To determine the ratio of the number of mops to the total number of brooms and mops, let's break down the problem step-by-step.
1. Identify the quantities given:
- Number of brooms: [tex]\(8\)[/tex]
- Number of mops: [tex]\(6\)[/tex]
2. Calculate the total number of brooms and mops:
[tex]\[
\text{Total number of brooms and mops} = 8 + 6 = 14
\][/tex]
3. Determine the ratio of the number of mops to the total number of brooms and mops:
[tex]\[
\text{Ratio} = \frac{\text{Number of mops}}{\text{Total number of brooms and mops}} = \frac{6}{14}
\][/tex]
4. Simplify the ratio:
- To simplify [tex]\(\frac{6}{14}\)[/tex], find the greatest common divisor (GCD) of 6 and 14.
- The GCD of 6 and 14 is 2, so we divide both the numerator and the denominator by 2.
[tex]\[
\frac{6}{14} = \frac{6 \div 2}{14 \div 2} = \frac{3}{7}
\][/tex]
5. Identify the correct answer from the given options:
The simplified ratio [tex]\(\frac{3}{7}\)[/tex] matches option D.
Therefore, the ratio of the number of mops to the total number of brooms and mops is [tex]\(\frac{3}{7}\)[/tex].
So, the answer is [tex]\( \boxed{D} \)[/tex].
