Question

Which fraction makes the statement TRUE?

2/10 < ___ < 7/11

1/10

9/9

6/13

12/13

Answer 1

To determine which fraction makes the statement \( \frac{2}{10} < \text{___} < \frac{7}{11} \) true, we can evaluate each option:

1. **For \( \frac{1}{10} \):**
\[
\frac{2}{10} = 0.2 \quad \text{and} \quad \frac{1}{10} = 0.1
\]
So, \( 0.1 < 0.2 \) is FALSE.

2. **For \( \frac{9}{9} \):**
\[
\frac{9}{9} = 1
\]
Since \( 1 > \frac{7}{11} \approx 0.6363 \), this does not satisfy the inequality \( \frac{2}{10} < 1 < \frac{7}{11} \). So, this is FALSE.

3. **For \( \frac{6}{13} \):**
To compare \( \frac{2}{10} \) with \( \frac{6}{13} \):
\[
\frac{2}{10} = 0.2 \quad \text{and} \quad \frac{6}{13} \approx 0.4615
\]
Since \( 0.2 < 0.4615 \), we have \( \frac{2}{10} < \frac{6}{13} \).

Now check if \( \frac{6}{13} < \frac{7}{11} \):
\[
\frac{7}{11} \approx 0.6363
\]
So, \( 0.4615 < 0.6363 \). This satisfies both parts of the inequality.

4. **For \( \frac{12}{13} \):**
\[
\frac{12}{13} \approx 0.9231
\]
Since \( 0.9231 > \frac{7}{11} \approx 0.6363 \), this does not satisfy the inequality. So this is FALSE.

The only fraction that satisfies the inequality \( \frac{2}{10} < \frac{6}{13} < \frac{7}{11} \) is **\( \frac{6}{13} \)**. Thus, the correct answer is:

\(\frac{6}{13}\)