To solve the problem of finding the ratio of the number of mops to the number of brooms in the janitor's closet, let's go through it step-by-step.
1. Identify the numbers of each item:
- Number of brooms: 8
- Number of mops: 6
2. Set up the ratio:
- We are asked to find the ratio of mops to brooms. This ratio is given by [tex]\(\frac{\text{mops}}{\text{brooms}}\)[/tex], which is [tex]\(\frac{6}{8}\)[/tex].
3. Simplify the ratio:
- To simplify [tex]\(\frac{6}{8}\)[/tex], divide both the numerator and the denominator by their greatest common divisor, which is 2.
- [tex]\[
\frac{6 \div 2}{8 \div 2} = \frac{3}{4}
\][/tex]
So, the ratio of the number of mops to the number of brooms is [tex]\(\frac{3}{4}\)[/tex].
4. Compare with the given options:
- A. [tex]\(\frac{3}{7}\)[/tex]
- B. [tex]\(\frac{4}{3}\)[/tex]
- C. [tex]\(\frac{3}{4}\)[/tex]
- D. [tex]\(\frac{7}{3}\)[/tex]
From the options, the correct ratio of [tex]\(\frac{3}{4}\)[/tex] is option C.
Therefore, the answer is:
C. [tex]\(\frac{3}{4}\)[/tex].
