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 |

[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 |

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 |

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 |

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 |

[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 |

[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 |

[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 |

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 |

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 |

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)