Which of the following fraction is the smallest ?

Question

Accepted Answer

To determine which fraction is the smallest among the given options, we need to compare the fractions 13/16, 17/21, and 15/19. The fourth option, "Mon Jul 08 2024 12:30:00 GMT+0530 (GMT+05:30)," is not a fraction and is irrelevant to the comparison.

### Explanation for Option 3 (15/19) as the Smallest Fraction:

1. **Convert Fractions to Decimal Form:**
   - 13/16 = 0.8125
   - 17/21 ≈ 0.8095
   - 15/19 ≈ 0.7895

2. **Comparison of Decimal Values:**
   - 0.8125 (13/16) is greater than 0.8095 (17/21).
   - 0.8095 (17/21) is greater than 0.7895 (15/19).

From the decimal values, it is clear that 15/19 has the smallest decimal value, making it the smallest fraction among the given options.

### Explanation for Why Other Options are Incorrect:

1. **Option 1 (13/16):**
   - The decimal value of 13/16 is 0.8125, which is larger than 0.7895 (15/19). Therefore, 13/16 is not the smallest fraction.

2. **Option 2 (17/21):**
   - The decimal value of 17/21 is approximately 0.8095, which is still larger than 0.7895 (15/19). Thus, 17/21 is not the smallest fraction.

3. **Option 4 (Mon Jul 08 2024 12:30:00 GMT+0530 (GMT+05:30)):**
   - This option is not a fraction and is irrelevant to the comparison. It cannot be considered in determining the smallest fraction.

In conclusion, based on the decimal conversion and comparison, Option 3 (15/19) is indeed the smallest fraction among the given options.