Question

erin finished a race in \\(\frac{1}{6}\\) hour. it took erin more time to finish the race than gianna. this is shown by the number sentence below. \\(\frac{1}{6} > \frac{?}{?}\\) which fraction makes the number sentence true? \\(circ \frac{1}{2}\\) \\(circ \frac{1}{8}\\) \\(circ \frac{1}{3}\\) \\(circ \frac{1}{4}\\)

Explanation:

Step1: Recall fraction comparison rule

For unit fractions (numerator = 1), the larger the denominator, the smaller the fraction. So we compare denominators.

Step2: Analyze each option

• Option $\frac{1}{2}$: Denominator 2 < 6, so $\frac{1}{2} > \frac{1}{6}$ (not valid as we need $\frac{1}{6} > \frac{?}{?}$).
• Option $\frac{1}{8}$: Denominator 8 > 6, so $\frac{1}{8} < \frac{1}{6}$ (check if $\frac{1}{6} > \frac{1}{8}$: yes, since 8 > 6).
• Option $\frac{1}{3}$: Denominator 3 < 6, so $\frac{1}{3} > \frac{1}{6}$ (not valid).
• Option $\frac{1}{4}$: Denominator 4 < 6, so $\frac{1}{4} > \frac{1}{6}$ (not valid). Wait, correction: Wait, the rule is for unit fractions, smaller denominator means larger fraction. Wait, $\frac{1}{n}$: as n increases, fraction decreases. So to have $\frac{1}{6} > \frac{1}{x}$, x must be greater than 6? Wait no, wait $\frac{1}{6} \approx 0.1667$, $\frac{1}{8} = 0.125$, so $\frac{1}{6} > \frac{1}{8}$. $\frac{1}{2}=0.5 > 0.1667$, $\frac{1}{3}\approx0.333 > 0.1667$, $\frac{1}{4}=0.25 > 0.1667$. Wait, only $\frac{1}{8}$ has denominator larger than 6, so $\frac{1}{8}$ is smaller than $\frac{1}{6}$. Wait, but the original problem's options: wait the user's marked option is $\frac{1}{4}$, but that's wrong. Wait, let's recalculate:

Wait, $\frac{1}{6} \approx 0.1667$, $\frac{1}{2}=0.5$ (0.5 > 0.1667: $\frac{1}{2} > \frac{1}{6}$), $\frac{1}{8}=0.125$ (0.125 < 0.1667: $\frac{1}{6} > \frac{1}{8}$), $\frac{1}{3}\approx0.333$ (0.333 > 0.1667: $\frac{1}{3} > \frac{1}{6}$), $\frac{1}{4}=0.25$ (0.25 > 0.1667: $\frac{1}{4} > \frac{1}{6}$). So only $\frac{1}{8}$ satisfies $\frac{1}{6} > \frac{1}{8}$. Wait, the user's marked option was $\frac{1}{4}$, which is incorrect. So the correct answer should be $\frac{1}{8}$.

Answer:

The correct fraction is $\frac{1}{8}$, so the option is: $\boldsymbol{\frac{1}{8}}$ (the option with $\frac{1}{8}$ text, e.g., if options are labeled, say B. $\frac{1}{8}$ then B. $\frac{1}{8}$)