McGraw Hill My Math Grade 3 Chapter 4 Lesson 4 Answer Key Arrays and Multiplication

All the solutions provided in McGraw Hill Math Grade 3 Answer Key PDF Chapter 4 Lesson 4 Arrays and Multiplication will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 3 Answer Key Chapter 4 Lesson 4 Arrays and Multiplication

Math in My World

Example 1
Mrs. Roberts baked a batch of bagels. She arranged the bagels in 3 equal rows of 4 bagels each on the cooling rack. How many bagels did she bake?

Find the total number of bagels. Use counters to model the array. Draw the array.

Explanation:
Mrs. Roberts baked a batch of bagels
She arranged the bagels in 3 equal rows of 4 bagels each on the cooling rack
I used counters to model the problem
I drew an array
3 rows of 4 rows will be
3 x 4 = 12
So, the total number of bagels are 12.

You can use repeated addition or multiplication to find the unknown

So, ___ rows of ___ is ___ or ___ × ___ = _____
The unknown is ____ Mrs. Roberts baked 12 bagels.

Explanation:
4 + 4 + 4 = 12 is the addition sentence
Use multiplication method
3 x 4 = 12 is the multiplication sentence
So, 3 rows of 4 is 12 or 3 x 4 = 12
The unknown number is 12.
Mrs. Roberts baked 12 bagels.

Example 2
One page of Elsa’s photo album is shown. Write two multiplication sentences to find how many photos are on the page.

Explanation:
One page of Elsa’s photo album is shown
There are 4 rows of photos and
Each row has 2 photos
The multiplication sentences that solve the problem are
4 x 2 = 12 and 2 x 4 = 12
So, One page of Elsa’s photo album has 12 photos.

Talk Math
What other operation uses the Commutative Property? Explain.

Commutative property is applicable only for addition and multiplication processes. Thus, it means we can change the position or swap the numbers when adding or multiplying any two numbers and the sum or the product will remain same.

Guided Practice

Write an addition sentence and a multiplication sentence to show equal rows.

Question 1.

1 + 1 = 2
2 x 1 = 2

Explanation:
There are 2 rows of counters with 1 counter in each row
So, The addition sentence that shows the above array is 1 + 1 = 2
The multiplication equation that show the above array is 2 x 1 = 2.

Question 2.

7 + 7 = 14
2 x 7 = 14

Explanation:
There are 2 rows of squares with 7 squares in each row
So, The addition sentence that shows the above array is 7 + 7 = 14
The multiplication equation that show the above array is 2 x 7 = 14.

Independent Practice

Write an addition sentence and a multiplication sentence to show equal rows.

Question 3.

____ + ___ + ____ = ____
____ × ___ = ____
6 + 6 + 6 = 18
3 x 6 = 18

Explanation:
There are 3 rows of counters with 6 counters in each row
So, The addition sentence that shows the above array is 6 + 6 +  6 = 18
The multiplication equation that show the above array is 3 x 6 = 18.

Question 4.

____ + ___ + ____ = ____
____ × ___ = ____
2 + 2 = 4
2 x 2 = 4

Explanation:
There are 2 rows of triangles with 2 triangles in each row
So, The addition sentence that shows the above array is 2 + 2 = 4
The multiplication equation that show the above array is 2 x 2 = 4.

Question 5.

____ + ____ + ___ + ____ = ____
____ × ___ = ____
4 + 4 + 4 + 4 = 16
4 x 4 = 16

Explanation:
There are 4 rows of squares with 4 squares in each row
So, The addition sentence that shows the above array is 4 + 4 + 4 + 4 = 16
The multiplication equation that show the above array is 4 x 4 = 16.

Question 6.

____ + ___ + ____ = ____
____ × ___ = ____
7 + 7 + 7 + = 21
3 x 7 = 21

Explanation:
There are 2 rows of paint colors with 7 paint colors in each row
So, The addition sentence that shows the above array is 7 + 7  + 7 = 21
The multiplication equation that show the above array is 3 x 7 = 21.

Question 7.

___ + ____ = ____
____ × ___ = ____
6 + 6 = 12
2 x 6 = 12

Explanation:
There are 2 rows of eggs with 6 eggs in each row
So, The addition sentence that shows the above array is 6 + 6 = 12
The multiplication equation that show the above array is 2 x 6 = 12.

Question 8.

___ + ____ = ____
____ × ___ = ____
3 + 3 = 6
2 x 3 = 6

Explanation:
There are 2 rows of diamonds shapes with 3 diamonds in each row
So, The addition sentence that shows the above array is 3 + 3 = 6
The multiplication equation that show the above array is 2 x 3 = 6.

Use the Commutative Property of Multiplication to find each missing number.

Question 9.
5 × 2 = ___.
2 × ___ = 10
5 x 2 = 10
2 x 5 = 10

Explanation:
According to the commutative property of multiplication, changing the order of the numbers we are multiplying does not change the product
5 x 2 will be equal to 2 x 5
If 5 x 2 = 10
So, 2 x 5 = 10
Therefore, the missing number is 5.

Question 10.
___ × 5 = 15
____ × 3 = 15
3 x 5 = 15
5 x 3 = 15

Explanation:
According to the commutative property of multiplication, changing the order of the numbers we are multiplying does not change the product
3 x 5 will be equal to 5 x 3
If 3 x 5 = 15
So, 5 x 3 = 15
Therefore, the missing numbers are 3 and 5.

Question 11.
3 × ____ = 27
9 × 3 = ____
3 x 9 = 27
9 x 3 = 27

Explanation:
According to the commutative property of multiplication, changing the order of the numbers we are multiplying does not change the product
3 x 9 will be equal to 9 x 3
If 3 x 9 = 27
So, 9 x 3 = 27
Therefore, the missing factor is 9 and product is 27.

Question 12.
Hope drew the array at the right. Write a multiplication sentence to represent the model.

___ × ___ = ____
3 x 8 = 24

Explanation:
Hope drew the above array
The given array has 3 rows of squares with 8 squares in each row
The multiplication sentence to represent the array is 3 x 8 =
3 x 8 = 24
So, the multiplication sentence is 3 x 8 = 24.

Problem Solving

For Exercises 13 and 14, draw an array to solve. Then write two multiplication sentences.

Question 13.
Bailey made a 3 by 4 array with her crackers. How many crackers does she have?

Explanation:
Bailey made a 3 by 4 array with her crackers
The multiplication equation that solves the problem is
3 x 4 = 12
So, Bailey have 12 crackers.

Question 14.
There are 4 waiters serving 5 tables each. How many tables do the waiters have altogether?

Explanation:
There are 4 waiters serving 5 tables each
The multiplication equation that solves the problem is
4 x 5 = 20
So, the waiters have 20 tables altogether.

HOT Problems

Question 15.
Mathematical PRACTICE 2 Reason Why do you sometimes have only one multiplication sentence for an array?
An array is an arrangement of a number in the form of rows and columns.
For example ,number
1= 1 × 1
4 = 2 × 2
K= m × n
m =Number of rows, n=Number of columns
First number represent number of rows, and second number represent number of columns
If both rows and columns are same in number or
If the both the factors of the sentence are same then their will only one multiplication sentence.

Question 16.
Mathematical PRACTICE 3 Find the Error Alyssa is using the numbers 2, 3, and 6 to show the Commutative Property. Find and correct her mistake.
3 × 2 = 6 so, 6 × 3 = 2
2 x 3 = 6 so, 3 x 2 = 6

Explanation:
Alyssa is using the numbers 2, 3, and 6 to show the Commutative Property
Commutative property states that product of 2 factors will be same even if the order of the factors change.
So, 2 x 3 = 6 and 3 x 2 = 6 are the correct multiplication sentences.

Question 17.
? Building on the Essential Question How can the Commutative Property be used to write multiplication sentences?
Commutative property states that when two numbers are multiplied together, the product is the same regardless of the order of the multiplicands.
Example: 2 x 4 = 8 and 4 x 2 = 8 are the multiplication sentences.

McGraw Hill My Math Grade 3 Chapter 4 Lesson 4 My Homework Answer Key

Practice

Write an addition sentence and a multiplication sentence to show equal rows.

Question 1.

____ + ____ + ____ = _____
____ × ____ = _____
4 + 4 + 4 = 12
3 x 4 = 12

Explanation:
There are 3 rows of Apples with 4 Apples in each row
So, The addition sentence that shows the above array is 4 + 4 + 4 = 12
The multiplication equation that show the above array is 3 x 4 = 12.

Question 2.

____ + ____ + ____ = _____
____ × ____ = _____
5 + 5 + 5 = 15
3 x 5 = 15

Explanation:
There are 3 rows of Apple Juice containers with 5 Apple Juice containers in each row
So, The addition sentence that shows the above array is 5 + 5 + 5 = 15
The multiplication equation that show the above array is 3 x 5 = 15.

Use the Commutative Property of Multiplication to find each missing number.

Question 3.
3 × 2 = 6 ___ × 3 = 6
2

Explanation:
According to the commutative property of multiplication, changing the order of the numbers we are multiplying does not change the product
3 x 2 will be equal to 2 x 3
If 3 x 2 = 6
So, 2 x 3 = 6
Therefore, the missing number is 2.

Question 4.
6 × 4 = 24 4 × ___ = 24
6

Explanation:
According to the commutative property of multiplication, changing the order of the numbers we are multiplying does not change the product
6 x 4 will be equal to 4 x 6
If 6 x 4 = 24
So, 4 x 6 = 24
Therefore, the missing number is 6.

Question 5.
8 × 6 = 48 6 × 8 = ____
48

Explanation:
According to the commutative property of multiplication, changing the order of the numbers we are multiplying does not change the product
8 x 6 will be equal to 6 x 8
If 8 x 6 = 48
Then 6 x 8 = 48
Therefore, the missing number is 48.

Question 6.
5 × 2 = 10 ___ × 5 = 10
2

Explanation:
According to the commutative property of multiplication, changing the order of the numbers we are multiplying does not change the product
5 x 2 will be equal to 2 x 5
If 5 x 2 = 10
So, 2 x 5 = 10
Therefore, the missing number is 5.

Problem Solving

Draw an array to solve. Then write two multiplication sentences.

Question 7.
Bottles of syrup are arranged in 4 rows of 7 bottles each. How many bottles of syrup are there in all?

Explanation:
Bottles of syrup are arranged in 4 rows of 7 bottles each
The multiplication equation that solves the problem is
4 x 7 = 28
So, there are 28 bottles of syrup in all.

Question 8.
A parking lot has 6 rows of 10 spaces. How many parking spaces are there altogether?

Explanation:
A parking lot has 6 rows of 10 spaces
The multiplication equation that solves the problem is
6 x 10 = 60
So, there are 60 parking spaces altogether.

Vocabulary Check

Question 9.
How can you use an array to show the Commutative Property?

Explanation:
The commutative property of multiplication can be neatly illustrated using an array. For example, the array above could be read as rows of, or as columns of. Or the array could be physically turned around to show that rows of has the same number as rows of.
That means we can use the numbers in either way
That is 2 x 3 = 6 and 3 x 2 = 6.

Test Practice

Question 10.
Which pair of number sentences represents the Commutative Property of Multiplication?
A. 3 × 6 = 18; 2 × 9 = 18
B. 6 × 7 = 42; 7 × 6 = 42
C. 4 × 5 = 20; 8 × 5 = 40
D. 9 + 11 = 20; 11 + 9 = 20