All the solutions provided in McGraw Hill Math Grade 4 Answer Key PDF Chapter 5 Lesson 3 Use the Distributive Property to Multiply will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 4 Answer Key Chapter 5 Lesson 3 Use the Distributive Property to Multiply
Draw It
Find 12 × 15.
1. Label 12 and 15 as the dimensions of the area model.
2. Separate the tens and ones of one factor. Label each part.
Write 15 as ____ and ____
12 × 15 = 12 × (10 + 5)
3. Find each product. Then add.
12 × 15 = 12 × (10 + 5)
= (12 × 10) + (12 × 5)
= ____ + ____
= _____
So, 12 × 15 = ____
Answer: So, 12 x 15 = 180.
Explanation: Given the figure,
Now, using the distributive property we will find the product value.
Then the value is 12 x 15 = 12 x (10 + 5)
Next, we will find each product
i.e., 12 x 10 + 12 x 5
= 120 + 60
= 180
Hence, the product of the given values is 180.
Talk About It
Question 1.
Mathematical PRACTICE 7 Identify Structure How would you use the Distributive Property to find 12 × 18? Then find the product.
Answer: Using the distributive property, the product of 12 x 18 is 216.
Explanation: Given that, the value is 12 x 18.
Now, we will find the value using the distributive property.
So, the given value is distributive as,
12 x 18 = 12 x( 10 + 8)
= 12 x 10 + 12 x 8
= 120 + 96
= 216.
Hence, the product of the given values is 216.
Question 2.
How would you use the Distributive Property to find 14 × 17? Then find the product.
Answer: Using the distributive property, the product of 14 x 17 is 238.
Explanation: Given that, the value is 14 x 17.
Now, we will find the value using the distributive property.
So, the given value is distributive as,
14 x 17 = 14 x( 10 + 7)
= 14 x 10 + 14 x 7
= 140 + 98
= 238.
Hence, the product of the given values is 238.
Practice It
Draw an area model. Then use the Distributive Property to find each product
Question 3.
Find 36 × 24.
36 × 24 = 36 × (20 + 4)
= (36 × 20) + (36 × 4)
= ____ + ____
= _____
Answer: 864
Explanation: Given that, the value is 36 x 24.
Now, we will find the value using the distributive property.
So, the given value is distributive as,
36 x 24 = 36 x( 20 + 4)
= 36 x 20 + 36 x 4
Then 36 x 20 is,
Now find 36 x 4 ,
Then the product values is 720 + 144
= 864.
Hence, the product of the given values is 864.
Question 4.
Find 47 × 19.
47 × 19 = 47 × (10 + 9)
= (47 × ____) + (47 × ____)
= ____ + ____
= ______
Answer: Using the distributive property, the product of 47 x 19 is 893.
The area model is,
Explanation: Given that, the value is 47 x 19.
Now, we will find the value using the distributive property.
So, the given value is distributive as,
47 x 19 = 47 x ( 10 + 9)
= 47 x 10 + 47 x 9
= 470 + 423
= 893
Hence, the product of the given values is 893.
Question 5.
Find 52 × 11.
52 × 11 = ___ × (___ + _____)
= (_____ × ____) + (_____ × ____)
= _____ × ____
= _______
Answer: Using the distributive property, the product of 52 x 11 is 572.
The area model is,
Explanation: Given that, the value is 52 x 11.
Now, we will find the value using the distributive property.
So, the given value is distributive as,
52 x 11 = 52 x ( 10 + 1)
= 52 x 10 + 52 x 1
= 520 + 52
= 572.
Hence, the product of the given values is 572.
Question 6.
Find 46 × 22.
46 × 22 = ____ × (____ + ____)
= (____ × ____) + (____ × ____)
= ____ × ____
= ______
Answer: Using the distributive property, the product of 46 x 22 is 1012.
The area model is,
Explanation: Given that, the value is 46 x 22.
Now, we will find the value using the distributive property.
So, the given value is distributive as,
46 x 22 = 46 x ( 20 + 2)
= 46 x 20 + 46 x 2
= 920 + 92
= 1012.
Hence, the product of the given values is 1012.
Apply It
Use the Distributive Property to solve.
Question 7.
Mathematical PRACTICE 7 Identify Structure There are 15 types of animals in each part of the zoo. The zoo has 12 parts. How many types of animals are there in all?
Answer: 180 types of animals are there in all.
Explanation: There are 15 types of animals in each part of the zoo.
The zoo has 12 parts.
Now, we will find out how many types of animals are there in all.
So, the values are 15 and 12.
Using the distributive property, distribute the values.
15 x 12 = 15 x ( 10 + 2)
= 15 x 10 + 15 x 2
= 150 + 30 = 180.
Therefore, 180 types of animals are there in all.
Question 8.
Write the multiplication sentence for the area model. Then find the product.
____ × ______ = _____
Answer: Using the distributive property, the product of 12 x 17 is 204.
Explanation: Given that, the value is 12 x 17.
Now, we will find the value using the distributive property.
So, the given value is distributive as,
12 x 17 = 12 x ( 10 + 7)
= 12 x 10 + 12 x 7
= 120 + 84
= 204.
Hence, the product of the given values is 204.
Question 9.
Mathematical PRACTICE 3 Find the Error Tim drew a model to find 11 × 25. Find and correct his mistake.
Answer: Using the distributive property, the product of 11 x 25 is 275.
The correct area model is,
Explanation: Given that, the value is 11 x 25.
Now, we will find the value using the distributive property.
So, the given value is distributive as,
11 x 25 = 11 x ( 20 + 5)
= 11 x 20 + 11 x 5
= 220 + 55
= 275.
Hence, the product of the given values is 275.
The given product value in a question is wrong.
Write About It
Question 10.
Why is the Distributive Property appropriate for two-digit multiplication? Explain.
Answer: We can use this property for two digit multiplication to rewrite an expression by distributing or breaking down a factor as a sum or difference of two numbers.
McGraw Hill My Math Grade 4 Chapter 5 Lesson 3 My Homework Answer Key
Practice
Draw an area model. Then use the Distributive Property to find each product.
Question 1.
73 × 34 = ____
73 × 34 = 73 × (30 + 4)
= (73 × ___) + (73 × ____)
= _____ + _____
= _______
Answer: Using the distributive property, the product of 73 x 34 is 2482.
The area model is below,
Explanation: Given that, the value is 73 x 34.
Now, we will find the value using the distributive property.
So, the given value is distributive as,
73 x 34 = 73 x ( 30 + 4)
= 73 x 30 + 73 x 4
The product of 73 x 30 is,
The product of 73 x 4 is,
The final product is, 2190 + 292 = 2482.
Hence, the product of the given values is 2482.
Question 2.
82 × 22 = _____
82 × 22 = 82 × (20 + 2)
= (82 × ___) + (82 × ____)
= _____ + ____
= _____
Answer: Using the distributive property, the product of 82 x 22 is 238.
The area model is,
Explanation: Given that, the value is 82 x 22.
Now, we will find the value using the distributive property.
So, the given value is distributive as,
82 x 22 = 82 x ( 20 + 2)
= 82 x 20 + 82 x 2
The product of 82 x 20 is,
Next, the product of 82 x 2 is,
The final product is 1640 + 164 = 1804.
Hence, the product of the given values is 1804.
Draw an area model. Then use the Distributive Property to find each product.
Question 3.
18 × 39 = ____
18 × 39 = ____ ×(____ + ____)
= (______ × _____) + (______ × _____)
= ______ × _____
= _______
Answer: Using the distributive property, the product of 18 x 39 is 702.
The area model is,
Explanation: Given that, the value is 18 x 39.
Now, we will find the value using the distributive property.
So, the given value is distributive as,
18 x 39 = 18 x ( 30 + 9)
= 18 x 30 + 18 x 9
The product of 18 x 30 is,
Next, the product of 18 x 9 is,
Add both the products is,
540 + 162 = 702
Hence, the product of the given values is 702.
Problem Solving
Question 4.
There are 48 nails in one box. How many nails are in 17 boxes?
_____ nails.
17 × 48 = ____ × (____ + ____)
= (______ × _____) + (______ × _____)
= ______ × _____
= _______
Answer: 816 mails are there in 17 boxes.
Explanation: Given that,
There are 48 nails in one box.
Now, we will find out how many nails are there in 17 boxes.
So, the given value is distributive as,
17 x 48 = 17 x ( 30 + 18)
= 17 x 30 + 17 x 18
First, multiply 17 x 30 is,
The product of 17 x 30 is 510.
Now, find the product of 17 x 18
The product of 17 x 18 is 306.
Now, add both the products is,
510 + 306 = 816
Hence, the total 816 nails are there in 17 boxes.
Question 5.
Each notebook has 64 pages. How many total pages are there in 33 notebooks?
_____ pages
33 × 64 = ____ × (____ + ____)
= (______ × _____) + (______ × _____)
= ______ × _____
= _______
Answer: The total 2112 pages are there in 33 notebooks.
Explanation: Given that,
Each notebook has 64 pages.
Now, we will find out how many total pages are there in 33 notebooks.
Using the distributive property, we will find the value.
i.e., 33 x 64 = 33 x (60 + 4)
= 33 x 60 + 33 x 4
The product of 33 x 60 is,
Next, the product of 33 x 4 is,
Add the both products i.e., 1980 + 132 = 2112
Hence, the total 2112 pages is there in 33 notebooks.
Question 6.
Each jar contains 55 buttons. There are 16 jars on the shelf. How many buttons are there altogether?
____ buttons
Answer: 880 buttons are there altogether.
Explanation: Given that,
Each jar contains 55 buttons.
There are 16 jars on the shelf.
Now, we will find the altogether buttons using the distributive property.
So, the given value is
55 x 16 = 55 x ( 10 + 6)
= 55 x 10 + 55 x 6
= 550 + 55 x 6
= 550 + 330
= 880
Hence, 880 buttons are there altogether.