Which of the following fraction is the least?

Question

Accepted Answer

To determine which fraction is the least among the given options, we need to compare the values of each fraction. The fractions provided are:

1. $\frac{12}{13}$
2. $\frac{14}{19}$
3. $\frac{17}{21}$
4. $\frac{25}{26}$

### Explanation for Option 2 ($\frac{14}{19}$) as the Correct Answer:

To compare these fractions, we can convert them to decimal form or find a common denominator. However, converting to decimal form is often more straightforward for comparison:

1. $\frac{12}{13} \approx 0.9231$
2. $\frac{14}{19} \approx 0.7368$
3. $\frac{17}{21} \approx 0.8095$
4. $\frac{25}{26} \approx 0.9615$

From these decimal approximations, it is clear that $\frac{14}{19} \approx 0.7368$ is the smallest value among the fractions. Therefore, Option 2 is indeed the least fraction.

### Explanation for Why Each of the Other Options is Incorrect:

1. **Option 1 ($\frac{12}{13}$)**: This fraction converts to approximately 0.9231, which is significantly larger than 0.7368. Hence, it is not the least fraction.

2. **Option 3 ($\frac{17}{21}$)**: This fraction converts to approximately 0.8095. While it is smaller than $\frac{12}{13}$ and $\frac{25}{26}$, it is still larger than $\frac{14}{19}$.

3. **Option 4 ($\frac{25}{26}$)**: This fraction converts to approximately 0.9615, which is the largest among all the given fractions. Therefore, it cannot be the least fraction.

In conclusion, based on the decimal approximations, $\frac{14}{19}$ is the smallest fraction, making Option 2 the correct answer.