Question

which statement is true? $\frac{2}{3} < \frac{2}{6}$ $\frac{3}{4} < \frac{3}{8}$ $\frac{3}{4} > \frac{3}{6}$ $\frac{1}{8} > \frac{1}{4}$

Explanation:

Step1: Simplify fractions for comparison

For $\frac{2}{6}$, simplify to $\frac{1}{3}$. Compare $\frac{2}{3}$ and $\frac{1}{3}$: $\frac{2}{3} > \frac{1}{3}$, so $\frac{2}{3} < \frac{2}{6}$ is false.

Step2: Compare fractions with same numerator

Compare $\frac{3}{4}$ and $\frac{3}{8}$: smaller denominator means larger value, so $\frac{3}{4} > \frac{3}{8}$, so $\frac{3}{4} < \frac{3}{8}$ is false.

Step3: Simplify and compare fractions

Simplify $\frac{3}{6}$ to $\frac{1}{2} = \frac{2}{4}$. Compare $\frac{3}{4}$ and $\frac{2}{4}$: $\frac{3}{4} > \frac{2}{4}$, so $\frac{3}{4} > \frac{3}{6}$ is true.

Step4: Compare fractions with same numerator

Compare $\frac{1}{8}$ and $\frac{1}{4}$: smaller denominator means larger value, so $\frac{1}{8} < \frac{1}{4}$, so $\frac{1}{8} > \frac{1}{4}$ is false.

Answer:

$\frac{3}{4} > \frac{3}{6}$