We included **H****MH Into Math Grade 5 Answer Key**** PDF** **Module 1 Lesson 3 Use a Pattern to Multiply by Multiples of 10, 100, and 1,000** to make students experts in learning maths.

## HMH Into Math Grade 5 Module 1 Lesson 3 Answer Key Use a Pattern to Multiply by Multiples of 10, 100, and 1,000

I Can use mental math to find the product of any two numbers that have one nonzero digit and are multiples of 10, 100, or 1,000.

**Step It Out**

1. Sixty students participate in a jump-a-thon, and each student jumps rope 400 times. What is the total number of jumps?

A. What multiplication equation models the total number of jumps?

_____________

B. Complete the multiplication fact.

6 × 4 = ___

C. Use the fact to complete the pattern.

6 × 40 = (6 × 4) × 10^{1} = ___

6 × 400 = (6 × 4) × 10^{2} = ____

60 × 400 = (6 × 10) × (4 × 10^{2})

= (6 × 4) × (10 × 10^{2})

= (6 × 4) × 10^{3}

= ______

D. What is the total number of jumps?

Answer:

Sixty students participate in a jump-a-thon, and each student jumps rope 400 times.

60 × 400

6 × 4 = 24

6 × 40 = (6 × 4) × 10^{1} = 24 × 10 = 240

6 × 400 = (6 × 4) × 10^{2} = 24 × 100 = 2400

60 × 400 = (6 × 10) × (4 × 10^{2}) = 60 × 400 = 24000

= (6 × 4) × (10 × 10^{2})

= (6 × 4) × 10^{3}

= 24 × 1000

= 24,000

Thus the total number of jumps were 24,000

**Turn and Talk** What is the relationship between the number of zeros in the two factors and the number of zeros in the product?

**Step It Out**

2. Fifty students each jump rope 2000 times during the jump-a-thon.

A. What multiplication equation models the number of jumps completed by the 50 students?

B. Complete the multiplication fact and the pattern.

5 × 2 = ____

5 × 20 = (5 × 2) × 10^{1} = ____

5 × 200 = (5 × 2) × 10^{2} = ___

5 × 2,000 = (5 × 2) × 10^{3} = ___

50 × 2,000 = (5 × 10) × (2 × 10^{3})

= (5 × 2) × (10 × 10^{3})

= (5 × 2) × 10^{4}

= _________

C. How many jumps were completed by these students? _______

Answer:

5 × 2 = 10

5 × 20 = (5 × 2) × 10^{1} = 10 × 10 = 100

5 × 200 = (5 × 2) × 10^{2} = 10 × 100 = 1000

5 × 2,000 = (5 × 2) × 10^{3} = 10 × 1000 = 10,000

50 × 2,000 = (5 × 10) × (2 × 10^{3})

= (5 × 2) × (10 × 10^{3})

= (5 × 2) × 10^{4}

= 10 × 10000

= 100,000

So, 100,000 jumps were completed by these students.

**Turn and Talk** Why is the total number of zeros in the product not always the same as the total number of zeros in the two factors?

**Check Understanding Math Board**

Question 1.

The 40 students in Leona’s grade each did 3,000 jumping jacks. How many jumping jacks is this? __________

Answer:

Given,

The 40 students in Leona’s grade each did 3,000 jumping jacks

3000

× 40

120000

**Multiply.**

Question 2.

70 × 600 = ____

Answer:

600

× 70

42000

70 × 600 = 42 × 10^{3}

Question 3.

30 × 8,000 = _______

Answer:

8000

× 30

240000

30 × 8,000 = 24 × 10^{4}

Question 4.

____ = 80 × 5,000

Answer:

5000

×80

400000

80 × 5,000 = 4 × 10^{5}

Question 5.

50 × 600 = ____

Answer:

600

×50

30000

50 × 600 = 3 × 10^{4}

**On Your Own**

**Complete the multiplication fact and pattern.**

Question 6.

6 × 9 = ___

(6 × 9) × 10^{1} = ____

(6 × 9) × 10^{2} = ____

(6 × 9) × 10^{3} = ___

Answer:

A multiplication fact is the product of two specific numbers.

6 × 9 = 54

(6 × 9) × 10^{1} = 54 × 10 = 540

(6 × 9) × 10^{2} = 54 × 100 = 5400

(6 × 9) × 10^{3} = 54 × 1000 = 54000

Question 7.

3 × 8 = ___

(3 × 8) × 10^{1} = ____

(3 × 8) × 10^{2} = ____

(3 × 8) × 10^{3} = ___

Answer:

A multiplication fact is the product of two specific numbers.

3 × 8 = 24

(3 × 8) × 10^{1} = 24 × 10 = 240

(3 × 8) × 10^{2} = 24 × 100 = 2400

(3 × 8) × 10^{3} = 24 × 1000 = 24000

Question 8.

5 × 4 = ___

(5 × 4) × 10^{1} = ____

(5 × 4) × 10^{2} = ____

(5 × 4) × 10^{3} = ___

(5 × 4) × 10^{4} = ___

Answer:

A multiplication fact is the product of two specific numbers.

5 × 4 = 20

(5 × 4) × 10^{1} = 20 × 10 = 200

(5 × 4) × 10^{2} = 20 × 100 = 2000

(5 × 4) × 10^{3} = 20 × 1000 = 20000

(5 × 4) × 10^{4} = 20 × 10000 = 200000

Question 9.

12 × 8 = ___

(12 × 8) × 10^{1} = ____

(12 × 8) × 10^{2} = ____

(12 × 8) × 10^{3} = ___

(12 × 8) × 10^{4} = ___

Answer:

A multiplication fact is the product of two specific numbers.

12 × 8 = 96

(12 × 8) × 10^{1} = 96 × 10 = 960

(12 × 8) × 10^{2} = 96 × 100 = 9600

(12 × 8) × 10^{3} = 96 × 1000 = 96000

(12 × 8) × 10^{4} = 96 × 10000 = 960000

**Find the unknown number.**

Question 10.

Answer:

Given,

40 × 70,000 = 28 × 10^{x}

2800000 =

28 × 10^{5} = 28 × 10^{x}

10^{5} = 10^{x}

x = 5

So, the unknown number is 5.

Question 11.

Answer:

Given,

60 × 500 = 3 × 10^{x}

30000 = 3× 10^{x}

3 ×10^{4} = 3× 10^{x}

10^{x} = 10^{4}

x = 4

So, the unknown number is 4.

Question 12.

Answer:

Given,

30 × x = 21 × 10^{6}

x = 21 × 10^{6} /30

x = 700,000

So, the unknown number is 700,000.

Question 13.

Answer:

Given,

50 × x = 2 × 10^{4}

50x = 20000

x = 20000/50

x = 400

So, the unknown number is 400.

**Multiply.**

Question 14.

80 × 400 = ___

Answer:

400

× 80

32000

80 × 400 = 32 × 10^{3}

Question 15.

50 × 200 = ___

Answer:

200

×50

10000

50 × 200 = 1 × 10^{4}

Question 16.

30 × 7,000 = ____

Answer:

7000

× 30

210,000

30 × 7,000 = 21 × 10^{4}

Question 17.

40 × 5,000 = ____

Answer:

5000

× 40

200,000

20000 can be written as 2 × 10^{5}

Question 18.

A shipping company buys 60 trucks for $30,000 each. What is the total cost? ____

Answer:

Given,

A shipping company buys 60 trucks for $30,000 each.

60 × 30,000 = $1,800,000

So, the total cost is $1,800,000

Question 19.

What is the total weight of 20 similar semi-truck cabs and trailers? ______

Answer:

The weight of semi truck can is 30,000 lb

The weight of 20 similar semi-truck cabs and trailers is 20 × 30,000 = 600,000 lbs

Question 20.

Thirty other students participate in the jump-a-thon, and they each jump rope 600 times. What is the total number of jumps?

Answer:

Given,

Thirty other students participate in the jump-a-thon, and they each jumped rope 600 times.

30 × 600 = 18000

The total number of jumps students made is 18,000.

Question 21.

Four hundred students each jump rope 70 times. What is the total number of jumps for this group of students?

Answer:

Given,

Four hundred students each jump rope 70 times.

400 × 70 = 28000

Thus the group of students jumps 28000 times.

Question 22.

**Use Repeated Reasoning** A store sells 50 basketball backboards and stands for $700 each. How much does the store earn from these sales? Use a multiplication fact and a pattern.

How much does the store earn? ____

Answer:

Given,

A store sells 50 basketball backboards and stands for $700 each.

50 × $700 = $35,000

Thus the store earns $35,000 for 50 basketball backboards.

Question 23.

**Use Structure** How many zeros are in the product of any nonzero whole number and 1,000? Explain your answer.

Answer:

It depends on the whole number.

Let us take 43 as the whole number.

43 × 1000 = 43000 (3 zeros)

50 × 1000 = 50000 (4 zeros)

Question 24.

**Use Repeated Reasoning** What is (3 × 10^{2}) × (9 × 10^{3})? Use a multiplication fact and a pattern.

What is the product? _______

Answer:

(3 × 10^{2}) × (9 × 10^{3})

(3 × 100) × (9 × 1000)

300 × 9000 = 2700000

So, the product of (3 × 10^{2}) × (9 × 10^{3}) is 2700000