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Factoring Word Problems - Page 3

Factoring Word Problems
  • Page 3
 21.  
Choose all the factors of 6.
a.
3, 2
b.
1, 2, 3, 6
c.
1, 2, 3
d.
6, 12, 18


Solution:

The number 6 is an even number, so it is divisible by 2.

It is also divisible by 3.

So, the factors of 6 are 1, 2, 3, 6.


Correct answer : (2)
 22.  
Which of the given expressions is equivalent to 3 × 6?
a.
3 × 5
b.
7 × 4
c.
9 × 2
d.
3 × 4


Solution:

3 × 6 = (3 × 3) × 2
[6 = 3 × 2.]

= 9 × 2

So, 9 × 2 is the same as 3 × 6.


Correct answer : (3)
 23.  
14 × 7 = 98. Identify the option that would give you the same product.
a.
2 × 6 × 7
b.
2 × 7 × 7
c.
2 × 7 × 9
d.
3 × 4 × 2


Solution:

14 × 7 = 98
[Original expression.]

14 × 7 = 2 × 7 × 7

So, 2 × 7 × 7 gives the same product as 14 × 7.


Correct answer : (2)
 24.  
Identify another way of writing the product 6 × 5.
a.
3 × 3 × 4
b.
2 × 4 × 5
c.
2 × 3 × 5
d.
3 × 3 × 5


Solution:

6 × 5
[Original expression.]

6 × 5 = 2 × 3 × 5

So, 2 × 3 × 5 is another way of writing the product of 6 × 5.


Correct answer : (3)
 25.  
Identify the expression that is equivalent to 3 × 10.
a.
3 × 5
b.
15 × 1
c.
3 × 6
d.
6 × 5


Solution:

10 = 2 × 5

3 × 10 = (3 × 2) × 5

= 6 × 5

So, 6 × 5 is the same as 3 × 10.


Correct answer : (4)
 26.  
2 × 6 = 12. Which of the given expressions has a product equal to 12?
a.
3 × 11
b.
7 × 3
c.
9 × 2
d.
4 × 3


Solution:

12 = 2 × 6
[Original expression.]

2 × 6 = (2 × 2) × 3
[6 = 2 × 3.]

= 4 × 3 = 12

So, 4 × 3 is equal to 12.


Correct answer : (4)
 27.  
The prime factorization of a number is 22 × 32 × 52. Identify the number.
a.
900
b.
800
c.
1,000
d.
700


Solution:

22 × 32 × 52 = 2 × 2 × 3 × 3 × 5 × 5

= 900

22 × 32 × 52 = 900


Correct answer : (1)
 28.  
Choose a rectangle that shows the factors of 21.

a.
Figure 1
b.
Figure 2
c.
Figure 4
d.
Figure 3


Solution:

To list the factors of 21, draw rectangles that have a total of 21 squares.

Figure 1 shows a rectangle with 21 squares.

So, Figure 1 represents the rectangle that shows the factors of 21.


Correct answer : (1)
 29.  
Choose a rectangle that shows the factors of 16.

a.
Figure 3
b.
Figure 2
c.
Figure 4
d.
Figure 1


Solution:

To list the factors of 16, draw rectangles that have a total of 16 squares.

Figure 2 shows a rectangle with 16 squares.

So, Figure 2 represents the rectangle that shows the factors of 16.


Correct answer : (2)
 30.  
Do the numbers 8 and 11 have a factor in common?
a.
Yes
b.
No


Solution:


The rectangle(s) showing the factors of 8 is given as:

Factors of 8: 1, 2, 4, 8
[Since 1 × 8 = 8 and 2 × 4 = 8.]


The rectangles showing the factors of 11 is given as:

Factors of 11: 1, 11
[Since 1 × 11 = 11.]

So, the numbers 8 and 11 do not have a factor in common.


Correct answer : (2)

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