Which of the following is the smallest fraction ?
`(8)/(25), (7)/(23), (11)/(23), (14)/(53)`

Options

A. `(8)/(25)`
B. `(7)/(23)`
C. `(11)/(23)`
D. `(14)/(53)`

Answer

To determine which of the given fractions is the smallest, we will convert each fraction to its decimal form for easy comparison.

**Step 1: Convert each fraction to decimal form.**

1. **Convert \( \frac{8}{25} \)**:
\[ \frac{8}{25} = 8 \div 25 = 0.32 \]

2. **Convert \( \frac{7}{23} \)**:
\[ \frac{7}{23} = 7 \div 23 \approx 0.3043 \]

3. **Convert \( \frac{11}{23} \)**:
\[ \frac{11}{23} = 11 \div 23 \approx 0.4783 \]

4. **Convert \( \frac{14}{53} \)**:
\[ \frac{14}{53} = 14 \div 53 \approx 0.2642 \]

**Step 2: Compare the decimal values.**

Now we have the decimal equivalents:
- \( \frac{8}{25} \approx 0.32 \)
- \( \frac{7}{23} \approx 0.3043 \)
- \( \frac{11}{23} \approx 0.4783 \)
- \( \frac{14}{53} \approx 0.2642 \)

**Step 3: Identify the smallest decimal value.**

From the decimal values calculated:
- \( 0.32 \) (from \( \frac{8}{25} \))
- \( 0.3043 \) (from \( \frac{7}{23} \))
- \( 0.4783 \) (from \( \frac{11}{23} \))
- \( 0.2642 \) (from \( \frac{14}{53} \))

The smallest decimal value is \( 0.2642 \), which corresponds to the fraction \( \frac{14}{53} \).

**Conclusion:**
The smallest fraction among the given options is \( \frac{14}{53} \).

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