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Which is the most accurate way to estimate 24%24\% of 5757?\newlineChoices:\newline(A) 14×56\frac{1}{4} \times 56\newline(B) 23×56\frac{2}{3} \times 56\newline(C) 14×59\frac{1}{4} \times 59\newline(D) 23×59\frac{2}{3} \times 59

Full solution

Q. Which is the most accurate way to estimate 24%24\% of 5757?\newlineChoices:\newline(A) 14×56\frac{1}{4} \times 56\newline(B) 23×56\frac{2}{3} \times 56\newline(C) 14×59\frac{1}{4} \times 59\newline(D) 23×59\frac{2}{3} \times 59
  1. Convert to fraction: Step 11: Convert 24%24\% to a fraction for easier calculation. 24%24\% is approximately 14\frac{1}{4}, since 25%25\% is exactly 14\frac{1}{4}.
  2. Apply fraction to choices: Step 22: Apply the fraction 14\frac{1}{4} to the closest numbers in the choices, which are 5656 and 5959. Calculate 14\frac{1}{4} of 5656 and 14\frac{1}{4} of 5959. \newline14×56=14\frac{1}{4} \times 56 = 14\newline14×59=14.75\frac{1}{4} \times 59 = 14.75
  3. Compare results with actual: Step 33: Compare these results with the actual 24%24\% of 5757. Calculate 24%24\% of 5757 directly.\newline24%24\% of 57=0.24×57=13.6857 = 0.24 \times 57 = 13.68
  4. Determine closest estimate: Step 44: Determine which of the calculated estimates (1414 or 14.7514.75) is closer to 13.6813.68. 1414 is closer to 13.6813.68 than 14.7514.75.
  5. Match closest estimate: Step 55: Match the closest estimate to the choices provided. The closest estimate, 1414, comes from 14×56\frac{1}{4} \times 56, which is choice (A).

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