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Factoring Word Problems - Page 2

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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