The value of which of the following fractions is less than twenty percent?

### Concept & Logic To compare fractions with a percentage, it is easiest to convert the percentage into a baseline fraction or convert all fractions into approximate percentages. $$20\% = \frac{20}{100} = \frac{1}{5}$$ ### Step-by-Step Solution **Calculation:** * Establish the baseline threshold: $20\% = \frac{1}{5} = 0.20$. We are looking for a fraction smaller than this. * Evaluate each option: * (a) $5/6$: Since $5$ is close to $6$, this is over $80\%$. ($\approx 83.33\%$) * (b) $2/3$: This is a standard fraction for $66.66\%$. * (c) $2/5$: This is exactly double $1/5$, so it equals $40\%$. * (d) $1/4$: This is exactly $25\%$. * (e) $2/11$: To compare $2/11$ with $1/5$, find a common numerator or convert to decimals. * $1/5 = 2/10$ * Comparing $2/11$ and $2/10$: Since $11$ is a larger denominator than $10$, the fraction $2/11$ must be smaller than $2/10$. * Therefore, $2/11 < 1/5$ (or $20\%$). ### Exam Strategy & Shortcut Memorize standard fraction-to-percentage conversions for numbers $1$ through $12$. $1/11 \approx 9.09\%$ Therefore, $2/11 \approx 18.18\%$. Since $18.18\% < 20\%$, you can immediately identify (e) as the correct answer without manually evaluating the other simpler fractions. ### Common Pitfall A common trap is attempting long division for every single fraction to find exact decimal values. This wastes valuable time. Use cross-multiplication or standard percentage equivalents to quickly eliminate options. ### Final Answer **Therefore, the correct answer is 2/11.**