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]
