Which is the most accurate way to estimate 75% of 45? Choices: (A)1/2 × 43 (B)1/2 × 44 (C)3/4 × 43 (D)3/4 × 44

Understand problem and identify operation: Step 1: Understand the problem and identify the correct operation to use. To find 75% of 45, we need to multiply 45 by 75/100, which simplifies to 3/4. So, we need to calculate 3/4 × 45. Compare choices to correct operation: Step 2: Compare the given choices to the correct operation. We need to find which choice closely estimates 3/4 × 45: (A) 1/2 × 43 (B) 1/2 × 44 (C) 3/4 × 43 (D) 3/4 × 44 We can see that choices (C) and (D) use the correct fraction, 3/4. Calculate estimates for choices: Step 3: Calculate the estimates for choices (C) and (D). For (C): 3/4 × 43 = 32.25 For (D): 3/4 × 44 = 33 Now, calculate the exact value of 3/4 × 45 for comparison: 3/4 × 45 = 33.75. Determine closest estimate: Step 4: Determine which choice is closest to the exact value. Comparing 32.25 and 33 to 33.75, we see that 33 is closer to 33.75. Therefore, choice (D) is the most accurate estimate.

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Math Problems

Grade 7

Estimate percents of numbers

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Q. Which is the most accurate way to estimate

75\%

45

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Choices:

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(A)

\frac{1}{2} \times 43

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(B)

\frac{1}{2} \times 44

\newline

(C)

\frac{3}{4} \times 43

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(D)

\frac{3}{4} \times 44

Understand problem and identify operation: Step $1$ : Understand the problem and identify the correct operation to use. $\newline$ To find $75\%$ of $45$ , we need to multiply $45$ by $\frac{75}{100}$ , which simplifies to $\frac{3}{4}$ . So, we need to calculate $\frac{3}{4} \times 45$ .
Compare choices to correct operation: Step $2$ : Compare the given choices to the correct operation. $\newline$ We need to find which choice closely estimates $\frac{3}{4} \times 45$ : $\newline$ (A) $\frac{1}{2} \times 43$ $\newline$ (B) $\frac{1}{2} \times 44$ $\newline$ (C) $\frac{3}{4} \times 43$ $\newline$ (D) $\frac{3}{4} \times 44$ $\newline$ We can see that choices (C) and (D) use the correct fraction, $\frac{3}{4}$ .
Calculate estimates for choices: Step $3$ : Calculate the estimates for choices (C) and (D). For (C): $\frac{3}{4} \times 43 = 32.25$ For (D): $\frac{3}{4} \times 44 = 33$ Now, calculate the exact value of $\frac{3}{4} \times 45$ for comparison: $\frac{3}{4} \times 45 = 33.75$ .
Determine closest estimate: Step $4$ : Determine which choice is closest to the exact value. Comparing $32.25$ and $33$ to $33.75$ , we see that $33$ is closer to $33.75$ . Therefore, choice (D) is the most accurate estimate.