There are 8 brooms and 6 mops in a janitor's closet. What is the ratio of the number of mops to the total number of brooms and mops?

A. [tex]\frac{4}{3}[/tex]
B. [tex]\frac{7}{3}[/tex]
C. [tex]\frac{3}{4}[/tex]
D. [tex]\frac{3}{7}[/tex]



Answer :

To solve the problem of finding the ratio of the number of mops to the total number of brooms and mops, we will follow these steps:

1. Identify the numbers of brooms and mops:
- There are 8 brooms.
- There are 6 mops.

2. Calculate the total number of brooms and mops:
- Total items = Number of brooms + Number of mops
- Total items = 8 + 6 = 14

3. Calculate the ratio of the number of mops to the total number of brooms and mops:
- Ratio = Number of mops / Total number of items
- Ratio = 6 / 14

4. Simplify the ratio if possible:
- To simplify, we find the greatest common divisor (GCD) of 6 and 14, which is 2.
- Dividing both numerator and denominator by 2:
[tex]\[ \frac{6}{14} = \frac{6 \div 2}{14 \div 2} = \frac{3}{7} \][/tex]

Therefore, the ratio of the number of mops to the total number of brooms and mops is [tex]\(\frac{3}{7}\)[/tex].

So, the correct answer is:
[tex]\[ \boxed{\text{D } \frac{3}{7}} \][/tex]