Question 9 of 25

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

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



Answer :

To find the ratio of the number of mops to the number of brooms, follow these steps:

1. Identify the quantities:
- Number of mops: 6
- Number of brooms: 8

2. Set up the ratio:
The ratio of mops to brooms is obtained by dividing the number of mops by the number of brooms.
[tex]\[ \text{Ratio of mops to brooms} = \frac{\text{Number of mops}}{\text{Number of brooms}} = \frac{6}{8} \][/tex]

3. Simplify the fraction:
To simplify the fraction \(\frac{6}{8}\), find the greatest common divisor (GCD) of 6 and 8, which is 2. Then divide both the numerator and the denominator by their GCD.
[tex]\[ \frac{6 \div 2}{8 \div 2} = \frac{3}{4} \][/tex]

4. Verify your simplified ratio:
The simplified ratio of the number of mops to the number of brooms is \(\frac{3}{4}\), which simplifies to 0.75 when converted to a decimal.

Thus, the correct answer is:
[tex]\[ \boxed{\frac{3}{4}} \][/tex]

So, the ratio of the number of mops to the number of brooms is [tex]\(\frac{3}{4}\)[/tex], which corresponds to option A.