All the solutions provided in McGraw Hill Math Grade 4 Answer Key PDF Chapter 4 Lesson 7 The Distributive Property will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 4 Answer Key Chapter 4 Lesson 7 The Distributive Property
Math in My World
Example 1
Chef Cora hard-boils six dozen eggs each day to make egg salad for sandwiches at the food court. How many eggs does she hard-boil each day?
There are 12 eggs in one dozen.
Find 6 × 12.
Decompose 12 into 10 + 2.
Think of 6 × 12 as (6 × 10) + (6 × 2).
So, Chef Cora hard-boils ___ eggs each day.
Answer:
Given that,
Chef Cora hard-boils six dozen eggs each day.
The number of eggs for each day is
1 dozen = 12 eggs.
So, 6 x 12
Decompose 12 into 10 + 2.
We can write 6 × 12 as (6 × 10) + (6 × 2).
So, Chef Cora hard-boils 72 eggs each day.
Example 2
Twenty-seven students are attending a performance at a children’s theater. Each admission ticket is $5. What is the total cost for the 27 students?
Let c represent the total. Write an equation.
c = ___ × 5
Find 27 × 5.
Since 27 × 5 = ____, c = ____
So, the total cost for 27 students is _____
Answer:
Given that,
Twenty-seven students are attending a performance at a children’s theater.
Each admission ticket is $5.
So, 25 x $5.
Since 27 × 5 = 135 where c = 135.
So, the total cost for 27 students is $135.
Talk Math
How can you use the Distributive Property or an area model to find 3 × 24?
Answer:
The distributive property of 3 × 24 is
3 × 24 = (3 x 20) + (3 x 4)
3 x 24 = 60 + 12.
3x 24 = 72.
The area model of 3 x 24 is
Guided Practice
Use the Distributive Property to multiply. Draw an area model.
Question 1.
12 × 9 = ____
Answer:
Distributive property of 12 x 9 is
12 x 9 = (10 x 9) + (2 x 9)
12 x 9 = 90 + 19.
12 x 9 = 108.
The area model of 12 x 9 is
Question 2.
22 × 6 = ____
Answer:
The distributive property of 22x 6 is
22 x 6 = (20 x 6) + (2 x 6)
22 x 6 = 120 + 12.
22 x 6 = 132.
The area model of 22 x 6 is
Independent Practice :
Use the Distributive Property to multiply. Draw an area model.
Question 3.
Answer:
The distributive property of 32 x 7 is
32 x 7 = (30 x 7) + (2 x 7)
32 x 7 = 210 + 14.
32 x 7 = 224.
The area model of 32 x 7 is
Question 4.
Answer:
The distributive property of 15 x 8 is
15 x 8 = (10 x 8) + (5 x 8)
15 x 8 = 80 + 40.
15 x 8 = 120.
The area model of 15 x 8 is
Question 5.
Answer:
The distributive property of 11 x 8 is
11 x 8 = (10 x 8) + (1 x 8)
11 x 8 = 80 + 8
11 x 8 = 88.
The area model of 11 x 8 is
Question 6.
Answer:
The distributive property of 63 x 4 is
63 x 4 = (60 x 4) + (3 x 4)
63 x 4 = 240 + 12.
63 x 4 = 252.
The area model of 63 x 4 is
Question 7.
Answer:
The distributive property of 55 x 6 is
55 x 6 = (50 x 6) + (5 x 6)
55 x 6 = 300 + 30.
55 x 6 = 330.
The area of 55 x 6 is.
Question 8.
Answer:
The distributive property of 49 x 9 is
49 x 9 is
49 x 9 = (40 x 9) + (9 x 9)
49 x 9 = 360 + 81.
49 x 9 = 441.
The area model of 49 x 9 is
Algebra Find each unknown number.
Question 9.
37 × 5 = s
s = ____
Answer:
Multiplication of 37 with 5 then you get 185.
37 x 5 = 185.
s = 185.
Therefore the unknown is 185.
Question 10.
99 × 9 = t
t = ____
Answer:
Multiplication of 99 with 9 then you get 891.
99 x 9 = 891.
t = 891.
Therefore the unknown is 891.
Question 11.
85 × 5 = v
v = ____
Answer:
Multiplication of 85 with 5 then you get 425.
85 x 5 = 425.
v = 425.
Therefore the unknown is 425.
Question 12.
Write an equation that represents the area model below.
_____ × ____ = _______
Answer:
In the model the number of rows are 6.
The number of columns are 17.
The equation that represents the area model is 17 x 6 = 102.
Problem Solving
Question 13.
Mr. Kline bought 4 sheets of postage stamps. Each sheet had 16 stamps. What is the total number of postage stamps Mr. Kline bought? Write an equation to solve.
s = ___ × ____
s = _____
Mr. Kline bought ____ stamps.
Answer:
Given that,
Mr. Kline bought 4 sheets of postage stamps.
Each sheet had 16 stamps.
s = 4 x 16
s = 64.
Mr. Kline bought 64 stamps.
Question 14.
The World of Maps store displays its maps on 3 shelves. There are 26 world maps on each shelf. How many world maps does the store have to sell? Write an equation to solve.
m = ___ × ____
m = ____
The store has ____ world maps.
Answer:
Given that,
The World of Maps store displays its maps on 3 shelves.
There are 26 world maps on each shelf.
m = 3 x 26
m = 78.
The store has 78 world maps.
HOT Problems
Question 15.
Mathematical PRACTICE 3 Find the Error Candace is finding 67 × 2. She thinks the product is 124. Find and correct her mistake.
Answer:
Multiplication of 67 with 2 then you get 134.
67 x 2 = 134.
She thinks the product is 124 is her mistake.
The correct product is 134.
Question 16.
? Building on the Essential Question How can the Distributive Property help when you are multiplying by a two-digit number?
Answer:
Distributive property of multiplication says that when the number is multiplied by the two digits number the first number can be distributed to the both of two numbers and multiplied by each separately. Then add the both products to get the real product.
McGraw Hill My Math Grade 4 Chapter 4 Lesson 7 My Homework Answer Key
Practice
Use the Distributive Property to multiply. Draw an area model.
Question 1.
Answer:
The distributive property of 28 x 4 is (20 x 4) + (8 x 4)
= 80 + 32
= 112.
The area model of 28 x 4 is
Question 2.
Answer:
The distributive property of 19 x 5 is
19 x 5 = (10 x 5) + (9 x 5)
19 x 5 = 50 +45.
19 x 5 = 95.
The area model of 19 x 5 is
Question 3.
Answer:
The distributive property of 41 x 6 is
41 x 6 = (40 x 6) + (1 x 6)
41 x 6 = 240 + 6.
41 x 6 = 246.
The area model of 41 x 6 is
Multiply. Use the Distributive Property.
Question 4.
75 × 6 = ___
Answer:
Distributive property of 75 x 6 is
75 x 6 = (70 x 6) + (5 x 6)
75 x 6 = 420 + 30.
75 x 6 = 450.
Question 5.
4 × 52 = ___
Answer:
Distributive property of 4 x 52 is
4 x 52 = (4 x 50) x (4 x 2)
4 x 52 = 200 + 8.
4 x 52 = 208.
Question 6.
8 × 38 = ____
Answer:
Distributive property of 8 x 32 is
8 x 32 = (8 x 30) + (8 x 2)
8 x 32 = 240 + 16.
8 x 32 = 256.
Question 7.
97 × 2 = ___
Answer:
Distributive property of 97 x 2 is
97 x 2 = (90 x 2) + (7 x 2)
97 x 2 = 180 + 14.
97 x 2 = 194.
Question 8.
7 × 63 = ____
Answer:
Distributive property of 7 x 63 is
7 x 63 = (7 x 60) + (7 x 3)
7 x 63 = 420 + 21.
7 x 63 = 441.
Question 9.
6 × 33 = ____
Answer:
Distributive property of 6 x 33 is
6 x 33 = (6 x 30) + (6 x 3)
6 x 33 = 180 + 18.
6 x 33 = 198.
Problem Solving
Question 10.
Mathematical PRACTICE 3 Justify Conclusions Paula can make 14 beaded bracelets in an hour. Tina can make 13 bracelets in an hour. In one week, Paula made bracelets for 6 hours, and Tina made bracelets for 8 hours. Who made more bracelets that week? Explain.
Answer:
Given that,
Paula can make 14 beaded bracelets in an hour.
Tina can make 13 bracelets in an hour.
In one week, Paula made bracelets for 6 hours
In one week, Tina made bracelets for 8 hours.
Paula made bracelets in all is 14 x 6 = 84.
Tina made bracelets in all is 13 x 8 = 104.
Therefore Tina made more bracelets than Paula.
Question 11.
Alejandro owns 3 sets of trains. Each set has 18 cars. How many train cars does Alejandro have altogether?
Answer:
Given that,
Alejandro owns 3 sets of trains.
Each set has 18 cars.
So, 3 x 18 = 54.
Therefore there are 54 train cars does Alejandro have altogether.
Vocabulary Check
Write Distributive Property or decompose on each line.
Question 12.
To ____ a number means to break it into parts.
Answer:
To decompose a number means to break it into parts.
Question 13.
The ____ states that you can multiply addends of a number, then add the products.
Answer:
The distributive property states that you can multiply addends of a number, then add the products.
Test Practice
Question 14.
Which expression represents the model?
A. (5 × 10) × (5 × 3)
B. 5 × 5 × 5 × 3
C. (5 × 10) + 3
D. (5 × 10) + (5 × 3)
Answer:
The number of rows are 5.
The number of columns are 13.
The area model is 5 x 13.
The distributive property of 5 x 13 is
(5 x 10) + (5 x 3).
Option D is the correct answer.