Question

what is the value of m in this proportion?
\\(\frac{\frac{1}{7}}{\frac{3}{4}} = \frac{\frac{1}{8}}{m}\\)
enter your answer as a fraction in simplest form in the box
\\(m = square\\)
\\(\circ\\) 8/9
\\(\circ\\) 7/8
\\(\circ\\) 1/56
\\(\circ\\) 5/17

Explanation:

Step1: Simplify left-hand side

$\frac{\frac{1}{7}}{\frac{3}{4}} = \frac{1}{7} \times \frac{4}{3} = \frac{4}{21}$

Step2: Set up cross-multiplication

$\frac{4}{21} = \frac{\frac{1}{6}}{m} \implies 4m = 21 \times \frac{1}{6}$

Step3: Solve for m

$4m = \frac{21}{6} = \frac{7}{2} \implies m = \frac{7}{2} \times \frac{1}{4} = \frac{7}{8}$

Answer:

$\frac{7}{8}$ (Option B: 7/8)