Which is the most accurate way to estimate 67% of 76? Choices: (A)2/3 × 73 (B)3/4 × 75 (C)3/4 × 73 (D)2/3 × 75

Convert to Fraction: Convert 67% to a fraction for easier comparison with the choices. Calculation: 67% = 67/100 ≈ 2/3 (since 66.67% is exactly 2/3).Calculate 2/3 of 76: Calculate 2/3 of 76 to compare with choice (A) and (D). Calculation: (2/3) × 76 = 50.67.Check Choice (A): Check choice (A) 2/3 × 73. Calculation: (2/3) × 73 = 48.67.Check Choice (B): Check choice (B) 3/4 × 75. Calculation: (3/4) × 75 = 56.25.Check Choice (C): Check choice (C) 3/4 × 73. Calculation: (3/4) × 73 = 54.75.Check Choice (D): Check choice (D) 2/3 × 75. Calculation: (2/3) × 75 = 50.Compare Results: Compare the results from Steps 2-6 to find the closest estimate to 50.67. Observation: Choice (D) 2/3 × 75 = 50 is the closest estimate.

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Math Problems

Grade 7

Estimate percents of numbers

Full solution

Q. Which is the most accurate way to estimate

67\%

76

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Choices:

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(A)

\frac{2}{3} \times 73

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(B)

\frac{3}{4} \times 75

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(C)

\frac{3}{4} \times 73

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(D)

\frac{2}{3} \times 75

Convert to Fraction: Convert $67\%$ to a fraction for easier comparison with the choices. $\newline$ Calculation: $67\% = \frac{67}{100} \approx \frac{2}{3}$ (since $66.67\%$ is exactly $\frac{2}{3}$ ).
Calculate $\frac{2}{3}$ of $76$ : Calculate $\frac{2}{3}$ of $76$ to compare with choice (A) and (D). $\newline$ Calculation: $\left(\frac{2}{3}\right) \times 76 = 50.67$ .
Check Choice (A): Check choice (A) $\frac{2}{3} \times 73$ . $\newline$ Calculation: $\left(\frac{2}{3}\right) \times 73 = 48.67$ .
Check Choice (B): Check choice (B) $\frac{3}{4} \times 75$ . $\newline$ Calculation: $(\frac{3}{4}) \times 75 = 56.25$ .
Check Choice (C): Check choice (C) $\frac{3}{4} \times 73$ . $\newline$ Calculation: $\left(\frac{3}{4}\right) \times 73 = 54.75$ .
Check Choice (D): Check choice (D) $\frac{2}{3} \times 75$ . $\newline$ Calculation: $\left(\frac{2}{3}\right) \times 75 = 50$ .
Compare Results: Compare the results from Steps $2$ - $6$ to find the closest estimate to $50.67$ . $\newline$ Observation: Choice (D) $\frac{2}{3} \times 75 = 50$ is the closest estimate.