To determine the ratio of the number of mops to the total number of brooms and mops, we'll go through the problem step-by-step:
1. Identify the given quantities:
- Number of brooms (B) = 8
- Number of mops (M) = 6
2. Calculate the total number of brooms and mops:
[tex]\[
\text{Total} = B + M = 8 + 6 = 14
\][/tex]
3. Determine the ratio of mops to the total number of brooms and mops:
[tex]\[
\text{Ratio} = \frac{M}{\text{Total}} = \frac{6}{14}
\][/tex]
4. Simplify the fraction:
To simplify [tex]\(\frac{6}{14}\)[/tex], find the greatest common divisor (GCD) of 6 and 14, which is 2. Then divide both the numerator and the 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]\[
\boxed{\frac{3}{7}}
\][/tex]
So the answer is:
[tex]\[
\boxed{D}
\][/tex]
