All the solutions provided in **McGraw Hill My Math Grade 3 Answer Key PDF Chapter 9 Lesson 1 Take Apart to Multiply **will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 3 Answer Key Chapter 9 Lesson 1 Take Apart to Multiply

When you take apart, or decompose, a factor, you 1 have smaller numbers that are easier to multiply.

**Build It**

Find 4 × 7.

1. Model 4 × 7.

Use color tiles to make a 4 × 7 array. Draw the array.

2. Decompose one factor.

- Take apart the 7.
- Separate 7 columns into 5 columns + 2 columns.

3. Find the products of each part. Then add.

So, 4 × 7 = ______________.

Answer: 4 × 7 = 28

Explanation:

Given, 4 × 7 = ( 4 × 5 ) + ( 4 × 2 )

28 = 20 + 8

28 = 28.

So, 4 × 7 = 28

**Try It**

Gretchen cut 6 oranges into 9 slices each. How many orange slices are there?

Find 6 × 9.

1. Outline a 6 × 9 array on the grid paper.

2. Decompose one factor.

Draw a vertical line through the array to decompose the factor 9 into 5 + 4. Write the addends above.

3. Find the product of each part.

Multiply. Then add the products.

So, 6 × 9 = _____________. There are _____________ orange slices.

Answer: There are 54 orange slices.

Explanation:

Given, 6 × 9 = ?

decompose the factor 9 into 5 + 4.

6 × 9 = ( 6 × 5) + ( 6 × 4)

54 = 30 + 24

54 = 54

So, There are 54 orange slices.

**Talk About It**

Question 1.

**Mathematical PRACTICE** Justify Conclusions In the example above, could the 6 have been decomposed instead of the 9? Explain.

Answer: Yes , 6 could have been decomposed instead of the 9

Explanation:

In the above example we have seen,

Given, 6 × 9 = ?

decompose the factor 9 into 5 + 4.

6 × 9 = ( 6 × 5) + ( 6 × 4)

54 = 30 + 24

54 = 54

What if 6 is decomposed,

decompose the factor 6 into 3 + 3.

6 × 9 = ( 3 × 9) + ( 3 × 9)

54 = 27 + 27

54 = 54

So, What ever the number is decomposed in the given product the result will be same .

Question 2.

How is decomposing a factor helpful in finding products?

Answer: To decompose is to break down numbers into parts.

Explanation:

As we said earlier, To decompose is to break down numbers into parts. which makes the calculation is easier to solve , by making the smaller products of the numbers,

So, it will be easy to decomposing a factor helpful in finding products.

Question 3.

Explain how using a known fact strategy is similar to decomposing a factor.

Answer: Decomposing a Factor (number) means to break apart the number to uncover the numbers within the factor.

Explanation:

known fact is a fact that you know by memory. expression. A combination of numbers and operations that represent a quantity. while decomposing is to break apart the number.

In both the cases we are using the same strategy as to break the numbers down for easy calculations,

So, a known fact strategy is similar to decomposing a factor.

**Practice It**

**Use color tiles to model the array. Decompose one factor. Then find the product for each part and add.**

Question 4.

Answer:

Explanation:

Given, 7 × 6

decompose the factor 6 into 3 + 3.

7 × 6 = ( 7 × 3 ) + ( 7 × 3)

42 = 21 + 21

So, 7 × 6 = 42.

Question 5.

Answer:

Explanation:

Given,

decompose the factor 7 into 4 + 3.

8 × 7 = ( 8 × 4 ) + ( 8 × 3 )

56 = 32 + 24

56 = 56

So, 8 × 7 = 56.

Question 6.

Decompose one factor. Color the array two colors to represent your numbers. Then find the product for each part and add.

Answer:

Explanation:

Given, 7 × 9 = ?

decompose the factor 9 into 5 + 4.

7 × 9 = ( 7 × 5 ) + ( 7 × 4 )

63 = 35 + 28

63 = 63

So, 7 × 9 = 63.

Question 7.

Decompose the fact a different way.

Answer:

Explanation:

Given, Decompose the fact a different way.

decompose the factor 9 into 6 + 3.

7 × 9 = ( 7 × 6 ) + ( 7 × 3 )

63 = 42 + 21

63 = 63

So, 7 × 9 = 63.

**Apply It**

**Mathematical PRACTICE** Identify Structure Decompose one factor. Find each product. Then add.

Question 8.

Mr. Daniels bought 9 packages of metal brackets to build some bookshelves. There are 8 brackets in each package. How many brackets did Mr. Daniels buy altogether?

Answer: Mr. Daniels bought 72 brackets altogether.

Explanation:

Given, Mr. Daniels bought 9 packages of metal brackets to build some bookshelves.

There are 8 brackets in each package.

Then, 9 × 8 =?

decompose the factor 8 into 4 + 4.

9 × 8 = ( 9 × 4 ) + ( 9 × 4 )

72 = 36 + 36

72 = 72

So, Mr. Daniels bought 72 brackets altogether.

Question 9.

Jenna is making 6 costumes for the dance recital. Each costume uses 9 feet of fabric. How much fabric does Jenna need altogether?

Answer: Jenna need 54 feet of fabric altogether

Explanation:

Given, Jenna is making 6 costumes for the dance recital. Each costume uses 9 feet of fabric.

Then 6 × 9 = ?

decompose the factor 9 into 5 + 4.

6 × 9 = ( 6 × 5 ) + ( 6 × 4 )

54 = 30 + 24

54 = 54

So, 6 × 9 = 54.

Question 10.

Eight horses each ate the number of apples shown. How many apples did they eat altogether?

Answer: 8 × 4 = 32 , Horses ate 32 apples altogether

Explanation:

Given, Eight horses each ate the number of apples shown.

There are 4 apples

then, 8 × 4 = ?

decompose the factor 8 into 4 + 4.

4 × 8 = ( 4 × 4 ) + ( 4 × 4 )

32 = 16 + 16

32 = 32

So, Horses ate 32 apples altogether

Question 11.

**Mathematical PRACTICE** Reason How could you change Exercise 8 so that Mr. Daniels buys a total of 81 brackets?

Answer: There should be 9 brackets in each package.

Explanation:

Given, Mr. Daniels bought 9 packages of metal brackets to build some bookshelves.

There are 8 brackets in each package.

To have a total of 81 brackets , we should change the number of brackets in each package

Then 8 brackets should be replaced by 9 brackets

thus, 9 × 9 = 81

So, There should be 9 brackets in each package.

**Write About It**

Question 12.

How does decomposing a factor allow you to group numbers differently?

Answer: Decomposition of a composite number means converting it into a product of smaller integers. this allows us to find factors of the numbers.so we can group number differently by this method using factors.

To decompose a number or set is to break it apart or separate it into two or more parts. To decompose numbers can mean to determine a sum positive rational numbers that give a specific value. To decompose numbers can also mean to factor a composite number.

### McGraw Hill My Math Grade 3 Chapter 9 Lesson 1 My Homework Answer Key

**Practice**

**Decompose one factor. Color the array two colors to represent your numbers. Then find the product for each part and add.**

Question 1.

Answer:

Explanation;

7 × 7 = ( 7 × 4 ) + ( 7 × 3 )

49 = 28 + 21

49 = 49

So, 7 × 7 = 49.

Question 2.

Answer:

Explanation:

6 × 8 = ( 6 × 4 ) + ( 6 × 4 )

48 = 24 + 24

48 = 48

So, 6 × 8 = 48

**Decompose one factor. Find each product. Then add. Decompose the fact a different way below.**

Question 3.

Answer:

Explanation:

Given, 8 × 8

decompose the factor 8 into 4 + 4.

8 × 8 = ( 8 × 4 ) + ( 8 × 4 )

64 = 32 + 32

64 = 64

So, 8 × 8 = 64

Another way is

Given, 8 × 8

decompose the factor 8 into 6 + 2.

8 × 8 = ( 8 × 6 ) + ( 8 × 2 )

64 = 48 + 16

64 = 64

So, 8 × 8 = 64

Question 4.

Answer:

Explanation:

Given, 5 × 7

decompose the factor 7 into 5 + 2.

5 × 7 = ( 5 × 5 ) + ( 5 × 2 )

35 = 25 + 10

35 = 35

So, 5 × 7 = 35

Another way is

Given, 5 × 7

decompose the factor 7 into 4 + 3.

5 × 7 = ( 5 × 4 ) + ( 5 × 3 )

35 = 20 + 15

35 = 35

So, 5 × 7 = 35

**Problem Solving**

**Decompose one factor. Find each product. Then add.**

Question 5.

**Mathematical PRACTICE** Identify Structure Orlando’s baby sister takes 3 naps a day. How many naps does she take in 9 days?

Answer: 3 × 9 = 27 , She takes 27 naps in 9 days

Explanation:

Given, Orlando’s baby sister takes 3 naps a day.

How many naps does she take in 9 days?

for each day 3 naps

for 9 days 3 × 9 = 27 naps,

So, She takes 27 naps in 9 days

Question 6.

Carli gets to the bus stop 5 minutes early each morning. How many minutes does she wait at the bus stop in 5 days?

Answer: 5 × 5 = 25, Totally she waits for 25 minutes in 5 days

Explanation:

Given, Carli gets to the bus stop 5 minutes early each morning.

She waits for 5 minutes for 5 days,

Then 5 × 5 = 25

So, Totally she waits for 25 minutes in 5 days

Question 7.

Every Monday, Wednesday, and Friday, Mr. Brennan walks 2 miles and jogs 4 miles. What is the total number of miles Mr. Brennan walks and jogs in two weeks?

Answer: Mr. Brennan walks and jogs 36 miles in two weeks

Explanation:

Given, Every Monday, Wednesday, and Friday,

Mr. Brennan walks 2 miles and jogs 4 miles.

total miles 2 + 4 = 6 miles

Number of days, are 3 days per week

Then for 2 weeks 3 × 2 = 6 days

thus 6 × 6 = 36.

So, Mr. Brennan walks and jogs 36 miles in two weeks.