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Factoring Word Problems
• Page 2
11.
5 × 8 = 40. Which of the given expressions has a product equal to 40? a. 10 × 2 b. 6 × 7 c. 10 × 4 d. 4 × 9

#### Solution:

5 × 8 = 40
[Original expression.]

5 × 8 = (5 × 2) × 4
[8 = 2 × 4.]

= 10 × 4 = 40

So, 10 × 4 is equal to 40.

Correct answer : (3)
12.
Which of the expressions is equal to 70? a. 2 × 7 × 5 b. 7 × 4 × 5 c. 3 × 2 × 5 d. 3 × 3 × 7

#### Solution:

2 × 35 = 70

2 × 35 = 2 × 7 × 5
[35 = 7 × 5.]

So, 2 × 7 × 5 is equal to 2 × 35.

Correct answer : (1)
13.
Identify the expression that would equal to 30. a. 5 × 3 × 2 b. 5 × 2 × 2 c. 5 × 3 d. 5 × 3 × 4

#### Solution:

5 × 6 = 30

5 × 6 = 5 × 3 × 2
[6 = 3 × 2.]

So, 5 × 3 × 2 is equal to 5 × 6.

Correct answer : (1)
14.
Which of the given expressions would have the product as 63? a. 7 × 3 b. 3 × 3 × 3 × 3 c. 7 × 3 × 3 d. 7 × 3 × 3 × 3

#### Solution:

7 × 9 = 63

7 × 9 = 7 × 3 × 3
[9 = 3 × 3.]

So, 7 × 3 × 3 is equal to 7 × 9.

Correct answer : (3)
15.
Which number is a multiple of 7? a. 49 b. 36 c. 55 d. 41

#### Solution:

The numbers 36, 41, and 55 are not divisible by 7, so, they are not multiples of 7.
[Use multiplication and division facts for 7.]

The number 49 is divisible by 7.

So, 49 is a multiple of 7.

Correct answer : (1)
16.
Which number is not a multiple of 6? a. 36 b. 18 c. 26 d. 42

#### Solution:

The numbers 18, 36, and 42 are divisible by 6, so, they are multiples of 6.
[Use multiplication and division facts for 6.]

The number 26 is not divisible by 6.

So, 26 is not a multiple of 6.

Correct answer : (3)
17.
Which of the expressions is the same as 2 × 9? a. 6 × 2 b. 6 × 3 c. 6 × 6 d. 3 × 4

#### Solution:

2 × 9 = (2 × 3) × 3
[9 = 3 × 3.]

= 6 × 3

So, 2 × 9 is the same as 6 × 3.

Correct answer : (2)
18.
Choose the prime factorization of 45. a. 5 × 3 × 3 b. 5 × 4 × 3 c. 5 × 4 × 2 d. 5 × 3 × 2

#### Solution: A factor tree written for 45 as the product of prime factors is:

So, the prime factorization of 45 is 5 × 3 × 3.

Correct answer : (1)
19.
Find the prime factorization of 20. a. 5 × 3 × 2 b. 7 × 2 × 2 c. 5 × 4 d. 5 × 2 × 2

#### Solution: A factor tree written for 20 as the product of prime factors is:

So, the prime factorization of 20 is 5 × 2 × 2.

Correct answer : (4)
20.
Find the prime factors of 78. a. 2, 3, and 13 b. 2 c. 2 and 3 d. 2, 4, and 13

#### Solution: A factor tree written for 78 as the product of prime factors is:

So, the prime factors of 78 are 2, 3, and 13.

Correct answer : (1)

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