Indira predicts that the actual difference of 19 - 7.82 will be greater than the estimate of 19 - 8 = 11. Is Indira correct? Explain how Indira might have arrived at that prediction without subtracting the actual numbers.

7.82 is a little less than 8 (it rounds to 8).
Therefore 19 - 7.82 will be a little more than 11
To be more accurate .82 is .18 away from 1
Therefore the exact answer would be 8.18

Answered by Trim | 2024-06-10

Indira predicted the actual difference would be greater than the estimated difference because subtracting a smaller exact number results in a larger difference than subtracting a slightly larger rounded number.
The actual value subtracted is 7.82, which is slightly less than 8. Because 7.82 is less than 8, subtracting 7.82 from 19 will result in a difference slightly greater than what we get when subtracting 8 from 19.
Therefore, the actual difference, 19 - 7.82, should be slightly greater than the estimated difference of 19 - 8.

Answered by SpencerDavis09 | 2024-07-26

Indira's prediction is correct; the actual difference of 19 − 7.82 is 11.18, which is greater than her estimate of 11 from 19 − 8 . She likely used reasoning about the proximity of 7.82 to 8 to arrive at this conclusion. Thus, her understanding of subtraction and rounding gave her a valid basis for her prediction.
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Answered by Trim | 2024-10-02