Which is the most accurate way to estimate $75\%$ of $45$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{2} \times 43$ $\newline$ (B) $\frac{1}{2} \times 44$ $\newline$ (C) $\frac{3}{4} \times 43$ $\newline$ (D) $\frac{3}{4} \times 44$

Full solution

Q. Which is the most accurate way to estimate

75\%

45

\newline

Choices:

\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

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.