## Big Ideas Math Book 3rd Grade Answer Key Chapter 10 Understand Fractions

Get the Big Ideas Math Answers Grade 3 Chapter 10 Understand Fractions according to the topics from this page. Most of the students think that fractions are difficult but if you understand the concept it is a very easy chapter among all. We have provided the step by step explanation for all the topics in a simple manner. So go through it and start your preparation with love and joy.

Lesson 1: Equal Parts of a Whole

Lesson 2: Understand a Unit Fraction

Lesson 3: Write Fractions of a Whole

Lesson 4: Fractions on a Number Line: Less Than 1

Lesson 5: Fractions on a Number line: Greater Than 1

### Lesson 10.1 Equal Parts of a Whole

Explore and Grow

Use the name of the equal parts to divide each rectangle. Write the number of equal parts for each rectangle.

Repeated Reasoning
How many equal parts are in a rectangle that is divided into eighths? Explain.

Think and Grow: Equal Parts of a Whole

The rectangle represents a whole. A whole is all of the parts of one shape or group.

2 equal parts, or halves

3 equal parts, or thirds

4 equal parts, or fourths

6 equal parts, or sixths

8 equal parts, or eighths

Example
Tell whether the shape shows equal parts or unequal parts. If the shape shows equal parts, then name them.

_____ parts.
_________

_____ parts.
_________

Show and Grow

Tell whether the shape shows equal parts or unequal parts. If the shape shows equal parts, then name them.

Question 1.

__6__ parts.

_____sixths____

i) 6
ii) sixths

Explanation:
From the above figure, we can see that the rectangle is divided into 6 parts and the parts are named as sixths and they are unequal

Question 2.
Tell whether the shape shows equal parts or unequal parts. If the shape shows equal parts, then name them.

____ parts.
_________

i) 4
ii) Fourths

Explanation:
From the above figure, we can see that the rhombus is divided into 4 equal parts and the parts are named as fourths.

Question 3.

_____ parts.
_________

i) 3
ii)Thirds

Explanation:
From the above figure, we can see that the rectangle is divided into 3 equal parts and the parts are named as thirds. They become three rectangles

Question 4.

_____ parts.
_________

i) 8
ii)Eighths

Explanation:
From the above figure, we can see that the  Rectangle is divided into 8 equal parts and the parts are named as eighths.

Question 5.

_____ parts.
_________

i) 4
ii) Fourths

Explanation:
From the above figure, we can see that the rhombus is divided into 4 equal parts and the parts are named as fourths.

Question 6.

_____ parts.
_________

i) 6
ii) sixths

Explanation:
From the above figure, we can see that the circle is divided into 6 equal parts and the parts are named as sixths.They are equal in parts after dividing it becomes 6 equal triangles.

Question 7.
Divide the rectangle into 2 equal parts. Then name the equal parts.

When a rectangle is divided into two equal parts then it becomes two halfs.

Question 8.

Divide the square into 6 equal parts. Then name the equal parts.

________

i) sixths

Explanation:
From the above figure, we can see that the square is divided into 6 equal parts and the parts are named as sixths.

Question 9.
YOU BE THE TEACHER
Newton says he divided each shape into fourths. Is he correct? Explain.

From the above figures we can see that they are divided.
From figure one and two they are divided equally and they are named as fourths.
From the third figure the circle is not divided equally.

Think and Grow: Modeling Real Life

Three students want to share a whiteboard to solve math problems. Each student wants to use an equal part of the board. Should the students divide the whiteboard into halves, thirds, or fourths?

Draw to show:

The students should divide the whiteboard into ____.

The students should divide the whiteboard into three equal parts and name the parts as thirds.
As the whiteboard looks like a rectangle if we divide the rectangle into three equal parts then it becomes three rectangles

Show and Grow

Question 10.
Six friends want to share an egg casserole. Each friend wants an equal part. Should the friends cut the casserole into halves, fourths, or sixths?

Friend should cut the egg casserole into six equal parts. And the name as sixths

Question 11.
Eight students need to sit around two tables. Each student needs an equal part of a table. Should the tables be divided into thirds, fourths, or sixths?

Explaination:
Each table should be divided into fourths as the eight students want to have equal parts

Question 12.
DIG DEEPER!
Ten friends want to share five rectangular sheets of paper. Each friend wants an equal part. Should the friend cut the sheets of paper into halves or thirds? Explain.

The friends should cut each sheet into halves.
As there are five papers if one paper is cutting in two parts it becomes two halves similarly all five.
All five into halves becomes 10

### Equal Parts of a Whole Homework & Practice 10.1

1 equal part, or whole

2 equal parts, or halves

3 equal parts, or third

4 equal parts, or fourths

6 equal parts, or sixths

8 equal parts, or eighths

Tell whether the shape shows equal parts or unequal parts. If the shape shows equal parts, then name them.

Question 1.

_____ parts.
_________

i) 6
ii) sixths

Explanation:
From the above figure, we can see that the rectangle is divided into 6 equal parts and the parts are named as sixths. They are equal.

Question 2.

_____ parts.
_________

i) 3
ii) thirds

Explanation:
From the above figure, we can see that the circle is divided into 3 unequal parts and the parts are named as fourths.

Question 3.

_____ parts.
_________

i) 4
ii) Fourths

Explanation:
From the above figure, we can see that the hexagon is divided into 4 equal parts and the parts are named as fourths.

Question 4.

_____ parts.
_________

i) 8
ii) eighths

Explanation:
From the above figure, we can see that the circle is divided into 8 equal parts and the parts are named as eighths.

Question 5.

_____ parts.
_________

i) 4
ii) Fourths

Explanation:
From the above figure, we can see that the rectangle is divided into 4 equal parts and the parts are named as fourths.

Question 6.

_____ parts.
_________

i) 3
ii) thirds

Explanation:
From the above figure, we can see that the triangle is divided into 3 unequal parts and the parts are named as thirds.

Question 7.
Divide the square into 3 equal parts. Then name the equal parts.

_____

Explanation:
If the square is divided into three equal parts the name is thirds

Question 8.
Divide the triangle into 2 equal parts. Then name the equal parts.

______

Explanation:
If the triangle is divided into two equal then it becomes two halves

Question 9.
Patterns
Use the pattern to divide the square into equal parts. Name the equal parts.

_____

Explanation:
According to the pattern, the sixth square is divided into 4 parts Horizontally. The name of the equal part is fourths.

Question 10.
Modeling Real Life
Eight friends want to share a lasagna. Each friend wants an equal part. Should the friends cut the lasagna into fourths, sixths, or eighths?

Explanation:
From the above figure the lasagna is to be shared between 8 friends. In order to share we have to cut the lasagna in to eight equal parts.

Therefore it becomes eighths

Question 11.
DIG DEEPER!
Twelve friends want to pull weeds from three community gardens. Each friend wants to pull weeds from an equal part. Should the friends divide each garden into thirds, fourths, or sixths?

Explanation

As twelve friends want to pull weeds from three community gardens. They have to get equal parts each community garden should be divided into four parts.

As each garden divided into four equal parts 3gardens*4parts=12people

3*4=12

So,twelve people get equal parts.

Review & Refresh

Question 12.
2 × (3 × 3) = ___18

Question 13.
(4 × 2) × 9 = ____72

Question 14.
2 × (8 × 5) = ____80

### Lesson 10.2 Understand a Unit Fraction

Explore and Grow

Match each shaded part to its name.

Precision
What is the same about each shape? What is different?

Think and Grow: Understand a Unit Fraction

A fraction is a number that represents part of a whole.

A unit fraction represents one equal part of a whole.

Example
What fraction of the whole is shaded?

Show and Grow

What fraction of the whole is shaded?

Question 1.

i(one thirds)

Three equal parts

Explanation:
The above figure shows that the circle is divided into 3 parts equally in which 1 part is shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part is one thirds.

Question 2.

i(one eighths)

Eight equal parts

Explanation:
The above figure shows that the square is divided into 8 parts equally in which 1 part are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part is one eighths.

Question 3.

i(one halves)

Two equal parts

Explanation:
The above figure shows that the parallelogram is divided into 2 parts equally in which 1 parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part is one halves.

Apply and Grow: Practice

What fraction of the whole is shaded?

Question 4.

i(one sixths)

Explanation:
The above figure shows that the rectangle is divided into 6 parts equally in which 1 parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part is one sixths.

Question 5.

iii (one fourths)

Explanation:
The above figure shows that the ellipse is divided into 4 parts equally in which one parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part is one fourths.

Question 6.

iii (one halves)

Explanation:
The above figure shows that the hexagon is divided into 2 parts equally in which one parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part is one halvess.

Question 7.

iii (one eighths)

Explanation:
The above figure shows that the rhombus is divided into 8 parts equally in which one parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part is one eighths.

Question 8.

iii (one fourths)

Explanation:
The above figure shows that the rectangle is divided into 4 parts equally in which one parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part is one fourths.

Question 9.

iii (one sixths)

Explanation:
The above figure shows that the triangle is divided into 8 parts equally in which 3 parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part is one eighths.

Question 10.
Divide the circle into 4 equal parts. Shade one part. What fraction of the whole is shaded?

iii (one fourths)

Explanation:
The above figure shows that the circle is divided into 4 parts equally in which one parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part is one fourths.

Question 11.
Divide the square into 3 equal parts. Shade one part. What fraction of the whole is shaded?

iii ( one thirds)

Explanation:
The above figure shows that the square is divided into 3 parts equally in which one parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part one thirds.

Question 12.
YOU BE THE TEACHER
Descartes says the part he shaded can be represented by a unit fraction. Is he correct? Explain.

Think and Grow: Modeling Real Life

For which nation’s flag can you use a unit fraction to represent the amount of green? Explain.
Flag of ____

Explain:

Flag of Nigeria:two thirds.

Flag of Mauritius:one fourths.

Flag of Seychelles:one fifths

Explanation:

The above figure shows that the flag of Nigeria is divided into 3 parts equally in which two  parts are green shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded parts is two thirds.

The above figure shows that the flag of Mauritius is divided into 4 parts equally in which one  parts are green shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded parts is one fourths.

The above figure shows that the flag of Seychelles is divided into 5 parts equally in which one  parts are green shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded parts is one fifths.

Show and Grow

Question 13.
For which nation’s flag can you use a unit fraction to represent the amount of red? Explain.

Flag of Bahrain:two thirds.

Flag of Australia:two thirds.

Flag of France:one thirds

Explanation:

The above figure shows that the flag of Bahrain is divided into 3 parts equally in which two  parts are red shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded parts is two thirds.

The above figure shows that the flag of Australia is divided into 3 parts equally in which one  parts are red shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded parts is one thirds.

The above figure shows that the flag of France is divided into 3 parts equally in which one  parts are red shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded parts is one thirds.

Question 14.
You paint a plate that has 4 equal parts. You paint two parts orange and one part red. You paint the rest of the plate yellow. What fraction of the plate is yellow?

One fourths

Question 15.
DIG DEEPER!
Draw a quilt square that has blue, red, and white parts, but only the blue part can be represented by a unit fraction.

### Understand a Unit Fraction Homework & Practice 10.2

What fraction of the whole is shaded?
Question 1.

Explanation:
The above figure shows that the circle is divided into 4 parts equally in which one parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part one sixths.

Question 2.

Explanation:
The above figure shows that the rectangle is divided into 8 parts equally in which one parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part one eighths.

Question 3.

Explanation:
The above figure shows that the square is divided into 3 parts equally in which one parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part one thirds.

Question 4.

Explanation:
The above figure shows that the triangle is divided into 4 parts equally in which one parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part one fourths.

Question 5.

Explanation:
The above figure shows that the parallelogram is divided into 2 parts equally in which one parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part one halves.

Question 6.
Divide the square into 6 equal parts. Shade one part. What fraction of the whole is shaded?

Explanation:
The above figure shows that the square is divided into 6 parts equally in which one parts are shaded. Therefore, the shaded part will be in the numerator and the total parts will be in the denominator. So, the fraction name of the shaded part one sixths.

Question 7.
Precision
Did Descartes label the shaded part correctly? Explain.

Explanation:
The above figure shows that the rectangle is divided into 8 parts equally in which one parts are shaded.  The shaded part will be in the numerator and the total parts will be in the denominator.

The precision done was wrong numerator place is changed with the denominator

Question 8.

DIG DEEPER!
You want to make a card. You fold a sheet of paper in half, then in half again. What fraction of the sheet of paper represents the front of the card?

Explanation:

One by fourth represent the front of the card

Question 9.
Writing
Explain how you know Newton ate $$\frac{1}{3}$$ of his taco.

Explanation

The above taco is divided into two three equal parts in that one by third of the taco is eaten as it has shown empty

Question 10.
Modeling Real Life
For which foods can you use a unit fraction to represent the amount eaten? Explain.

Explanation:

From the above figures.

• Wheat is uncountable so we can’t represent as units we can’t share the wheat as units.
• The leaves are also uncountable.
• Apple is countable we can represent as units.
• Maize is also uncountable so we can’t represent as units we can’t share the wheat as units.

Question 11.
Modeling Real Life
You prepare a rectangular dip tray that has 6 equal parts. Three parts are hummus, one part is queso, and one part is guacamole. The rest of the tray is salsa. What fraction of the tray is salsa?

Explanation:

The total number of parts are 6

In that 3 parts one third part is hummus.

One part meant one sixth part is queso.

One by sixth part is guacamole.

The remaining one by sixth part is salsa.

Review & Refresh

Compare

Question 12.

Question 13.

Answer: 30 is greater than 20.

Question 14.

Answer: 42 is equal to 42.

### Lesson 10.3 Write Fractions of a Whole

Explore and Grow

Write a fraction for the shaded part of each whole.

Reasoning
All of the equal parts of a shape are shaded. What do you know about the numerator and denominator of the fraction that describes the shaded parts?

Think and Grow: Fractions of a Whole

Example
What fraction of the whole is shaded?

Show and Grow

What fraction of the whole is shaded?

Question 1.

Explanation:
There are 4 blocks in the square out of which 3 parts are shaded. Each part of the square is 1/4 and the name for the shaded part is three fourths. The fraction of the shaded part is 3/4 three fouth.

Question 2.

Explanation:
There are 6 blocks in the rectangle out of which 6 parts are shaded. Each part of the rectangle is 1/6 and the name for the shaded part whole. The fraction of the shaded part is whole.

Question 3.

Explanation:
There are 8 blocks in the circle out of which 5 parts are shaded. Each part of the circle is 1/8 and the name for the shaded part is Five Eights. The fraction of the shaded part is 5/8.

Question 4.

Explanation:
There are 6 blocks in the hexagon out of which 2 parts are shaded. Each part of the hexagon is one sixth.the name for the shaded parts is two sixths. The fraction of the shaded part is 2/6.

Apply and Grow: Practice

What fraction of the whole is shaded?

Question 5.

Explanation:
There are 6 blocks in the rectangle out of which 4 parts are shaded. Each part of the rectangle is 1/6 and the name for the shaded part is four sixths. The fraction of the shaded part is 4/6.

Question 6.

Explanation:
There are 3 blocks in the circle out of which 3 parts are shaded. Each part of the circle is 1/3 and the name for the shaded part is whole. The fraction of the shaded part is 3/3.

Question 7.

Explanation:
There are 8 blocks in the square out of which 5 parts are shaded. Each part of the square is 1/8 and the name for the shaded part is Five Eights. The fraction of the shaded part is 5/8.

Question 8.

Explanation:
There are 4 blocks in the hexagon out of which 3 parts are shaded. Each part of the hexagon is 1/4 and the name for the shaded part is three fourths. The fraction of the shaded part is 3/4.

Question 9.
Divide the rectangle into eighths. Shade three of the equal parts. What fraction of the whole is shaded?

Explanation:
There are 8 blocks in the rectangle out of which 3 parts are shaded. Each part of the rectangle is 1/8 and the name for the shaded part is three Eights. The fraction of the shaded part is 3/8.

Question 10.
Divide the triangle in half. Shade two of the equal parts. What fraction of the whole is shaded?

Explanation:
If we divide There are 2 blocks in the triangle out of which 2 parts are shaded means the whole is shaded the fraction is 2/2

Question 11.
DIG DEEPER!
Newton is thinking of a fraction. What is his fraction?

Explanation:

According to Newton let us consider a rectangular shape in that it is divided into 6 parts. Here conditions are the number should be odd and greater than three so the number will be five.

There fore the fraction is 5/6.

Think and Grow: Modeling Real Life

You are making a stained glass window that has 6 equal parts. You finish 1 part of the window. What fraction of the window do you have left to finish?

Draw to show:
You have of the window left to finish.

Show and Grow

Question 12.
You color 8 equal parts of a banner for a school play. You write the title in 4 of the parts. What fraction of the banner does not have the title?

Explanation:
There are 8 blocks in the rectangle out of which 4 parts are written title. Each part of the rectangle is 1/8 and the name for the shaded is two eigths. The fraction of the shaded part is 2/8.

Question 13.
A fruit tray has 4 equal parts. One part of the tray has grapes. Another part of the tray has pineapple. The rest of the tray has watermelon. What fraction of the tray has watermelon?

Explanation:
There are 4 blocks in the rectangle out of which 1 is filled with grapes and the other with pineapple. Each part of the rectangle is 1/4 and the name for the covered watermelon is two fourths . The fraction of the shaded part is 2/4.

Question 14.
DIG DEEPER!
You divide a flower bed into equal parts. You plant sunflowers in 1 part. You plant daisies in the other 2 parts. What fraction of the flower bed has sunflowers?

### Write Fractions of a Whole Homework & Practice 10.3

What fraction of the whole is shaded?
Question 1.

Explanation:
There are 6 blocks in the square out of which 4 parts are shaded. Each part of the square is 4/6 and the name for the shaded part is four sixths. The fraction of the shaded part is 4/6.

Question 2.

Explanation:
There are 2 blocks in the triangle out of which 2 parts are shaded. Each part of the triangle is 1/2 and the name for the shaded part is whole. The fraction of the shaded part is 2/2.

Question 3.

Explanation:
There are 8 blocks in the octagon out of which 5 parts are shaded. Each part of the octagon is 1/8 and the name for the shaded part is Five Eights. The fraction of the shaded part is 5/8.

Question 4.

Explanation:
There are 6 blocks in the circle out of which 5 parts are shaded. Each part of the circle is 1/6 and the name for the shaded part is Five sixths. The fraction of the shaded part is 5/6.

Question 5.

Explanation:

Rectangle is divided into 4 parts in it 2 parts are shaded. Fraction is 2/4

Question 6.
Divide the rectangle into sixths. Shade 2 of the equal parts. What fraction of the whole is shaded?

Explanation:

The fraction of the whole shaded is 2/6.

Question 7.
Divide the square into thirds. Shade 2 of the equal parts. What fraction of the whole is shaded?

Answer:2/3 parts of the square is shared

Question 8.

Open-Ended
Divide and shade the square to show more than $$\frac{4}{8}$$, but less than $$\frac{8}{8}$$. What fraction of the whole is shaded?

The square is divided into 8 parts in that four are already shaded 3/8

Question 9.
Reasoning
A pool has 4 swim lanes. Swimmers are using all of the lanes. Draw and shade a model that represents the lanes being used. Then write a fraction for your model.

Question 10.
Patterns
What fraction of each circle is shaded? Think: What do you notice about the numerators? Model and write the next fraction.

Answer:1/6, 2/6, 3/6 and the partsnof the circle to be shaded is 4/6

Question 11.
Modeling Real Life
A vegetable tray has 8 equal parts. Three parts have peppers. One part has broccoli. Another part has tomatoes. The rest of the tray has carrots. What fraction of the tray has carrots?

• Three parts are peppers 3/8.
• One part is broccoli 1/8.
• One part is tomatoes 1/8.
• The remaining 3 parts are carrots that is 3/8.

Question 12.
DIG DEEPER!
You divide an art canvas into equal parts. You paint 1 part blue, 2 parts orange, and the last part yellow. What fraction of the canvas is painted orange?

Explanation:

Canvas divided into two parts out of 4.

Review & Refresh

Complete the fact family.

Question 13.
6 × ___ = 42
___ × ___ = 42
42 ÷ 7 = ___
42 ÷ ___ = 7

6×7=42

7×6=42

42/7=6

42/6=7

Question 14.
9 × ___ = 9
___ × 9 = 9
9 ÷ 1 = ___
9 ÷ ___ = 1

9×1=9

1×9=9

9÷1=9

1÷9=9

### Lesson 10.4 Fractions on a Number Line : Less Than 1

Explore and Grow

Use the $$\frac{1}{6}$$ Fraction Strips to complete the fractions on the number line. Then plot $$\frac{3}{6}$$ on the number line.

Precision
Plot $$\frac{6}{6}$$ on the number line. What do you notice? Explain.

Think and Grow: Fractions on a Number Line: Less Than 1

Every number on a number line represents a distance from 0. The distance from 0 to 1 is one whole. A number line can be divided into any number of equal parts or distances.
Example:
Plot $$\frac{3}{4}$$ on the number line.
Step 1: Divide the length from 0 to 1 into ___ equal parts.
Step 2: Label each tick mark on the number line.

Show and Grow

Plot the fraction on the number line.

Question 1.

One 1/2 is 1/2

1×1/2 is 1/2

Explanation:

Divided the length from 0 to 1 into 2 equal parts. Labeled each tick mark on the number line as 1/2

Question 2.

Two 1/6 is 2/6

Explanation:

Divided the length from 0 to 1 into 6 equal parts. Labeled each tick mark on the number line as 1/6.

Apply and Grow: Practice

Plot the fraction on a number line.
Question 3.

Two 1/4s are 2/4

Explanation:

Divided the length from 0 to 1 into 4 equal parts. Labeled each tick mark on the number line as 1/4.

Question 4.

The above figure shows the number line 0 to 1

Question 5.

The above figure is a number line

Question 6.
$$\frac{6}{8}$$

6/8

Explanation:

Divided the length from 0 to 1 into 8 equal parts. Labeled each tick mark on the number line as 1/8.and the latex is 6/8.

Question 7.
$$\frac{3}{4}$$

Explanation:

Divided the length from 0 to 1 into 4 equal parts. Labeled each tick mark on the number line as 1/4.

Question 8.
Structure
Complete the number line.

The above number line is divided into seven equal parts. They are0 , 1/7,2/7, 3/7 4/7, 5/7, 6/7 ,1

Question 9.
Writing
How are the number lines the same? How are they different?

Answer: The both number lines are same because both are divided into same equal parts.

Think and Grow: Modeling Real Life

Three laps around a walking trail is 1 mile. How many laps does it take you to walk $$\frac{2}{3}$$ mile?
Model:

You need to walk ___ laps to walk $$\frac{2}{3}$$ mile.

Explanation:

Mark first 0 and 1

Then divide it into 3 equal parts as 1/3 2/3,

That is 2 times of 1/3 is 2/3

Show and Grow

Question 10.
You follow a recipe and make four servings. How many servings can you make using $$\frac{1}{4}$$ of each ingredient in the recipe?

Answer: Four 1/4 of ingredients can be served.

Explanation:

There are four types of ingredients making once with one ingredient as 1/4.

Question 11.
DIG DEEPER!
A gymnast needs to take 8 equal-sized steps to get from one end of a balance beam to the other. She starts on the left end of the beam and takes 6 steps. What fraction of the beam is behind her? What fraction of the beam is in front of her?

Fraction of the beam behind her is 4/6.

Fraction of the beam front of her is 2/6.

Question 12.
DIG DEEPER!
A tightrope walker needs to take 6 equal-sized steps to get from one end of a tightrope to the other. He starts on the left side of the rope and takes 5 steps. What fraction of the rope is behind him? What fraction of the rope is in front of him ?

The fraction of the beam behind him is 5/6.

Fraction of the beam front of him is 1/6.

### Fractions on a Number Line : Less Than 1 Homework & Practice 10.4

Plot the fraction on a number line.

Question 1.

Question 2.
$$\frac{3}{8}$$

The above number line is divided into eight equal parts and the latex is 3×1/8 is 3 /8th parts of 0-1

Question 3.
$$\frac{1}{4}$$

The above number line is divided into four equal parts and the latex is 1×1/4 is 1/4th parts of 0-1

Question 4.

$$\frac{2}{6}$$

The above number line is divided into eight equal parts and the latex is 3×1/8 is 3 /8th parts of 0-1

Question 5.
$$\frac{5}{8}$$

The above number line is divided into eight equal parts and the latex is

5×1/8 is 5/8th parts of 0-1

Question 6.
Logic
What fraction is located halfway between 0 and 1?

Ans: The fraction is located halfway between 0 and 1 is 1/2 and 1/2.

Question 7.
YOU BE THE TEACHER
Your friend draws a number line and plots $$\frac{2}{6}$$. Is your friend correct? Explain.

My friend marked the correct point but he did not divided into equal parts.

Question 8.
Structure
Which number line shows $$\frac{2}{3}$$ ?

Question 9.
Modeling Real Life
Four laps around a soccer ﬁeld is 1 mile. How many laps does it take you to run $$\frac{3}{4}$$ mile?

Question 4.
DIG DEEPER!
A diver needs to take 8 equal-sized steps before diving into the pool. She starts at the beginning of the diving board and takes 6 steps. What fraction of the diving board is behind the diver? What fraction of the diving board is in front of the diver?

The diving behind the driver is 5/6 and the diving board in front of the driver is 1/6

Review & Refresh

Find the area of the shape.

Question 11.

Area = _21/70__ square units.

Question 12.

Area = __20/70_ square units.

### Lesson 10.5 Fractions on a Number line: Greater Than 1

Explore and Grow

Divide each circle into halves. Shade three halves. Write the fraction.

Precision
Complete the fractions on the number line. Plot $$\frac{3}{2}$$ on the number line. What do you notice? Explain.

Think and Grow : Fractions on a Number Line: Greater Than 1

When the numerator is greater than the denominator, the fraction is greater than one whole.

You can show fractions greater than one whole on a number line.

Example:
Plot $$\frac{2}{3}$$ on the number line.
Step 1: Divide each whole into ___ equal parts.

Show and Grow

Question 1.
Plot $$\frac{15}{8}$$ on the number line

The above number line is divided into sixteen equal parts that is from  0 to 2 and the latex is fifteen of 1/8 is 15/8

Apply and Grow: Practice

Plot the fraction on the number line.

Question 2.
$$\frac{7}{4}$$

Explanation:

The number line is divided into eight equal parts from 0 to 2. Each part is divided as 1/4. The latex is seven parts of 1/4

Question 3.
$$\frac{9}{6}$$

Explanation: above number line is divided into nine equal parts 9/6 is the nine of 1/6

Question 4.
$$\frac{5}{3}$$

Explanation:

The above number line is divided into six equal parts three from 0 to 1 and three from 1 to 2. 5×1/3 =5/3

Structure
Complete the number line.

Question 5.

Answer: the number line is divided into eight equal parts 1/8

From 0 to 1 is 4 parts and from 1 to 2 is 4 parts.

Question 6.

The above number line is divided in twelve equal parts.

From 0 to 1 is 1/6 and from 0 to 2 is 1/6.

Number Sense
Draw and shade a model for the plotted fraction.

Question 7.

3/2

Explanation:

Divided the length from 0 to 1 to two parts.and 1 to 2 two parts total 4 parts

Question 8.

Explanation:

The above number line is divided into eight equal parts and are represented 1/4.

Think and Grow: Modeling Real Life

How far is the aquarium from the bank?

The aquarium is ___ miles from the bank.

Show and Grow

Use the number line to answer the questions.

Question 9.
How far is the gas station from the school?

Explanation:the school is 5/4 of the total distance from school to gas station.

Question 10.
A post office is the same distance from the restaurant as it is from the hospital. How far is the post office from the school?

Explanation:

10/4 miles to the school A

As shown in figure postoffice is the same distance from the restaurant and to the hospital.

Question 11.
DIG DEEPER!
How far is the gas station from the hospital?

The gas station is 7/4 miles from the hospital.

Question 12.
DIG DEEPER!
How far is the library from the amusement park?

3 miles far from the amusement park to the library.

### Fractions on a Number line: Greater Than 1 Homework & Practice 10.5

Plot the fraction on a number line.

Question 1.
$$\frac{8}{6}$$

Question 2.
$$\frac{3}{2}$$

3/2

Explanation:

Divided the length from 0 to 1 into 2 equal parts.  And divided the 1 to 2 to two equal parts.Labeled each tick mark on the number line as 1/2.and the latex is 3/2.

Question 3.
$$\frac{7}{4}$$

7/4

Explanation:

Divided the length from 0 to 1 into 4 equal parts and again 1 to 2 it is divided into 4 parts.Labeled each tick mark on the number line as 1/4.and the latex is 7/4

Question 4.
$$\frac{7}{6}$$

7/6

Explanation:

Divided the length from 0 to 1 into 12 equal parts. Labeled each tick mark on the number line as 1/6.and the latex is 7/6.

Question 5.
$$\frac{4}{3}$$

4/3

Explanation:

Divided the length from 0 to 1 into 8 equal parts. Labeled each tick mark on the number line as 1/8.and the latex is 4/3.

Question 6.
$$\frac{6}{4}$$

6/4

Explanation:

Divided the length from 0 to 1 into 8 equal parts. Labeled each tick mark on the number line as 1/8.and the latex is 6/4.

Question 7.
YOU BE THE TEACHER
Newton says 2 is between 1 and $$\frac{9}{8}$$ on a number line. Is he correct? Explain.

Explanation: consider a number line and mark 0 to 3 in between divide the line in to eight equal parts each16/8 is 2.

Question 8.
Writing
Explain what the numerator $$\frac{7}{4}$$ of the fraction represents.

Explanation:

As the number line dividing basis it is divided into 8 equal parts as is greater side.

Question 9.
DIG DEEPER!
What fraction is shaded? Plot the fraction on the number line.

Question 10.

Modeling Real Life
Use the number line to answer the questions.

Question 11.
How far is the grocery store from the school ?

Explanation:

The grocery store is two miles away from the school.

From the above figure, we can see that each part is divided into 4 equal parts in that way school is 2 miles away.

Question 12.
A playground is the same distance from the grocery store as it is from the library. How far is the playground from the mall?

Explanation:

The grocery store is 1 mile away from the play ground.as it has the same distance each.

Review & Refresh

Question 13.
25 Nearest ten: ___30

The 10 which comes after 25 is 30

Question 14.
182 Nearest hundred: ___200

The 100 which comes after 182 is 200.

Question 1.
You, your friend, and your cousin are making spinners for a board game.
a. You design a spinner with 3 equal parts for your game. Draw the equal parts.

b. Your friend designs a spinner that is split into sixths. Does this spinner work for your game?
c. Your cousin wants to design a spinner that is $$\frac{1}{3}$$ blue, $$\frac{2}{3}$$ yellow, and $$\frac{1}{3}$$ red. Is your cousin correct? Explain.

Answer: the spinner is divided into three equal parts to play the game.

B. The spinner which is divided by my friend is useful for the game as he spotted the circle into 6 equal parts it is shown.

C. He is wrong because he divided the circle into 3 parts and saying coloring as four parts.

Question 2.
Use the game board above to ﬁnd the area of each color in square inches. Which color has the greatest area?

Explanation:

Blue color has 4 inches length in to breadth.

L*B.

2*2=4

Area of the blue surface is4 into no of blocks is 4*12 is 24.

Question 3.

Design a spinner that has 8 equal parts. One part is red, two parts are blue, one part is yellow, and the rest is green.
a. What fraction of the spinner is green?

b. Which colour are you most likely to spin ? Explain

### Understand Fractions Activity

Fraction Spin and Cover

Directions:

1. Take turns using the spinners to ﬁnd which fraction model to cover.
2. Use a counter to cover the fraction model.
3. Repeat this process until you cover all of the models.
4. The player with the most fraction models covered wins!

### Understand Fractions Chapter Practice

10.1 Equal Parts of a Whole

Tell whether the shape shows equal parts or unequal parts. If the shape shows equal parts, then name them.

Question 1.

Explanation: the above rectangle is divided into 6 equal parts. and name  sixths.

Question 2.

Explanation:

The above triangle is divided into 4 equal parts which are equal in size. they name as fourths.

Question 3.

Explanation:

The above circle is divided but it is not equal. the name as ninths.

Question 4.

Explanation:The above square is divided into three equal parts. and named as thirds.

Question 5.
Divide the triangle into two equal parts. Then name the equal parts.

Explanation: the above circle is divided into two equal parts. they named as halves.

Question 6.
Divide the circle into eight equal parts. Then name the equal parts.

Explanation: the circle is divided into eight equal parts. the named as eighths.

10.2 Understand a Unit Fraction

What fraction of the whole is shaded?

Question 7.

Explanation: the above rectangle is divided into 6 parts and in that one part is shaded. that is 1/6

Question 8.

Explanation: the above parallelogram is divided into three equal parts in which one part is coloured. That is 1/3

Question 9.
Divide the square into four equal parts. Shade one part. What fraction of the whole is shaded?

Explanation:The above square is divided into four parts in which one is shaded. that is 1/4th part of the whole is shaded.

Question 10.
Divide the circle into eight equal parts. Shade one part. What fraction of the whole is shaded?

Explanation: the above circle is divided into eight equal parts. in that one part is shaded. the whole part shaded is 1/8.

Question 11.
Modeling Real Life
Descartes arranges his bedroom into four equal parts. His bed takes up two parts. His dresser takes up one part. The rest of his bedroom is free space. What fraction of Descartes’s bedroom is free space?

10.3 Write Fractions of a Whole

Question 12.

Explanation: from the above semicircle the number of divided parts are 4. In that three are shaded that is 3/4th of the whole is shaded.

Question 13.

Explanation: the above triangle is divided into two equal parts in that two equal parts are shaded. so the whole part is shaded.

Question 14.
Divide the circle into sixths. Shade 4 of the equal parts. Then write a fraction for the shaded parts.

Explanation: the circle is divided into 6.the 4 parts are shaded the shaded part is 4/6.

Question 15.
Divide the square into thirds. Shade 2 of the equal parts. Then write a fraction for the shaded parts.

Explanation.

The square is divided into three equal parts of two equal parts are shaded. the shaded part is 2/3.

Question 16.
Modeling Real Life
A circular mandala poster is divided into eight equal parts. You color one part red, three parts green, and two parts yellow. What fraction of the poster do you have left to color?

Explanation: the circle mandala poster is divided into 8 equal parts.

Red=1

Green=3

Yellow=2

The two parts should be colored.

10.4 Fractions on a Number Line: Less Than 1

Plot the fraction on the number line

Question 17.
$$\frac{3}{4}$$

Explanation:

Divided the length from 0 to 1 into 4 equal parts. Point and mark each tick mark on the number line as 1/4 that of divided parts and the latex is 3 of 1/4 s are 3/4

Question 18.
$$\frac{5}{6}$$

Divided the length from 0 to 1 into 6 equal parts. Point and mark each tick mark on the number line as 1/6 that of divided parts and the latex is 5 of 1/6 s are 5/6.

Question 19.
$$\frac{2}{3}$$

Explanation:

Divided the length from 0 to 1 into 3 equal parts. Point and mark each tick mark on the number line as 1/3 that of divided parts and the latex is 2 of 1/3 s are 2/3.

Plot the fraction on a number line.

Question 20.
$$\frac{3}{6}$$

Explanation:

Divided the length from 0 to 1 into 6 equal parts. Point and mark each tick mark on the number line as 1/6 that of divided parts and the latex is 3 of 1/6 s are 3/6.

Question 21.
$$\frac{5}{8}$$

Explanation:

Divided the length from 0 to 1 into 8 equal parts. Point and mark each tick mark on the number line as 1/8 that of divided parts and the latex is 5 of 1/8s are 5/8.

Question 22.
Modeling Real Life
You follow a recipe and make three servings. How many servings can you make using $$\frac{1}{3}$$ of each ingredient in the recipe?

10.5 Fractions on a Number Line: Greater Than 1

Plot the fraction on the number line.

Question 23.
$$\frac{4}{3}$$

Explanation:

Divided the length from 0 to 1 and 1 to 2 into 6 equal parts. Point and mark each tick mark on the number line as 1/3 that of divided parts and the latex is 4 of 1/3 s are 4/3.

Question 24.
$$\frac{9}{6}$$

Explanation:

Divided the length from 0 to 1 and 1 to 2 into 12 equal parts. Point and mark each tick mark on the number line as 1/6 that of divided parts and the latex is 9 of 1/6 s are 9/6.

Question 25.
Structure
Complete the number line.

Divided the length from 0 to 1 and 1 and 2 into 1/2 equal parts. Point and mark each tick mark on the number line as 1/2 and 3/2.

Question 26.
Number Sense
What fraction is shaded? Plot the fraction on the number line

Explanation:

The above two circles are divided into 16 equal parts.

From 0 to 1 eight equal parts which are fully shaded.

From 1 to 2 eight equal parts in that 6 parts are shaded.

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