Which of the following uses estimation to check $267-154=113$?
A) $270-150=120$
B) $300-200=100$
C) $300-150=150$
D) $113+154=267$
Answer (2)
Option A rounds 267 to 270 and 154 to 150, resulting in 270 − 150 = 120 .
Option B rounds 267 to 300 and 154 to 200, resulting in 300 − 200 = 100 .
Option C rounds 267 to 300 and 154 to 150, resulting in 300 − 150 = 150 .
Option A provides the closest estimation to the actual result, so the answer is A .
Explanation
Understanding the Problem We are asked to identify which of the given options uses estimation to check the subtraction 267 − 154 = 113 . Estimation involves rounding numbers to make calculations simpler and approximate the result. We need to determine which option provides the closest approximation to the original subtraction.
Analyzing Each Option Let's analyze each option:
Option A: 270 − 150 = 120 . Here, 267 is rounded to 270, and 154 is rounded to 150. The result is 120. To check how close this estimation is, we find the absolute difference between the estimation and the actual result: ∣120 − 113∣ = 7 .
Option B: 300 − 200 = 100 . Here, 267 is rounded to 300, and 154 is rounded to 200. The result is 100. The absolute difference between the estimation and the actual result is: ∣100 − 113∣ = 13 .
Option C: 300 − 150 = 150 . Here, 267 is rounded to 300, and 154 is rounded to 150. The result is 150. The absolute difference between the estimation and the actual result is: ∣150 − 113∣ = 37 .
Option D: 113 + 154 = 267 . This option performs the exact addition to verify the subtraction, not an estimation.
Comparing the Results Comparing the absolute differences, we have:
Option A: ∣120 − 113∣ = 7 Option B: ∣100 − 113∣ = 13 Option C: ∣150 − 113∣ = 37
The smallest absolute difference is 7, which corresponds to Option A. Therefore, Option A provides the closest estimation.
Final Answer The option that uses estimation to check 267 − 154 = 113 is 270 − 150 = 120 , which is option A.
Examples
Estimating calculations is a useful skill in everyday life. For example, when you're at the grocery store, you can quickly estimate the total cost of your items by rounding each price to the nearest dollar. If you have items costing $2.65, $1.22, $3.49, and $0.89, you can estimate the total as $3 + $1 + $3 + $1 = $8. This helps you ensure you have enough money and can quickly check if the cashier makes a mistake. Estimation is also helpful in science for quick data verification and in engineering for preliminary design checks.
The option that uses estimation to check 267 − 154 = 113 is Option A: 270 − 150 = 120 , as it provides the closest approximation with a difference of 7 from the actual result.
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