×3) = 3/12
So, 4/12 < 3/12
Then, 1/3 < 1/4

Question 8.
\(\frac{4}{5}\) _____ \(\frac{8}{10}\)

Answer:
\(\frac{4}{5}\) = \(\frac{8}{10}\)

Explanation:
Compare 4/5 and 8/10
Multiply the numerator and denominator of 4/5 with 2
(4×2) ÷ (5×2) = 8/10
So, 8/10 = 8/10
Then, 4/5 = 8/10

Question 9.
\(\frac{3}{4}\) _____ \(\frac{2}{6}\)

Answer:
\(\frac{3}{4}\) < \(\frac{2}{6}\)

Explanation:
Compare 3/4 and 2/6
Multiply the numerator and denominator of 3/4 with 6
(3×6) ÷ (4×6) = 18/24
Multiply the numerator and denominator of 2/6 with 4
(2×4) ÷ (6×4) = 8/24
So, 18/24 < 8/24
Then, 3/4 < 2/6

Question 10.
\(\frac{1}{2}\) _____ \(\frac{5}{8}\)

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

Explanation:
Compare 1/2 and 5/8
Multiply the numerator and denominator of 1/2 with 4
(1×4) ÷ (2×4) = 4/8
So, 4/8 < 5/8
Then, 1/2 < 5/8

Reason Quantitatively Algebra Find a number that makes the statement true.

Question 11.
\(\frac{1}{2}>\frac { □ }{ 3 } \)
□ = ______

Answer:
1

Explanation:
1/2 > x/3
Multiply the numerator and denominator of 1/2 with 3
(1×3) ÷ (2×3) = 3/6
Multiply the numerator and denominator of x/3 with 2
(Xx2) ÷ (3×2) = 2x/6
3/6 > 2x/6
So, x= 1
Then, 3/6 > 2/6
1/2 > 1/3

Question 12.
\(\frac{3}{10}>\frac { □ }{ 5 } \)
□ = ______

Answer:
1

Explanation:
3/10 > x/5
Multiply the numerator and denominator of x/5 with 2
(Xx2) ÷ (5×2) =2x/10
3/10 > 2x/10
So, x=1
3/10 > 2/10
3/10 > 1/5

Question 13.
\(\frac{5}{12}>\frac { □ }{ 3 } \)
□ = ______

Answer:
1

Explanation:
5/12 > x/3
Multiply numerator and denominator of x/3 with 4
(Xx4) ÷(3×4) = 4x/12
5/12 > 4x/12
So, x = 1
Then, 5/12 > 4/12
5/12 > 1/3

Question 14.
\(\frac{2}{3}>\frac { 4 }{ □ } \)
□ = ______

Answer:

Explanation:

Question 15.
Students cut a pepperoni pizza into 12 equal slices and ate 5 slices. They cut a veggie pizza into 6 equal slices and ate 4 slices. Use fractions to compare the amounts of each pizza that were eaten.
Type below:
_________

Answer:
\(\frac{5}{12}\) < \(\frac{4}{6}\)

Explanation:
As per the given data,
Students cut a pepperoni pizza into 12 equal slices and ate 5 slices
=5/12
They cut veggie pizza into 6 equal slices and ate 4 slices = 4/6
Compare 5/12 and 4/6
Multiply the numerator and denominator of 4/6 with 2
(4×2) ÷ (6×2) = 8/12
So, 5/12 < 8/12
Then, 5/12 < 4/6

Page No. 368

Question 16.
Jerry is making a strawberry smoothie. Which measure is greatest, the amount of milk, cottage cheese, or strawberries?

a. What do you need to find?
Type below:
_________

Answer:
I need to find the greatest measure from milk, cottage cheese, or strawberries

Question 16.
b. How will you find the answer?
Type below:
_________

Answer:
Equal the denominators of 3/4, 2/6, and 8/12
Multiply the numerator and denominator of 3/4 with 3
(3×3) ÷ (4×3) = 9/12
Multiply the numerator and denominator of 2/6 with 2
(2×2) ÷ (6×2) = 4/12
Compare 4/12 < 8/12 < 9/12
So, 2/6 < 8/12 <3/4

Question 16.
c. Show your work.
Type below:
_________

Answer:
2/6 < 8/12 < 3/4

Question 16.
d. Jerry needs more ________ than the other two ingredients.
________

Answer:
Jerry needs more strawberries than the other two ingredients

Question 17.
Angie, Blake, Carlos, and Daisy went running. Angie ran \(\frac{1}{3}\) mile, Blake ran \(\frac{3}{5}\) mile, Carlos ran \(\frac{7}{10}\) mile, and Daisy ran \(\frac{1}{2}\) mile. Which runner ran the shortest distance? Who ran the greatest distance?
The shortest distance: ________
The greatest distance: ________

Answer:
The shortest distance: \(\frac{1}{3}\)
The greatest distance: \(\frac{7}{10}\)

Explanation:
As per the given data,
Angie, Blake, Carlos, and Daisy went running
Angie ran 1/3 mile, Blake ran 3/5 mile, Carlos ran 7/10 mile, and Daisy ran 1/2 mile
Least common denominator of 1/3, 3/5, 7/10, and 1/2 =30
(1x 10)/(3×10), (3×6)/(5×6), (7×3)/(10×3), (1×15)/(2×15)
10/30, 18/30, 21/30, 15/30
10/30 < 15/30 < 18/30 < 21/30
1/3 < 1/2 < 3/5 < 7/10
The shortest distance ran by Angie and that is 1/ 3
The greatest distance ran by Carlos and that is 7/10

Question 18.
Elaine bought \(\frac{5}{8}\) pound of potato salad and \(\frac{4}{6}\) pound of macaroni salad for a picnic. Use the numbers to compare the amounts of potato salad and macaroni salad Elaine bought.

Type below:
_________

Answer:
As per the given data,
Elaine bought 5/8 pound of potato salad and 4/6 pound of macaroni salad for a picnic
Multiply the numerator and denominator of 5/8 with 6
(5×6) / (8×6) = 30/48
Multiply the numerator and denominator of 4/6 with 8
(4×8) / (6×8) = 32/48
30/48 < 32/48
So, 5/8 < 4/6
Elaine bought more macaroni salad than potato salad

Common Core – Compare Fractions – Page No. 369

Compare. Write <, >, or =

Question 1.

Answer:
\(\frac{1}{5}\) < \(\frac{2}{10}\)

Explanation:

Question 2.
\(\frac{1}{5}\) _____ \(\frac{2}{10}\)

Answer:
\(\frac{1}{5}\) = \(\frac{2}{10}\)

Explanation:
1/5 and 2/10
Think: 10 is a common denominator
1/5 = (1×2) / (5×2) = 2/10
2/10 = 2/10
So, 1/5 = 2/10

Question 3.
\(\frac{2}{4}\) _____ \(\frac{2}{5}\)

Answer:
\(\frac{2}{4}\) > \(\frac{2}{5}\)

Explanation:
2/4 and 2/5
20 is a common denominator
2/4 = (2×5)/(4×5) = 10/20
2/5 = (2×4)/(5×4) = 8/20
10/20 > 8/20
So, 2/4 > 2/5

Question 4.
\(\frac{3}{5}\) _____ \(\frac{7}{10}\)

Answer:
\(\frac{3}{5}\) < \(\frac{7}{10}\)

Explanation:
3/5 and 7/10
10 is a common denominator
3/5 = (3×2)/(5×2) = 6/10
7/10
6/10 < 7/10
So, 3/5 < 7/10

Question 5.
\(\frac{4}{12}\) _____ \(\frac{1}{6}\)

Answer:
\(\frac{4}{12}\) > \(\frac{1}{6}\)

Explanation:
4/12 and 1/6
12 is a common denominator
4/12
1/6 = (1×2)/(6×2) = 2/12
4/12 > 2/12
So, 4/12 > 1/6

Question 6.
\(\frac{2}{6}\) _____ \(\frac{1}{3}\)

Answer:
\(\frac{2}{6}\) = \(\frac{1}{3}\)

Explanation:
2/6 and 1/3
6 is a common denominator
2/6
1/3 = (1×2)/(3×2) = 2/6
So, 2/6 =2/6
So, 2/6 = 1/3

Question 7.
\(\frac{1}{3}\) _____ \(\frac{2}{4}\)

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

Explanation:
1/3 and 2/4
12 is a common denominator
1/3 = (1×4)/(3×4) = 4/12
2/4 = (2×3)/(4×3) = 6/12
4/12 < 6/12
So, 1/3 < 2/4

Question 8.
\(\frac{2}{5}\) _____ \(\frac{1}{2}\)

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

Explanation:
2/5 and 1/2
10 is a common denominator
2/5 = (2×2)/(5×2) = 4/10
1/2 = (1×5)/(2×5) = 5/10
4/10 < 5/10
So, 2/5 < 1/2

Question 9.
\(\frac{4}{8}\) _____ \(\frac{2}{4}\)

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

Explanation:
4/8 and 2/4
8 is a common denominator
4/8
2/4 = (2×2)/(4×2) = 4/8
2/4 = 4/8
So, 4/8 = 2/4

Question 10.
\(\frac{7}{12}\) _____ \(\frac{2}{4}\)

Answer:
\(\frac{7}{12}\) < \(\frac{2}{4}\)

Explanation:
7/12 and 2/4
12 is a common denominator
7/12
2/4 = (2×3)/(4×3) = 6/12
7/12 < 6/12
So, 7/12 < 2/4

Question 11.
\(\frac{1}{8}\) _____ \(\frac{3}{4}\)

Answer:
\(\frac{1}{8}\) <  \(\frac{3}{4}\)

Explanation:
1/8 and 3/4
8 is a common denominator
1/8
3/4 = (3×2)/(4×2) = 6/8
1/8 < 6/8
So, 1/8 < 3/4

Question 12.
A recipe uses \(\frac{2}{3}\) of flour and \(\frac{5}{8}\) cup of blueberries. Is there more flour or more blueberries in the recipe?
more _____

Answer:
flour

Explanation:
From the given data,
A recipe uses 2/3 of flour and 5/8 cup of blueberries
Common denominator is 24
2/3 = (2×8)/(3×8) = 16/24
5/8 = (5×3)/(8×3) = 15/24
16/24 > 15/24
So, 2/3 > 5/8
So, flour is more in the recipe

Question 13.
Peggy completed \(\frac{5}{6}\) of the math homework and Al completed \(\frac{4}{5}\) of the math homework. Did Peggy or Al complete more of the math homework?
_________

Answer:
Peggy completed more work than Al

Explanation:
As per the given data,
Peggy completed 5/6 of the math homework
A1 completed 4/5 of the math homework
30 is a common denominator
5/6 = (5×5)/(6×5) = 25/30
4/5 = (4×6)/(5×6) =24/30
25/30 > 24/30
So, 5/6 > 4/5
So, Peggy completed more work than Al

Common Core – Compare Fractions – Page No. 370

Question 1.
Pedro fills a glass \(\frac{2}{4}\) full with orange juice. Which of the following fractions is greater than \(\frac{2}{4}\)?
Options:
a. \(\frac{3}{8}\)
b. \(\frac{4}{6}\)
c. \(\frac{5}{12}\)
d. \(\frac{1}{3}\)

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

Explanation:
\(\frac{4}{6}\) > \(\frac{2}{4}\)

Question 2.
Today Ian wants to run less than \(\frac{7}{12}\) mile. Which of the following distances is less than \(\frac{7}{12}\) mile?
Options:
a. \(\frac{3}{4}\) mile
b. \(\frac{2}{3}\) mile
c. \(\frac{5}{6}\) mile
d. \(\frac{2}{4}\) mile

Answer:
d. \(\frac{2}{4}\) mile

Explanation:
\(\frac{2}{4}\) is less than \(\frac{7}{12}\)

Question 3.
Ms. Davis traveled 372,645 miles last year on business. What is the value of 6 in 372,645?
Options:
a. 6
b. 60
c. 600
d. 6,000

Answer:
c. 600

Explanation:
Ms. Davis traveled 372, 645 miles last year on business
The value of 6 in 372,645 is 600

Question 4.
One section of an auditorium has 12 rows of seats. Each row has 13 seats. What is the total number of seats in that section?
Options:
a. 25
b. 144
c. 156
d. 169

Answer:
c. 156

Explanation:
From the given information
One section of an auditorium has 12 rows of seats
Each row has 13 seats = 13×12 = 156 seats
So, the total number of seats in the auditorium = 156 seats

Question 5.
Sam has 12 black-and-white photos and 18 color photos. He wants to put the photos in equal rows so each row has either black-and-white photos only or color photos only. In how many rows can Sam arrange the photos?
Options:
a. 1, 2, 3, or 6 rows
b. 1, 3, 6, or 9 rows
c. 1, 2, or 4 rows
d. 1, 2, 3, 4, 6, or 9 rows

Answer:
a. 1, 2, 3, or 6 rows

Explanation:
As per the given information
Sam has 12 black and white photos 18 color photos
He wants to put the photos in equal rows
So each row has either black and white photos only or color photos only
H.C.F of 12 and 18 is 6
Rows of 6.
2 rows of black equal 12.
3 rows of white equals 18.

Question 6.
The teacher writes \(\frac{10}{12}\) on the board. He asks students to write the fraction in simplest form. Who writes the correct answer?
Options:
a. JoAnn writes \(\frac{10}{12}\)
b. Karen writes \(\frac{5}{12}\)
c. Lynn writes \(\frac{6}{5}\)
d. Mark writes \(\frac{5}{6}\)

Answer:
d. Mark writes \(\frac{5}{6}\)

Explanation:
As per the given data,
The teacher writes 10/12 on the board
He asks students to write the fraction in simplest form
For the simplest form of 10/12, divide the 10/12 with 2
(10÷2)/(12÷2) = 5/6
5/6 is the simplest form of 10/12
So, Mark writes the correct answer

Page No. 373

Question 1.
Locate and label points on the number line to help you write \(\frac{3}{10}, \frac{11}{12}, \text { and } \frac{5}{8}\) in order from least to greatest.

Type below:
___________

Answer:

Explanation:
3/10, 11/12, 5/8
3/10 is closer to 0
11/12 is closer to 1
5/8 is closer to 1/2
So, 3/10 < 5/8 < 11/12

Write the fraction with the greatest value.

Question 2.
\(\frac{7}{10}, \frac{1}{5}, \frac{9}{10}\)
\(\frac{□}{□}\)

Answer:
\(\frac{9}{10}\)

Explanation:
7/10, 1/5, and 9/10
7/10 is closer to 1/2
1/5 is closer to 0
9/10 is closer to 1
So, 9/10 > 7/10 > 1/5
Greatest value is 9/10

Question 3.
\(\frac{5}{6}, \frac{7}{12}, \frac{7}{10}\)
\(\frac{□}{□}\)

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

Explanation:
7/12 is less than 1/2
7/10 and 5/6 are greater than 1/2
Compare 5/6 and 7/12
Multiply the numerator and denominator of 5/6 with 2
(5×2)/(6×2) = 10/12 > 7/12
So, 5/6 > 7/12
Compare 5/6 and 7/10
Multiply the 5/6 with 10
(5×10)/(6×10) = 50/60
Multiply the 7/10 with 6
(7×6)/(10×6) = 42/60
So, 5/6> 7/10
So, 7/12 <7/10<5/6

Question 4.
\(\frac{2}{8}, \frac{1}{8}, \frac{2}{4}, \frac{2}{6}\)
\(\frac{□}{□}\)

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

Explanation:
2/8, 1/8, 2/4, 2/6
Common denominator of 4,6,8 = 24
(2×3)/(8×3), (1×3)/(8×3), (2×6)/(4×6), (2×4)/(6×4)
6/24, 3/24, 12/24, 8/24
Compare the numerator values
12/24 > 8/24 > 6/24 > 3/24
So, 2/4 > 2/6 > 2/8 >1/8

Write the fractions in order from least to greatest.

Question 5.
\(\frac{1}{4}, \frac{3}{6}, \frac{1}{8}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{1}{8}, \frac{3}{6}, \frac{1}{4}\)

Explanation:
1/4, 3/6, 1/8
1/ 4 is closer to 1/2
3/6 is equal to 1/2
1/8 is closer to 0
So, 1/8 < 3/6 < 1/4

Question 6.
\(\frac{3}{5}, \frac{2}{3}, \frac{3}{10}, \frac{4}{5}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{4}{5}, \frac{3}{10}, \frac{3}{5}, \frac{2}{3}\)

Explanation:
3/5, 2/3, 3/10, 4/5
3/5 is closer to 1/2
2/3 is greater than 1/2
3/10 is less than 1/2
4/5 is closer to 0
So, 4/5 < 3/10 < 3/5 < 2/3

Question 7.
\(\frac{3}{4}, \frac{7}{12}, \frac{5}{12}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{5}{12}, \frac{7}{12}, \frac{3}{4}\)

Explanation:
3/4, 7/12, 5/12
3/ 4 is closer to 1
7/12 is greater than 1/2
5/ 12 is closer to 1/2
So, 5/12 < 7/12 < 3/4

Write the fractions in order from least to greatest.

Question 8.
\(\frac{2}{5}, \frac{1}{3}, \frac{5}{6}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{1}{3}, \frac{2}{5}, \frac{5}{6}\)

Explanation:
2/5, 1/3, 5/6
2/5 is closer to 1/2
1/3 is closer to 0
5/6 is closer to 1
So, 1/3 < 2/5 < 5/6

Question 9.
\(\frac{4}{8}, \frac{5}{12}, \frac{1}{6}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{1}{6}, \frac{5}{12}, \frac{4}{8}\)

Explanation:
4/8, 5/12, 1/6
4/8 is equal to1/2
5/12 is closer to 1/2
1/6 is closer to 0
So, 1/6 < 5/12 < 4/ 8

Question 10.
\(\frac{7}{100}, \frac{9}{10}, \frac{4}{5}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{7}{100}, \frac{4}{5}, \frac{9}{10}\)

Explanation:
7/100, 9/10, 4/5
7/100 is closer to 0
9/10 is closer to 1
4/5 is greater than 1/2
So, 7/100 < 4/5 < 9/10

Reason Quantitatively Algebra Write a numerator that makes the statement true.

Question 11.
\(\frac{1}{2}<\frac { □ }{ 10 } <\frac{4}{5}\)
□ = _____

Answer:
6 or 7

Explanation:
1/2 < x/10 < 4/5
Common denominator is 10
(1×5)/(2×5) < x/10 < (4×2)/(5×2)
5/10 < x/10 < 8/10
Then, x = 6 or 7

Question 12.
\(\frac{1}{4}<\frac{5}{12}<\frac { □ }{ 6 } \)
□ = _____

Answer:
6

Explanation:
1/4 < 5/12 < x/6
Common denominator is 24
(1×6)/(4×6) < (5×2)/(12×2) < 4x/(6×4)
6/24 < 10/24 < 4x/24
If x = 6, then 4x = 24
So, 6/24 < 10/24 < 24/24

Question 13.
\(\frac { □ }{ 8 } <\frac{3}{4}<\frac{7}{8}\)
□ = _____

Answer:
1,2,3,4,5

Explanation:
x/8 < 3/4 < 7/8
Common denominator is 8
x/8 < (3×2)/(4×2) < 7/8
x/8 < 6/8 < 7/8
so x = 1,2,3,4,5

Page No. 374

Question 14.
Nancy, Lionel, and Mavis ran in a 5-kilometer race. The table shows their finish times. In what order did Nancy, Lionel, and Mavis finish the race?

a. What do you need to find?

Answer:
In which Nancy, Lionel, and Mavis finished the race?

Question 14.
b. What information do you need to solve the problem?
Type below:
_________

Answer:
the amount of time it took each runner to finish the race

Question 14.
c. What information is not necessary?
Type below:
_________

Answer:
the distance of the race

Question 14.
d. How will you solve the problem?
Type below:
_________

Answer:
By using the running race time of Nancy, Lionel, and Mavis

Question 14.
e. Show the steps to solve the problem.
Type below:
_________

Answer:
Common denominator of 2/3, 7/12, 3/4 is 12
(2×4)/(3×4), (7/12), (3×3)/(4×3)
8/12, 7/12, 9/12
7/12 < 8/12 < 9/12
7/12 < 2/3 < 3/4
Lionel < Nancy < Mavis

Question 14.
f. Complete the sentences.
The runner who finished first is _______.
The runner who finished second is _______.
The runner who finished third is _______.
The first: _______
The second: _______
The third: _______

Answer:
Lionel finished the race first
Nancy finished the race second
Mavis finished the race third
Lionel
Nancy
Mavis

Common Core – Compare and Order Fractions – Page No. 375

Write the fractions in order from least to greatest.

Question 1.
\(\frac{5}{8}, \frac{2}{12}, \frac{8}{10}\)

Answer:
\(\frac{2}{12}, \frac{5}{8}, \frac{8}{10}\)

Explanation:

Question 2.
\(\frac{1}{5}, \frac{2}{3}, \frac{5}{8}\)
Type below:
_________

Answer:
\(\frac{1}{5}, \frac{5}{8}, \frac{2}{3}\)

Explanation:

1/5, 2/3, 5/8
1/5 is closer to 0
2/3 is greater than 1/2
5/8 greater than 1/2
1/5 < 5/8 < 2/3

Question 3.
\(\frac{1}{2}, \frac{2}{5}, \frac{6}{10}\)
Type below:
_________

Answer:
\(\frac{2}{5}, \frac{1}{2}, \frac{6}{10}\)

Explanation:

1/2, 2/5, 6/10
1/2 is equal to 1/2
2/5 is less than 1/2
6/10 is greater than 1/2

Question 4.
\(\frac{4}{6}, \frac{7}{12}, \frac{5}{10}\)
Type below:
_________

Answer:
\(\frac{5}{10}\) < \(\frac{7}{12}\) < \(\frac{4}{6}\)

Explanation:

4/6, 7/12, 5/10
4/6 is closer to 1
7/12 is greater than 1/2
5/10 is equal to 1/2

Question 5.
\(\frac{1}{4}, \frac{3}{6}, \frac{1}{8}\)
Type below:
_________

Answer:
\(\frac{1}{8}\) < \(\frac{1}{4}\) < \(\frac{3}{6}\)

Explanation:

1/4, 3/6, 1/8
1/4 is less than 1/2
3/6 is equal to 1/2
1/8 is closer to 0

Question 6.
\(\frac{1}{8}, \frac{3}{6}, \frac{7}{12}\)
Type below:
_________

Answer:
\(\frac{1}{8}\) < \(\frac{7}{12}\) < \(\frac{3}{6}\)

Explanation:

1/8, 3/6, 7/12
1/8 is closer to 0
3/6 is equal to 1/2
7/12 is greater than 1/2

Question 7.
\(\frac{8}{100}, \frac{3}{5}, \frac{7}{10}\)
Type below:
_________

Answer:
\(\frac{8}{100}\) < \(\frac{3}{5}\) < \(\frac{7}{10}\)

Explanation:

8/100, 3/5, 7/10
8/100 is closer to 0
3/5 is greater than 1/2
7/10 is closer to 1

Question 8.
\(\frac{3}{4}, \frac{7}{8}, \frac{1}{5}\)
Type below:
_________

Answer:
\(\frac{1}{5}\) < \(\frac{3}{4}\) < \(\frac{7}{8}\)

Explanation:

3/4, 7/8, 1/5
3/4 is greater than 1/2
7/8 is closer to 1
1/5 is closer to 0

Question 9.
Amy’s math notebook weighs \(\frac{1}{2}\) pound, her science notebook weighs \(\frac{7}{8}\) pound, and her history notebook weighs \(\frac{3}{4}\) pound. What are the weights in order from lightest to heaviest?
Type below:
_________

Answer:
\(\frac{1}{2}\) pound, \(\frac{3}{4}\) pound, \(\frac{7}{8}\) pound

Explanation:
From the given data,
Amy’s math notebook weighs 1/2 pound
Science notebook weighs 7/8 pound
History notebook weighs 3/4 pound
7/8 is closer to 1
3/4 is greater than 1/2
1/2 < 3/4 < 7/8
So, Amy’s math notebook weight < history notebook weight < science notebook

Question 10.
Carl has three picture frames. The thicknesses of the frames are \(\frac{4}{5}\) inch, \(\frac{3}{12}\) inch, and \(\frac{5}{6}\) inch. What are the thicknesses in order from least to greatest?
Type below:
_________

Answer:
\(\frac{3}{12}\) inch, \(\frac{4}{5}\) inch, \(\frac{5}{6}\) inch

Explanation:
As per the given data,
Carl has three picture frames
The thickness of the frames are 4/5 inch, 3/12 inch, 5/6 inch
4/5 is greater than 1/2
3/12 is less than 1/2
5/6 is closer to 1
3/12 < 4/5 < 5/6

Common Core – Compare and Order Fractions – Page No. 376

Question 1.
Juan’s three math quizzes this week took him \(\frac{1}{3}\) hour, \(\frac{4}{6}\) hour, and \(\frac{1}{5}\) hour to complete. Which list shows the lengths of time in order from least to greatest?
Options:
a. \(\frac{1}{3}\) hour, \(\frac{4}{6}\) hour, \(\frac{1}{5}\) hour
b. \(\frac{1}{5}\) hour, \(\frac{1}{3}\) hour, \(\frac{4}{6}\) hour
c. \(\frac{1}{3}\) hour, \(\frac{1}{5}\) hour, \(\frac{4}{6}\) hour
d. \(\frac{4}{6}\) hour, \(\frac{1}{3}\) hour, \(\frac{1}{5}\) hour

Answer:
b. \(\frac{1}{5}\) hour, \(\frac{1}{3}\) hour, \(\frac{4}{6}\) hour

Explanation:
From the given information
Juan’s three math quizzes this week took him 1/3 hour, 4/6 hour, and 1/5 hour
Compare 1/3 and 1/2
1/3 is less than 1/2
4/6 is greater than 1/2
1/5 is closer to 0
1/5 < 1/3 < 4/6
So, Juan’s math quizzes times from least to greatest is 1/5, 1/3, 4/6

Question 2.
On three days last week, Maria ran \(\frac{3}{4}\) mile, \(\frac{7}{8}\) mile, and \(\frac{3}{5}\) mile. What are the distances in order from least to greatest?
Options:
a. \(\frac{3}{4}\) mile, \(\frac{7}{8}\) mile, \(\frac{3}{5}\) mile
b. \(\frac{3}{5}\) mile, \(\frac{3}{4}\) mile, \(\frac{7}{8}\) mile
c. \(\frac{7}{8}\) mile, \(\frac{3}{4}\) mile, \(\frac{3}{5}\) mile
d. \(\frac{7}{8}\) mile, \(\frac{3}{5}\) mile, \(\frac{3}{4}\) mile

Answer:
b. \(\frac{3}{5}\) mile, \(\frac{3}{4}\) mile, \(\frac{7}{8}\) mile

Explanation:
As per the information
On three days last week, Maria ran 3/4 mile, 7/8 mile, and 3/5 mile
3/4 is greater than 1/2
7/8 is closer to 1
3/5 is greater than 1/2
Compare 3/5 and 3/4
3/4 is greater than 3/5
So, 3/5 < 3/4 < 7/8
Distance from least to greatest is 3/5, 3/4 , 7/8

Question 3.
Santiago collects 435 cents in nickels. How many nickels does he collect?
Options:
a. 58
b. 78
c. 85
d. 87

Answer:
d. 87

Explanation:
As per the given data,
Santiago collects 435 cents in nickels
1 nickel worth is 5 cents
Then, nickels per 435 cents = 435/5 = 87
So, Santiago collects 87 nickels

Question 4.
Lisa has three classes that each last 50 minutes. What is the total number of minutes the three classes last?
Options:
a. 15 minutes
b. 150 minutes
c. 153 minutes
d. 156 minutes

Answer:
b. 150 minutes

Explanation:
From the given data,
Lisa has three classes that each last 50 minutes
The total number of minutes the three classes last = 3×50 =150 minutes

Question 5.
Some students were asked to write a composite number. Which student did NOT write a composite number?
Options:
a. Alicia wrote 2.
b. Bob wrote 9.
c. Arianna wrote 15.
d. Daniel wrote 21.

Answer:
a. Alicia wrote 2.

Explanation:
As per the information
Some students were asked to write a composite number
a. Alicia wrote 2
Factors of 2 is 1 and 2
b. Bob wrote 9
Factors of 9 is 1, 3, 9
c. Arianna wrote 15
Factors of 15 is 1, 3, 5, 15
d. Daniel wrote 21
Factors of 21 is 1,3,7,21
So, Alicia did not write a composite number

Question 6.
Mrs. Carmel serves \(\frac{6}{8}\) of a loaf of bread with dinner. Which fraction is equivalent to \(\frac{6}{8}\)?
Options:
a. \(\frac{2}{4}\)
b. \(\frac{9}{16}\)
c. \(\frac{2}{3}\)
d. \(\frac{3}{4}\)

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

Explanation:
As per the given information
Mrs. Carmel serves 6/8 of a loaf of bread with dinner
To find the equivalent fraction of 6/8, simplify the 6/8 by dividing with the 2
(6÷2)/(8÷2) = ¾
So, the equivalent fraction of 6/8 is 3/4

Page No. 377

Question 1.
For numbers 1a–1d, tell whether the fractions are equivalent by selecting the correct symbol.
a. \(\frac{4}{16}\) _____ \(\frac{1}{4}\)

Answer:
\(\frac{4}{16}\) = \(\frac{1}{4}\)

Explanation:
4/16 and 1/4
Divide the numerator and denominator of 4/16 with 4
(4÷4)/(16÷4) = 1/4
So, 4/16 = 1/4

Question 1.
b. \(\frac{3}{5}\) _____ \(\frac{12}{15}\)

Answer:
\(\frac{3}{5}\) ≠ \(\frac{12}{15}\)

Explanation:
3/5 and 12/15
Multiply the numerator and denominator of 3/5 with 3
(3×3)/(5×3) = 9/15
So, 3/5 ≠ 12/15

Question 1.
c. \(\frac{5}{6}\) _____ \(\frac{25}{30}\)

Answer:
\(\frac{5}{6}\) = \(\frac{25}{30}\)

Explanation:
c. 5/6 and 25/30
Multiply the numerator and denominator of 5/6 with 5
(5×5)/(6×5) = 25/30
So, 5/6 = 25/30

Question 1.
d. \(\frac{6}{10}\) _____ \(\frac{5}{8}\)

Answer:
\(\frac{6}{10}\) ≠ \(\frac{5}{8}\)

Explanation:
6/10 and 5/8
Divide the numerator and denominator of 6/10 with 2
(6÷2)/(10÷2) = 3/5
6/10 ≠5/8

Question 2.
Juan’s mother gave him a recipe for trail mix.
\(\frac{3}{4}\) cup cereal \(\frac{2}{3}\) cup almonds
\(\frac{1}{4}\) cup peanuts \(\frac{1}{2}\) cup raisins
Order the ingredients used in the recipe from least to greatest.
Type below:
_________

Answer:
As per the given data,
Juan’s mother gave him a recipe for trail mix
3/4 cup cereal and 2/3 cup almonds
1/4 cup peanuts and 1/2 cup raisins
3/4 is closer to 1
2/3 is greater than 1/2
1/4 is less than 1/2
1/2 is equal to 1/2
So, 1/4 < 1/2 <2/3 < 3/4
So, Jaun’s mother gave him a recipe for trail mix in order
1/4 cup of peanuts < 1/2 cup of raisins < 2/3 cup almonds < 3/4 cup of cereals

Question 3.
Taylor cuts \(\frac{1}{5}\) sheet of construction paper for an arts and crafts project. Write \(\frac{1}{5}\) as an equivalent fraction with the denominators shown.

Type below:
_________

Answer:
From the given data,
Taylor cuts 1/5 sheet of construction paper for an arts and crafts project
So, the equivalent fractions of 1/5
Multiply the numerator and denominator of 1/5 with 2
(1×2)/(5×2) = 2/10
Multiply the numerator and denominator of 1/5 with 3
(1×3)/(5×3) = 3/15
Multiply the numerator and denominator of 1/5 with 5
(1×5)/(5×5) = 5/25
Multiply the numerator and denominator of 1/5 with 8
(1×8)/(5×8) = 8/40
So, the equivalent fractions of 1/5 are 2/10, 3/15, 5/25, 8/40

Question 4.
A mechanic has sockets with the sizes shown below. Write each fraction in the correct box.
\(\frac{7}{8} in. \frac{3}{16} in. \frac{1}{4} in. \frac{3}{8} in. \frac{4}{8} in. \frac{11}{16} in.\)

Type below:
_________

Answer:

Explanation:
As per the given data,
A mechanic has sockets with the sizes 7/8 inch, 3/16 inch, 1/4 inch, 3/8 inch, 4/8 inch, 11/16 inch
7/8 is greater than 1/2
3/16 is less than 1/2
1/4 is less than 1/2
3/8 is less than 1/2
4/8 is equal to 1/2
11/16 is greater than 1/2

Page No. 378

Question 5.
Darcy bought \(\frac{1}{2}\) pound of cheese and \(\frac{3}{4}\) pound of hamburger for a barbecue. Use the numbers to compare the amounts of cheese and hamburger Darcy bought.

Answer:

Explanation:
From the given data,
Darcy bought 1/2 pound of cheese and 3/4 pound of hamburger for a barbecue
3/4 is greater than 1/2

Question 6.
Brad is practicing the piano. He spends \(\frac{1}{4}\) hour practicing scales and \(\frac{1}{3}\) hour practicing the song for his recital. For numbers 6a–6c, select Yes or No to tell whether each of the following is a true statement.
a. 12 is a common denominator of \(\frac{1}{4}\) and \(\frac{1}{3}\).
i. yes
ii. no

Answer:
i. yes

Explanation:
12 is a common denominator of 1/3 and 1/4

Question 6.
b. The amount of time spent practicing scales can be rewritten as \(\frac{3}{12}\).
i. yes
ii. no

Answer:
i. yes

Explanation:
b. The amount of time spent practicing scales can be rewritten as 3/12
Multiply the numerator and denominator of 1/4 with 3
(1×3)/(4×3) = 3/12
Yes, amount of time spent practicing scales can be rewritten as 3/12

Question 6.
c. The amount of time spent practicing the song for the recital can be rewritten as \(\frac{6}{12}\).
i. yes
ii. no

Answer:
ii. no

Explanation:
c. The amount of time spent practicing the song for the recital can be rewritten as 6/12
The amount of time spent practicing for the song for his recital = 1/3
Multiply the numerator and denominator of 1/3 with 4
(1×4)/(3×4) = 4/12
No, time spent practicing the song for the recital can not be written as 6/12

Question 7.
In the school chorus, \(\frac{4}{24}\) of the students are fourth graders. In simplest form, what fraction of the students in the school chorus are fourth graders?
\(\frac{□}{□}\)

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

Explanation:
As per the given information,
In the school chorus,
4/24 of the students are fourth graders
For the simplest form of 4/24
Divide the numerator and denominator of 4/24 with 4
(4÷4)/(24÷4) =1/6
The simplest form of 4/24 is 1/6

Question 8.
Which pairs of fractions are equivalent? Mark all that apply.
a. \(\frac{8}{12} \text { and } \frac{2}{3}\)
b. \(\frac{3}{4} \text { and } \frac{20}{24}\)
c. \(\frac{4}{5} \text { and } \frac{12}{16}\)
d. \(\frac{7}{10} \text { and } \frac{21}{30}\)

Answer:
a. \(\frac{8}{12} \text { and } \frac{2}{3}\)

Explanation:
a. 8/12 and 2/3
Multiply the numerator and denominator of 2/3 with 4
(2×4)/(3×4) = 8/12
So, 8/12 = 2/3
b. 3/4 and 20/24
Multiply the numerator and denominator of 3/4 with 6
(3×6)/(4×6) = 18/24
c. 4/5 and 12/16
4/5 ≠ 12/16
d. 7/10 and 21/30
Multiply the numerator and denominator of 7/10 with 3
(7×3)/(10×3) =21/30
So, 7/10 = 21/30

Question 9.
Sam worked on his science fair project for \(\frac{1}{4}\) hour on Friday and \(\frac{1}{2}\) hour on Saturday. What are four common denominators for the fractions? Explain your reasoning.

Answer:
From the given data,
Sam worked on his science fair project for 1/4 hour on Friday and 1/2 hour on Saturday
4,8,12,16 are all common denominators because they all multiples of 2 and 4

Page No. 379

Question 10.
Morita works in a florist shop and makes flower arrangements. She puts 10 flowers in each vase, and \(\frac{2}{10}\) of the flowers are daisies.
Part A
If Morita makes 4 arrangements, how many daisies does she need? Show how you can check your answer.
_____ daisies

Answer:
8 daisies

Explanation:
If Morita makes 4 arrangements, 4 X 2 = 8.

Question 10.
Part B
Last weekend, Morita used 10 daisies to make flower arrangements. How many flowers other than daisies did she use to make the arrangements? Explain your reasoning.
_____ other flowers

Answer:
40 other flowers

Explanation:
If she used 10 daises, she must have made 5 arrangements. In each vase, she put \(\frac{2}{10}\) of the flowers are daisies. So, remaining flowers for each vase = 10 – 2 = 8. If she made 5 arrangements, 8 X 5 = 40 other flowers.

Question 11.
In Mary’s homeroom, \(\frac{10}{28}\) of the students have a cat, \(\frac{6}{12}\) have a dog, and \(\frac{2}{14}\) have a pet bird. For numbers 11a–11c, select True or False for each statement.
a. In simplest form, \(\frac{5}{14}\) of the students have a cat.
i. True
ii. False

Answer:
i. True

Explanation:
In simplest form 5/14 of the students have a cat
From the above, 10/28 of the students have a cat
Divide the numerator and denominator of 10/28 with 2
(10÷2)/(28÷2) = 5/14
True

Question 11.
b. In simplest form, \(\frac{2}{4}\) of the students have a dog.
i. True
ii. False

Answer:
i. True

Explanation:
In simplest form, 2/4 of the students have a dog
From the above, 6/12 of the students have a dog
Divide the 6/12 with 3
(6 = 2/4
True

Question 11.
c. In simplest form, \(\frac{1}{7}\) of the students have a pet bird.
i. True
ii. False

Answer:
i. True

Explanation:
In the simplest form, 1/7 of the students have a pet bird
From the data, 2/14 of the students have a pet bird
Divide the numerator and denominator of 2/14 with 2
(2÷2)/(14÷2) = 1/7
True

Page No. 380

Question 12.
Regina, Courtney, and Ellen hiked around Bear Pond. Regina hiked \(\frac{7}{10}\) of the distance in an hour. Courtney hiked \(\frac{3}{6}\) of the distance in an hour. Ellen hiked 38 of the distance in an hour. Compare the distances hiked by each person by matching the statements to the correct symbol. Each symbol may be used more
than once or not at all.

Type below:
_________

Answer:

Explanation:
From the given information
Regina, Courtney, and Ellen hiked around Bear Pond
Regina hiked 7/10 of the distance in an hour
Courtney hiked 3/6 of the distance in an hour
Ellen hiked 3 /8 of the distance in an hour
Compare 7/10 and 3/6
The common denominator of 7/10 and 3/6 is 30
(7×3)/(10×3) and (3×5)/(6×5)
21/30 and 15/30
So, 21/30 > 15/30
So, 7/10 > 15/30
Compare 3/8 and 3/6
The common denominator of 3/8 and 3/6 is 24
(3×3)/(8×3) and (3×4)/(6×4)
9/24 and 12/24 = 9/24 < 12/24 = 3/8 < 3/6
Compare 7/10 and 3/8
The common denominator of 7/10 and 3/8 is 40
(7×4)/(10×4) and (3×5)/(8×5)
28/40 >15/40 = 7/10 > 3/8

Question 13.
Ramon is having some friends over after a baseball game. Ramon’s job is to make a vegetable dip. The ingredients for the recipe are given.

Part A
Which ingredient does Ramon use the greater amount of, buttermilk or cream cheese? Explain how you found your answer.
Type below:
_________

Answer:
Ramon use 5/8 cup of buttermilk and 1/2 cup cream cheese
By comparing these two ingredients
The common denominator of 5/8 and 1/2 are 8
(1×4)/(2×4) =4/8
So, 5/8 > 4/8
So, 5/8 cup buttermilk is > ½ cup cream cheese

Question 13.
Part B
Ramon says that he needs the same amount of two different ingredients. Is he correct? Support your answer with information from the problem.
______

Answer:
Ramon says that he needs the same amount of two ingredients
Yes, Ramon uses 3/4 cup parsley and 6/8 cup scallions
Multiply the 3/4 with 2
(3×2)/(4×2) = 6/8
So, Ramon uses the same amount that is 3/4 cup for parsley and scallions

Page No. 381

Question 14.
Sandy is ordering bread rolls for her party. She wants \(\frac{3}{5}\) of the rolls to be whole wheat. What other fractions can represent the part of the rolls that will be whole wheat? Shade the models to show your work.

Type below:
_________

Answer:

Explanation:
As per the information,
Sandy is ordering bread rolls for her party
She wants 3/5 of the rolls to be whole wheat
For an equivalent fraction of 3/5, multiply with 5
(3×5)/(5×5) = 15/25
Again multiply the 15/25 with 4
(15×4)/(25×4) = 60/100

Question 15.
Angel has \(\frac{4}{8}\) yard of ribbon and Lynn has \(\frac{3}{4}\) yard of ribbon. Do Angel and Lynn have the same amount of ribbon? Shade the model to show how you found your answer. Explain your reasoning.

Type below:
_________

Answer:

Angel and Lynn didn’t have the same amount of ribbon. 4/8 is a greater fraction compared to 3/4. So, Angel’s ribbon is long compared to Lynn’s ribbon.

Question 16.
Ella used \(\frac{1}{4}\) yard of red ribbon. Fill in each box with a number from the list to show equivalent fractions for \(\frac{1}{4}\). Not all numbers will be used.

Type below:
_________

Answer:

Explanation:
1/4 = 2/8 = 4/16 = 3/12

Page No. 382

Question 17.
Frank has two same-size rectangles divided into the same number of equal parts. One rectangle has \(\frac{3}{4}\) of the parts shaded, and the other has \(\frac{1}{3}\) of the parts shaded.
Part A
Into how many parts could each rectangle be divided? Show your work by drawing the parts of each rectangle.

_____ parts

Answer:

12 parts

Question 17.
Part B
Is there more than one possible answer to Part A? If so, did you find the least number of parts into which both rectangles could be divided? Explain your reasoning.
Type below:
_________

Answer:
Yes, as long it is a multiple of 12.
And yes,12 is the least in order to have 1 rectangle have 3/4 shaded and the other 1/3 shaded.

Question 18.
Suki rode her bike \(\frac{4}{5}\) mile. Claire rode her bike \(\frac{1}{3}\) mile. They want to compare how far they each rode their bikes using the benchmark \(\frac{1}{2}\). For numbers 18a–18c, select the correct answers to describe how to solve the problem.
a. Compare Suki’s distance to the benchmark:
\(\frac{4}{5}\) _____ \(\frac{1}{2}\)

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

Explanation:
The fraction \(\frac{4}{5}\) is not equal to \(\frac{1}{2}\).

Question 18.
b. Compare Claire’s distance to the benchmark:
\(\frac{1}{3}\) _____ \(\frac{1}{2}\)

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

Explanation:
The fraction \(\frac{1}{3}\) is not equal to \(\frac{1}{2}\)

Question 18.
c. Suki rode her bike _____ Claire.

Answer:
Suki rode her bike faster than Claire.

Page No. 387

Use the model to write an equation.

Question 1.

Type below:
_________

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

Question 2.

Type below:
_________

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

Question 3.

Type below:
_________

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

Question 4.

Type below:
_________

Answer:
1 – \(\frac{5}{8}\) = \(\frac{8}{8}\) – \(\frac{5}{8}\) = \(\frac{3}{8}\)

Use the model to solve the equation.

Question 5.

\(\frac{3}{4}-\frac{1}{4}\) = \(\frac{□}{□}\)

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

Question 6.

\(\frac{5}{6}+\frac{1}{6}\) = \(\frac{□}{□}\)

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

Question 7.
Reason Abstractly Sean has \(\frac{1}{5}\) of a cupcake and \(\frac{1}{5}\) of a large cake.
a. Are the wholes the same? Explain.
______

Answer:
Yes; From the given information, the fraction of the cupcake and large cake are the same.

Explanation:

Question 7.
Does the sum \(\frac{1}{5}+\frac{1}{5}=\frac{2}{5}\) make sense in this situation? Explain.
______

Answer:
Yes; it makes sense. From the given data, 1 part is out of 5 parts. So, adding two fractions (1 part is out of 5 parts), the complete fraction becomes 2/5.

Question 8.
Carrie’s dance class learned \(\frac{1}{5}\) of a new dance on Monday, and \(\frac{2}{5}\) of the dance on Tuesday. What fraction of the dance is left for the class to learn on Wednesday?
\(\frac{□}{□}\)

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

Explanation:
The fraction of left for the class to learn on Wednesday is \(\frac{3}{5}\).

Page No. 388

Question 9.
Samantha and Kim used different models to help find \(\frac{1}{3}+\frac{1}{6}\). Whose model makes sense? Whose model is nonsense? Explain your reasoning below each model.

Answer:
Both Samantha and Kim’s statements make sense. Because both models have an equal number of fractions for each diagram.

Question 10.
Draw a model you could use to add \(\frac{1}{4}+\frac{1}{2}\).
Type below:
___________

Answer:

Question 11.
Cindy has two jars of paint. One jar is \(\frac{3}{8}\) full. The other jar is \(\frac{2}{8}\) full. Use the fractions to write an equation that shows the amount of paint Cindy has.


Type below:
___________

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

Explanation:

Conclusion:

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