Question

Part A
Estimate 1012−38
using benchmark values. Your equation must show the estimate for each fraction and the final estimate for the expression.



(2 points)

Question 2
Part B
Solve 1012−38
. Show your solution as an equation.

(2 points)

Question 3
Part C
Calculate the difference between your estimate in Part A and the actual value you calculated in Part B. Be sure to show this solution as an equation.

Based on this difference, do you think your estimate for Part A was reasonable? Explain.

(2 points)

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Answer 1

Part A — Estimate using benchmarks:
10 1/2 ≈ 11 (1/2 rounds up), and 3 1/8 ≈ 3 (1/8 rounds down).
Estimate: 11 − 3 = 8

Part B — Exact calculation:
10 1/2 − 3 1/8
= 21/2 − 25/8
= 84/8 − 25/8
= 59/8
= 7 3/8

Part C — Difference between estimate and actual:
Difference = 8 − 7 3/8 = 5/8 (which is 0.625)
Since the estimate is only 5/8 (less than 1) higher than the actual value, the estimate was reasonable (it was slightly high because we rounded the minuend up and the subtrahend down).