Question

Which fraction makes this true? 2/10< blank < 7/11? A. 9/9 b. 6/13 c. 12/13 d. 1/10

Answer 1

To determine which fraction fits the inequality \( \frac{2}{10} < \text{blank} < \frac{7}{11} \), we first convert \( \frac{2}{10} \) and \( \frac{7}{11} \) to decimal form for easier comparison.

1. **Convert \( \frac{2}{10} \):**
\[
\frac{2}{10} = 0.2
\]

2. **Convert \( \frac{7}{11} \):**
\[
\frac{7}{11} \approx 0.6363 (repeating)
\]

Now we need to find a fraction from the given options that falls between 0.2 and approximately 0.6363.

Now, let's evaluate each option:

**A. \( \frac{9}{9} \):**
\[
\frac{9}{9} = 1
\]
(Not between 0.2 and 0.6363)

**B. \( \frac{6}{13} \):**
\[
\frac{6}{13} \approx 0.4615
\]
(Between 0.2 and 0.6363)

**C. \( \frac{12}{13} \):**
\[
\frac{12}{13} \approx 0.9231
\]
(Not between 0.2 and 0.6363)

**D. \( \frac{1}{10} \):**
\[
\frac{1}{10} = 0.1
\]
(Not between 0.2 and 0.6363)

Based on this analysis, the only fraction that satisfies \( \frac{2}{10} < \frac{6}{13} < \frac{7}{11} \) is:

\[
\boxed{\frac{6}{13}}
\]