Question

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what is the value of m in this proportion?
\\(\frac{\frac{1}{5}}{\frac{2}{3}} = \frac{\frac{1}{4}}{m}\\)
enter your answer as a fraction in simplest form in the box.
\\(m = \square\\)

Explanation:

Step1: Simplify left-hand fraction

$\frac{\frac{1}{5}}{\frac{2}{3}} = \frac{1}{5} \times \frac{3}{2} = \frac{3}{10}$

Step2: Set up cross-multiplication

$\frac{3}{10} = \frac{1}{4m}$
$3 \times 4m = 10 \times 1$

Step3: Solve for m

$12m = 10$
$m = \frac{10}{12} = \frac{5}{6}$

Answer:

$\frac{5}{6}$