Which fraction among 3/11, 4/7 and 5/8 is the smallest?

Options

A. `3//11`
B. `4//7`
C. `5//8`
D. All are equal

Answer

To determine which fraction among \( \frac{3}{11} \), \( \frac{4}{7} \), and \( \frac{5}{8} \) is the smallest, we can follow these steps:

### Step 1: Compare \( \frac{3}{11} \) and \( \frac{4}{7} \)

To compare these two fractions, we can cross-multiply:

\[ 3 \times 7 = 21 \]
\[ 4 \times 11 = 44 \]

Now, we compare the results:

- Since \( 21 < 44 \), we conclude that \( \frac{3}{11} < \frac{4}{7} \).

### Step 2: Compare \( \frac{3}{11} \) and \( \frac{5}{8} \)

Next, we compare \( \frac{3}{11} \) and \( \frac{5}{8} \) using cross-multiplication again:

\[ 3 \times 8 = 24 \]
\[ 5 \times 11 = 55 \]

Now, we compare these results:

- Since \( 24 < 55 \), we conclude that \( \frac{3}{11} < \frac{5}{8} \).

### Step 3: Compare \( \frac{4}{7} \) and \( \frac{5}{8} \)

Now, we compare \( \frac{4}{7} \) and \( \frac{5}{8} \):

\[ 4 \times 8 = 32 \]
\[ 5 \times 7 = 35 \]

Now, we compare these results:

- Since \( 32 < 35 \), we conclude that \( \frac{4}{7} < \frac{5}{8} \).

### Conclusion

From the comparisons, we have established that:

- \( \frac{3}{11} < \frac{4}{7} \)
- \( \frac{3}{11} < \frac{5}{8} \)

Thus, the smallest fraction among \( \frac{3}{11} \), \( \frac{4}{7} \), and \( \frac{5}{8} \) is \( \frac{3}{11} \).

### Final Answer

The smallest fraction is \( \frac{3}{11} \).

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