Which of the following fractions is greater than $$\frac{3}{4}$$ and less than $$\frac{5}{6}$$?

### Concept & Logic To find a fraction that falls within a specific range, convert the lower and upper bounds into percentages or decimals, then evaluate the given options against those bounds. ### Step-by-Step Solution * First, establish the target range by converting the boundary fractions to decimals: * Lower bound: $$\frac{3}{4} = 0.75$$ * Upper bound: $$\frac{5}{6} \approx 0.833$$ * We need an option whose value is strictly between $$0.75$$ and $$0.833$$. * Next, convert the given options into decimals: (a) $$\frac{1}{2} = 0.50$$ (b) $$\frac{2}{3} \approx 0.667$$ (c) $$\frac{4}{5} = 0.80$$ (d) $$\frac{9}{10} = 0.90$$ * Comparing the options to our range ($$0.75 < x < 0.833$$): * $$0.50$$ is too small. * $$0.667$$ is too small. * $$0.80$$ falls perfectly within the range. * $$0.90$$ is too large. ### Exam Strategy & Shortcut **Percentage Equivalents:** Memorizing standard fraction-to-percentage conversions makes this a $$5$$-second question. Bounds: $$75\%$$ and $$83.33\%$$. Options: $$50\%$$, $$66.66\%$$, $$80\%$$, $$90\%$$. It is immediately obvious that only $$80\%$$ ($$\frac{4}{5}$$) fits in the required gap. ### Common Pitfall Attempting to equalize the denominators for all six fractions (the two bounds plus the four options) by finding a massive common multiple. This is entirely unnecessary and wastes critical time. ### Final Answer **Therefore, the correct answer is option (c).**