Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. which of the following is a true statement? $\frac{11}{15} < \frac{4}{5}$ $\frac{5}{6} > \frac{10}{12}$ $\frac{3}{4} < \frac{4}{6}$ $\frac{8}{16} = \frac{1}{4}$

Explanation:

Step1: Analyze $\frac{11}{15} < \frac{4}{5}$

Convert $\frac{4}{5}$ to fifteenths: $\frac{4}{5}=\frac{4\times3}{5\times3}=\frac{12}{15}$. Now compare $\frac{11}{15}$ and $\frac{12}{15}$. Since $11 < 12$, $\frac{11}{15}<\frac{12}{15}$, so $\frac{11}{15} < \frac{4}{5}$ is true? Wait, let's check other options too.

Step2: Analyze $\frac{5}{6} > \frac{10}{12}$

Simplify $\frac{10}{12}$: $\frac{10\div2}{12\div2}=\frac{5}{6}$. So $\frac{5}{6}=\frac{10}{12}$, so this statement is false.

Step3: Analyze $\frac{3}{4} < \frac{4}{6}$

Simplify $\frac{4}{6}=\frac{2}{3}$. Find a common denominator for $\frac{3}{4}$ and $\frac{2}{3}$, which is 12. $\frac{3}{4}=\frac{9}{12}$, $\frac{2}{3}=\frac{8}{12}$. Since $9 > 8$, $\frac{3}{4}>\frac{2}{3}$, so this statement is false.

Step4: Analyze $\frac{8}{16} = \frac{1}{4}$

Simplify $\frac{8}{16}=\frac{1}{2}$. $\frac{1}{2}
eq\frac{1}{4}$, so this statement is false.

Wait, but in Step1, $\frac{4}{5}=\frac{12}{15}$, and $\frac{11}{15}<\frac{12}{15}$, so $\frac{11}{15} < \frac{4}{5}$ is true. Wait, but let's re - check. Wait, the first option: $\frac{11}{15}$ and $\frac{4}{5}=\frac{12}{15}$. So 11/15 is less than 12/15, so 11/15 < 4/5 is true. But wait, when I checked the second option, 5/6 and 10/12: 10/12 simplifies to 5/6, so they are equal. Third option: 3/4 is 0.75, 4/6 is approximately 0.666, so 3/4 is greater than 4/6, so that's false. Fourth option: 8/16 is 0.5, 1/4 is 0.25, so false. So the true statement is $\frac{11}{15} < \frac{4}{5}$.

Answer:

$\boldsymbol{\frac{11}{15} < \frac{4}{5}}$ (the option with $\frac{11}{15} < \frac{4}{5}$)