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.