The least among the following fractions is

### Concept & Logic For proper fractions where the difference between the denominator and numerator is identical, the fraction with the smallest values has the least magnitude. ### Step-by-Step Solution * Given fractions: $$\frac{15}{16}, \frac{19}{20}, \frac{24}{25}, \frac{34}{35}$$ * Observe the difference between the denominator and numerator for each fraction: $$16 - 15 = 1$$ $$20 - 19 = 1$$ $$25 - 24 = 1$$ $$35 - 34 = 1$$ * Since the differences are identical ($$1$$), the fraction with the smallest numerator and denominator is the smallest in value. * Comparing the numerators: $$15 < 19 < 24 < 34$$. * Therefore, the least fraction is $$\frac{15}{16}$$. ### Exam Strategy & Shortcut **Gap Rules for Fractions:** When the gap $$(D - N)$$ is constant, as the numbers grow larger, the fraction approaches $$1$$. Thus, the smallest numbers yield the smallest fraction value. You can instantly mark $$\frac{15}{16}$$ within $$2$$ seconds. ### Common Pitfall Attempting to find a common denominator via LCM for large numbers like $$16, 20, 25, 35$$, which leads to tedious and error-prone calculations. ### Final Answer **Therefore, the correct answer is option (a).**