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