Question

what numerator makes the statement true? enter the correct answer in the box. show hints \\(\frac{1}{4} < \frac{5}{12} < \frac{\square}{6}\\)

Explanation:

Step1: Convert to common denominator

Convert all fractions to denominator 12:
$\frac{2}{4} = \frac{6}{12}$, $\frac{\square}{6} = \frac{2\square}{12}$

Step2: Simplify the inequality

Substitute into the inequality:
$\frac{6}{12} < \frac{8}{12} < \frac{2\square}{12}$
Ignore the common denominator:
$8 < 2\square$

Step3: Solve for the numerator

Isolate $\square$:
$\square > \frac{8}{2} = 4$
From the options, the smallest integer greater than 4 is 5, and $\frac{5}{6}=\frac{10}{12}$ which satisfies $\frac{8}{12}<\frac{10}{12}$.

Answer:

5