All the solutions provided in **McGraw Hill Math Grade 5 Answer Key PDF Chapter 10 Lesson 1 Part of a Number** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 10 Lesson 1 Part of a Number

You can use bar diagrams to find parts of a number.

Answer:

– The first step is to draw the rectangular strip.

– Next, look at the denominator of the fraction which we want to model.

– The denominator describes how many equal parts the whole is divided into. It’s the bottom number.

– The denominator of 1/4 is 4.

– That means you should divide the rectangular strip into 4 equal parts.

– The numerator describes the number of parts you have. It’s the top number.

– The numerator of 1/4 is 1.

The above-given 1/4 of 16

**Draw It**

Lelah threw 16 pitches in the first inning of a softball game. Of the pitches she threw, \(\frac{3}{4}\) of them were strikes. How many strikes did she throw in the first inning?

Find \(\frac{3}{4}\) of 16.

1. The bar diagram represents the number of pitches she threw.

Answer:

The above-given fraction: 3/4

3/4 x 16 = 3 x 4 = 12

In fraction, 3/4; the denominator is 4 so they are divided into 4 equal parts.

The numerator is 3, so they had shown 3 equal parts. 3 x 4 = 12

Therefore, the number of pitches she threw are 12.

2. Since the denominator is 4, the bar diagram was divided into ____ equal sections.

Each section of the bar represents ____ pitches.

Answer:

The above-given fraction is 3/4

The denominator is 4 so the bar diagram is also divided into 4 equal parts. Each section represents 4 pitches.

Representation:

3. Use the diagram to determine \(\frac{3}{4}\) of 16.

4 + 4 + 4 = _____

\(\frac{3}{4}\)-of 16 is ____

So, Lelah threw ____ strikes.

Answer:

By using the diagram we can add the pitches

4 + 4 + 4 = 12

or we can use multiplication method

3/4 x 16 = 3 x 4 = 12

Therefore, Lelah threw 12 strikes.

**Try It**

**Find \(\frac{1}{3}\) of 15 using a bar diagram.**

1. Label the bar diagram that represents 15.

**Helpful Hint**

The word “of” means to multiply. So, \(\frac{1}{3}\) of 15 means \(\frac{1}{3}\) × 15.

Answer:

The above-given hint:

1/3 x 15 is equal to 5

The above boxes were divided

2. Since the denominator is 3, the bar diagram was divided into ____ equal sections.

Each section of the bar represents _____

Answer:

The boxes were divided into 3 sections. And each section of the bar represents 5

3. Use the diagram to determine \(\frac{1}{3}\) of 15.

\(\frac{1}{3}\) of 15 is the same as 15 ÷ 3, which is the same as \(\frac{1}{3}\) × 15.

What is \(\frac{1}{3}\) of 15? ____

So, \(\frac{1}{3}\) of 15 = _____

Answer:

The above-given latex sentence can be written as

1/3 of 15

= 1/3 x 15

= 5

Therefore, the answer is 5.

**Talk About It**

Question 1.

**Mathematical PRACTICE 6 Explain to a Friend** Explain why \(\frac{1}{4}\) of 16 is the same as 16 ÷ 4.

Answer:

To find 1/4 of 16, draw a bar diagram that represents 16. Then divide it into fourths. One of the fourths is 1/4 of 16, which is the same as 16 ÷ 4.

1/4 of 16 is equal to 4

16 ÷ 4 is equal to 4.

Question 2.

Explain why \(\frac{3}{4}\) of 16 is the same as 3 × 16 ÷ 4.

Answer:

If 1/4 of 16 is the same as 16 ÷ 4, then 3/4 of 16 is the same as 3 x 16 ÷ 4, since 3/4 is three times as large as 1/4.

3/4 of 16 = 3/4 x 16 = 12

3 x 16 ÷ 4

3 x 16 = 48

48 ÷ 4 = 12

both are equal.

**Practice It**

**Draw a bar diagram to find each product.**

Question 3.

12 × \(\frac{1}{2}\) = _____

Answer:

The above-given problem is

12 x 1/2

2 x 6 = 12

we can cancel 2 and 12

Therefore, the answer is 6

The bar diagram can be represented as

Since the denominator is 2, the bar diagram was divided into 2 equal sections.

Each section of the bar represents 6.

Question 4.

\(\frac{2}{3}\) of 15 = _____

Answer:

The above-given problem is:

2/3 of 15

2/3 x 15

3 x 5 = 15 (3 and 15 gets cancel)

5 x 2 = 10

The bar diagram can be represented as;

Since the denominator is 3, the bar diagram was divided into 3 equal sections.

Each section of the bar represents 5.

Question 5.

\(\frac{2}{3}\) of 8 = _____

Answer:

The above-given problem:

2/3 of 8

2/3 x 8

Express 2/3 x 18 as a single fraction.

then the fraction is 2 x 18/3

in the 3rd table, 18 get cancelled 6 times.

3 x 6 = 18

6 x 2 = 12

Therefore, 2/3 of 18 is equal to 12

Since the denominator is 2, the bar diagram was divided into 2 equal sections.

Each section of the bar represents 6.

Question 6.

9 × \(\frac{1}{3}\) = _____

Answer:

The above-given problem:

9 x 1/3 is equal to 3

The bar diagram can be represented as:

Since the denominator is 3, the bar diagram was divided into 3 equal sections.

Each section of the bar represents 3.

Question 7.

8 × \(\frac{1}{4}\) = _____

Answer:

The above-given problem;

8 x 1/4 = 2

The bar diagram can be represented as:

Since the denominator is 4, the bar diagram was divided into 4 equal sections.

Each section of the bar represents 2.

Question 8.

\(\frac{1}{2}\) of 16 = _____

Answer:

The above-given problem:

1/2 of 16

1/2 x 16 = 8

The bar diagram can be represented as:

Since the denominator is 2, the bar diagram was divided into 2 equal sections.

Each section of the bar represents 8.

Question 9.

25 × \(\frac{2}{5}\) = _____

Answer:

The above-given problem;

25 x 2/5 = 5 x 2 = 10

The bar diagram can be represented as:

Since the denominator is 5, the bar diagram was divided into 5 equal sections.

Each section of the bar represents 5.

Question 10.

24 × \(\frac{3}{4}\) = _____

Answer:

The above-given problem

24 x 3/4 = 6 x 3 = 18

The bar diagram can be represented as:

Since the denominator is 4, the bar diagram was divided into 4 equal sections.

Each section of the bar represents 6.

**Apply It**

**Draw a bar diagram to help solve Exercises 11 and 12.**

Question 11.

Leon used plant fertilizer on \(\frac{4}{7}\) of his potted flowers. If he has 28 potted flowers, on how many did he use plant fertilizer?

Answer:

The amount of fertilizer used by Leon for his potted flowers = 4/7

The estimation of potted flowers = 28

The number of plant fertilizer did he use = X

X = 4/7 x 28

X = 4 x 4

X = 16

Therefore, he used 16 plant fertilizers for 28 potted flowers.

The bar diagram can be represented as:

Since the denominator is 7, the bar diagram was divided into 7 equal sections.

Each section of the bar represents 4.

Question 12.

**Mathematical PRACTICE 5 Use Math Tools** Jeremy washed \(\frac{3}{8}\) of the plates from dinner. If 16 plates were used, how many plates did Jeremy wash?

Answer:

The number of plates he washed = 3/8

The estimation of the number of plates used = 16

The number of plates did Jeremy washed = X

X = 3/8 x 16

X = 3 x 2

X = 6

Therefore, he washed 6 plates.

The bar diagram can be represented as:

Since the denominator is 8, the bar diagram was divided into 8 equal sections.

Each section of the bar represents 2.

Question 13.

**Mathematical PRACTICE 4 Model Math** Write a real-world problem that could represent the bar diagram shown.

Answer:

From the bar diagram, we can write as

2/3 of 12

2/3 x 12 = 4 x 2 = 8

The real-world problem could be shamvitha had $12 to spend at the store. She spent 2/3 of the money he had on chocolates. How much did she spend?

Shamvitha spent $8.

**Write About It**

Question 14.

How can I use models to find part of a number?

Answer:

I can draw a bar diagram to model the number. I divided it into equal parts. One or more of the parts represents the part of the number.

### McGraw Hill My Math Grade 5 Chapter 10 Lesson 1 My Homework Answer Key

**Practice**

**Draw a bar diagram to find each product**

Question 1.

\(\frac{2}{3}\) of 36 = ____

Answer:

The above-given problem:

2/3 of 36.

2/3 x 36 = 2 x 12 = 24

The bar diagram can be represented as:

Since the denominator is 3, the bar diagram was divided into 3 equal sections.

Each section of the bar represents 12.

Question 2.

35 × \(\frac{3}{5}\) = ____

Answer:

The above-given diagram:

35 x 3/5 = 7 x 3 = 21

The bar diagram can be represented as:

Since the denominator is 5, the bar diagram was divided into 5 equal sections.

Each section of the bar represents 7.

**Problem Solving**

**Draw a bar diagram to help solve Exercises 3-5.**

Question 3.

Hope used \(\frac{1}{3}\) of the flour in the container to make cookies. If the container holds 12 cups of flour, how many cups did Hope use?

Answer:

The amount of flour Hope used to make cookies = 1/3

The estimated cups of flour container holds = 12

The number of cups Hope uses = X

X = 1/3 x 12

X = 4

Therefore, Hope uses 4 cups of flour.

The bar diagram can be written as:

Since the denominator is 3, the bar diagram was divided into 3 equal sections.

Each section of the bar represents 4.

Question 4.

Elijah used \(\frac{3}{4}\) of the memory on his cell phone memory card. If the memory card can hold 32 gigabytes, how many gigabytes did Elijah use?

Answer:

The amount of memory Elijah used = 3/4

The estimated amount of memory = 32 gigabytes

The number of gigabytes Elijah used = X

X = 3/4 x 32

X = 3 x 8

X = 24

Therefore, Elijah used 24 gigabytes.

The bar diagram can be represented as

Since the denominator is 4, the bar diagram was divided into 4 equal sections.

Each section of the bar represents 8.

Question 5.

**Mathematical Practice 4 Model Math** Jeremy used \(\frac{5}{6}\) of a loaf of bread throughout the week. If there were 24 slices of bread, how many slices did Jeremy use?

Answer:

The amount of bread Jeremy used = 5/6

The estimated slices of bread = 24

The number of slices she used = X

X = 5/6 x 24

X = 5 x 4

X = 20

Therefore, she uses 20 slices.

The bar diagram can be represented as:

Since the denominator is 6, the bar diagram was divided into 6 equal sections.

Each section of the bar represents 4.

Question 6.

Write a real-world problem that could represent the bar diagram shown.

Answer:

From the above bar diagram,

3/5 x 15 = 3 x 3 = 9

The real-world problem could be sham had $15 to spend at the store. She spent 3/5 of the money he had on drinks. How much did she spend?

Shamvitha spent $9.