Which one of the following shows the best percentage?

### Concept & Strategy To compare fractions and determine which represents the highest percentage, convert them into decimals or percentages. The fraction with the highest numerical value represents the "best" percentage. $$ \text{Percentage} = \left(\frac{\text{Numerator}}{\text{Denominator}}\right) \times 100 $$ ### Step-by-Step Solution * **Calculation:** Let us evaluate each option systematically. Option (a): $ \frac{384}{540} $ Simplify the fraction: $ \frac{384}{540} = \frac{38.4}{54} $. Calculate percentage: $ \approx 71.11\% $ Option (b): $ \frac{425}{500} $ Simplify the fraction: Multiply numerator and denominator by 2 to get a base of 1000. $ \frac{850}{1000} = \frac{85}{100} $ Calculate percentage: $ 85\% $ Option (c): $ \frac{570}{700} $ Simplify the fraction: $ \frac{57}{70} $. $ 7 \times 8 = 56 $, so it is slightly more than $ \frac{56}{70} $ (which is 80%). Calculate percentage: $ \approx 81.42\% $ Option (d): $ \frac{480}{660} $ Simplify the fraction: $ \frac{48}{66} = \frac{8}{11} $. Calculate percentage: Since $ \frac{1}{11} = 9.09\% $, $ \frac{8}{11} = 8 \times 9.09\% = 72.72\% $. Comparing all values: 71.11%, 85%, 81.42%, 72.72%. The highest value is 85%. ### Exam Strategy & Shortcut Instead of full division, use estimation and baseline comparisons. Look at (b): 425 out of 500 is clearly 85%. Now look at (c): 570 out of 700. 80% of 700 is 560, so 570 is roughly 81-82%. Look at (d): 480 out of 660. 70% of 660 is 462, so 480 is around 72-73%. Look at (a): 384 out of 540. 70% of 540 is 378, so it is just over 71%. It is immediately obvious that (b) is the highest without doing exact decimal calculations. ### Common Pitfall A common mistake is trying to find a common denominator for all four fractions. Given the large and diverse denominators (540, 500, 700, 660), this approach will consume an immense amount of time and is highly prone to arithmetic errors. ### Final Answer **Therefore, the correct answer is $\frac{425}{500}$.**