Question

estimate the percent of the number

1. 52% of 83
2. 24% of 45

Explanation:

Problem 17: Estimate 52% of 83

Step1: Round 52% and 83

Round 52% to 50% (or 0.5) and 83 to 80 for easier estimation.

Step2: Calculate the estimate

Multiply the rounded values: $0.5\times80 = 40$. (A more precise estimate: 52% is close to 50%, 83 is close to 80, so 50% of 80 is 40. If we use 52% of 83, $0.52\times83 = 43.16$, and the estimate can also be thought of as 50% of 83 is 41.5, and 2% of 83 is 1.66, so 41.5 + 1.66 = 43.16, but for estimation, 40 or 43 are reasonable. Here we use the simpler rounding to 50% and 80.)

Step1: Round 24% and 45

Round 24% to 25% (or 0.25) and 45 remains as 45 (or round 45 to 40 or 50; 45 is close to 40 or 50, but 25% of 45 is easy).

Step2: Calculate the estimate

25% of a number is $\frac{1}{4}$ of the number. So $\frac{1}{4}\times45 = 11.25$. (If we round 24% to 20% and 45 to 50, 20% of 50 is 10, but 24% is closer to 25%, so 11.25 is a better estimate. The precise value is $0.24\times45 = 10.8$)

Answer:

Approximately 43 (or 40, depending on rounding method; the precise value is 43.16)

Problem 18: Estimate 24% of 45