Which of the following uses estimation to check $267-154=113$?
A) $300-150=150$
B) $113+154=267$
C) $270-150=120$
D) $300-200=100$
Answer (2)
Analyze each option to determine if it uses estimation.
Option A: 300 − 150 = 150 uses estimation.
Option B: 113 + 154 = 267 is an exact calculation, not estimation.
Option C: 270 − 150 = 120 uses estimation and rounds to the nearest ten.
Option D: 300 − 200 = 100 uses estimation.
Option C provides the best estimation by rounding to the nearest ten, so the answer is C .
Explanation
Understanding the Problem We need to determine which of the given options uses estimation to check the subtraction 267 − 154 = 113 . Estimation involves rounding numbers to make calculations easier. We will examine each option to see which one best represents an estimation of the original problem.
Analyzing Option A Option A: 300 − 150 = 150 . This option rounds 267 to 300 and 154 to 150. This is a valid estimation.
Analyzing Option B Option B: 113 + 154 = 267 . This option checks the original subtraction by adding the result to the subtrahend. This is an exact calculation, not an estimation.
Analyzing Option C Option C: 270 − 150 = 120 . This option rounds 267 to 270 and 154 to 150. This is also a valid estimation.
Analyzing Option D Option D: 300 − 200 = 100 . This option rounds 267 to 300 and 154 to 200. This is another valid estimation.
Comparing the Estimations Now, let's compare the estimations to the original result of 113. Option A gives 150, Option C gives 120, and Option D gives 100. The question asks which option uses estimation. Options A, C, and D all use estimation. However, we want the best estimation. Rounding to the nearest ten is generally a better estimation than rounding to the nearest hundred. Option C rounds to the nearest ten (267 to 270), while options A and D round to the nearest hundred. Therefore, option C is the best choice.
Final Answer The best option that uses estimation to check the subtraction is C) 270 − 150 = 120 .
Examples
Estimation is a useful tool in everyday life. For example, when you are at the grocery store, you can estimate the total cost of your items to make sure you don't exceed your budget. If you have items that cost $2.50, $3.20, $1.80, and $4.10, you can round these to $3, $3, $2, and $4, respectively. Your estimated total would be $3 + $3 + $2 + $4 = $12. This allows you to quickly check if you have enough money without needing to calculate the exact total.
To estimate 267 − 154 = 113 , we evaluate the options. Options A, C, and D use estimation, but Option C ( 270 − 150 = 120 ) is the best approximation compared to the original result of 113.
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