We included HMH Into Math Grade 4 Answer Key PDF Module 8 Lesson 4 Multiply Using Partial Products to make students experts in learning maths.
HMH Into Math Grade 4 Module 8 Lesson 4 Answer Key Multiply Using Partial Products
I Can multiply two 2-digit numbers using different methods.
Step It Out
1. Oranges grow on trees in a group, with very little undergrowth, called a grove.
A section of an orange grove has 32 rows with 24 trees in a row. How many orange trees are in the section?
Multiply. 32 × 24
A. Find and record the partial products. Line up the partial products by place value.
Answer:
From the figure, product can be found by using partial products.
32 x 24 = ( 20 x 30 ) + ( 20 x 2 ) + ( 4 x 30 ) + ( 4 x 2 )
= ( 600 ) + ( 40 ) + ( 120 ) + ( 8 )
= 768
Therefore, there are 768 orange trees are in the section.
Turn and Talk Why is it important to align the partial products by place value?
Answer:
It is important to align the partial products by place value because it provides the foundation for regrouping and multiple digit multiplications as well as the starting point for the understanding of other base systems.
Step It Out
2. Oranges are often packaged in crates so that they can be shipped to different places. How many oranges are packed in 62 crates to be shipped?
Answer:
Given,
Oranges are often packaged in crates so that they can be shipped to different places.
There are a total of 62 crates.
Each crate contains 48 oranges.
Total number of oranges = Number of crates x number of oranges
So, 48 x 62 =
48 x 62 = ( 60 x 40 ) + ( 60 x 8 ) + ( 2 x 40 ) + ( 2 x 8 )
= ( 2400 ) + ( 480 ) + ( 80 ) + ( 16 ) = 2,976
Therefore, total number of oranges are 2,976.
Turn and Talk How does the product compare with your estimate? How does the comparison help you to determine if your answer is reasonable?
Answer:
The estimated product may be greater than or less than the actual product. But, the estimated product is approximate to the actual product.
Check Understanding Math Board
Estimate. Then use partial products to find the product.
Question 1.
Estimate: _______
Answer:
35 is near to 30
47 is near to 50
So, 30 x 50 = 1500
Therefore, 35 x 47 approximately equals 1500.
product of 35 x 47 = 1645.
Question 2.
Estimate: _______
Answer:
89 is near to 90
67 is near to 70
so, 90 x 70 = 6300
Therefore, 89 x 67 approximately equals 6300.
product of 89 x 67 is 5963.
On Your Own
Question 3.
There are 87 seats available for a concert. Each ticket costs the same amount. How much would all of the tickets cost for the available seats? _______
Answer:
Given,
There are 87 seats available for a concert. Each ticket costs the same amount.
Cost of each ticket = $55
Cost of all tickets = 87 x $55 =
87 x $55 = ( 50 x 80 ) + ( 50 x 7 ) + ( 5 x 80 ) + ( 5 x 7 )
= 4000 + 350 + 400 + 35 = 4,785
Therefore, cost of all tickets = $4,785.
Question 4.
Mr. Edgar works 38 hours each week for 49 weeks every year. How many hours does he work in a year? ____
Answer:
Given,
Mr. Edgar works 38 hours each week for 49 weeks every year.
Total hours = number of hours in each week x number of weeks
= 38 x 49
= 
= ( 40 x 30 ) + ( 40 x 8 ) + ( 9 x 30 ) + ( 9 x 8 )
= 1200 + 320 + 270 + 72 = 1,862
Therefore, the Total number of hours he works in a year is 1,862.
Use Structure Estimate. Then use partial products to find the product.
Question 5.
Estimate: ________
Answer:
29 is near to 30
53 is near to 50
So, 29 x 53 = 30 x 50 = 1500
Therefore, 29 x 53 approximately equals 1500.
29 x 53 = ( 50 x 20 ) + ( 50 x 9 ) + ( 3 x 20 ) + ( 3 x 9 )
= 1000 + 450 + 60 + 27 = 1537
Therefore, value of 29 x 53 is 1,537.
Question 6.
Estimate: ________
Answer:
61 is near to 60
19 is near to 20
So, 61 x 19 = 60 x 20 = 1200
Therefore, 61 x 19 approximately equals 1200.
61 x 19 = ( 10 x 60 ) + ( 10 x 1 ) + ( 9 x 60 ) + ( 9 x 1)
= 600 + 10 + 540 + 9 = 1,159
Therefore, value of 61 x 19 is 1,159.
Question 7.
Estimate: ________
Answer:
14 is near to 10
79 is near to 80
So, 14 x 79 = 10 x 80 = 800
Therefore, 14 x 79 approximately equals 800.
14 x 79 = ( 70 x 10 ) + ( 70 x 4 ) + ( 9 x 10 ) + ( 9 x 4)
= 700 + 280 + 90 + 36= 1,106
Therefore, value of 14 x 79 is 1,106.
Question 8.
Estimate: ________
Answer:
92 is near to 90
38 is near to 40
so, 92 x 38 = 90 x 40 = 3600
Therefore, 92 x 38 approximately equlas 3600.
92 x 38 = ( 30 x 90 ) + ( 30 x 2 ) + ( 8 x 90 ) + ( 8 x 2)
= 2700 + 60 + 720 + 16 = 3496
Therefore, value of 92 x 38 is 3496.
Question 9.
Estimate: ________
Answer:
46 is near to 50
58 is near to 60
So, 46 x 58 = 50 x 60 = 3000
Therefore, 46 x 58 approximately equals 3000
46 x 58 = ( 50 x 40 ) + ( 50 x 6 ) + ( 8 x 40 ) + ( 8 x 6 )
= 2000 + 300 + 320 + 48 = 2,668
Therefore, value of 46 x 58 is 2,668.
Question 10.
Estimate: ________
Answer:
85 is near to 80
76 is near to 80
So, 85 x 76 = 80 x 80 = 6,400
Therefore, 85 x 76 approximately equals 6,400
85 x 76 = ( 70 x 80 ) + ( 70 x 5 ) + ( 6 x 80 ) + ( 6 x 5 )
= 5600 + 350 + 480 + 30 = 6,460
Therefore, value of 85 x 76 is 6,460.
Question 11.
Use Repeated Reasoning How can you use the product 2 × 54 to find the product 22 × 54?
Answer:
Question 12.
Model with Mathematics There are 52 cards in a deck of fact cards. How many cards are in 36 decks? Write an equation and solve.
Answer:
Given,
There are 52 cards in a deck of fact cards.
How many cards are in 36 decks
Total cards = number of cards x number of decks
= 36 x 52
36 x 52 = ( 50 x 30 ) + ( 50 x 6 ) + ( 2 x 30 ) + ( 2 x 6 )
= 1500 + 300 + 60 + 12 = 1,872
Therefore, value of 36 x 52 is 1,872.
Rewrite the problem. Then use partial products to find the product.
Question 13.
65 × 33 = ___
Answer:
65 x 33 = ( 30 x 60 ) + ( 30 x 5 ) + ( 3 x 60 ) + ( 3 x 5 )
= 1800 + 150 + 180 + 15 = 2,145
Therefore, value of 65 x 33 is 2,145.
Question 14.
21 × 42 = ___
Answer:
21 x 42 = ( 40 x 20 ) + ( 40 x 1 ) + ( 2 x 20 ) + ( 2 x 1 )
= 800 + 40 + 40 + 2 = 882
Therefore, value of 21 x 42 is 882.
Question 15.
24 × 84 = __
Answer:
24 x 84 = ( 80 x 20 ) + ( 80 x 4 ) + ( 4 x 20 ) + ( 4 x 4 )
= 1600 + 320 + 80 + 16 =2016
Thereofe, value of 24 x 84 is 2016.
Question 16.
97 × 56 = ___
Answer:
97 x 56 = ( 50 x 90 ) + ( 50 x 7 ) + ( 6 x 90 ) + ( 6 x 7 )
= 4500 + 350 + 540 + 42 = 5,432
Therefore, value of 97 x 56 is 5,432