When rounding both numbers to the nearest ten, 748 would round to 750 and 431 would round to 430. Therefore, estimating the difference using rounding to the nearest ten would be 750 - 430 = 320.
When rounding both numbers to the nearest hundred, 748 would round to 700 and 431 would round to 400. Therefore, estimating the difference using rounding to the nearest hundred would be 700 - 400 = 300.
Rounding to the nearest ten results in a closer estimate in this case. This is because rounding to the nearest ten is more precise as it keeps more of the original value intact. When rounding to the nearest hundred, both numbers are rounded to the nearest hundred which can result in a larger difference between the rounded values.
Jack needs to find the difference of 748−431
by estimating.
Round both numbers to the nearest ten, and round both numbers to the nearest hundred.
Does rounding to the nearest ten or nearest hundred make a closer estimate?
Explain your answer.
3 answers
Cardel and Malia found the difference of 456−212
Cardel added 4 to both numbers, then subtracted.
Malia subtracted 2 from both numbers, then subtracted.
Will Cardel's way, Malia's way, or both ways find the correct answer?
Try both ways and show your work. Explain why each way works or does not work. Then, find the difference.
Cardel added 4 to both numbers, then subtracted.
Malia subtracted 2 from both numbers, then subtracted.
Will Cardel's way, Malia's way, or both ways find the correct answer?
Try both ways and show your work. Explain why each way works or does not work. Then, find the difference.
Here's how Cardel and Malia can find the difference of 456 - 212 using their methods:
Cardel:
Adding 4 to both numbers: (456 + 4) - (212 + 4) = 460 - 216 = 244
Malia:
Subtracting 2 from both numbers: (456 - 2) - (212 - 2) = 454 - 210 = 244
Both Cardel's and Malia's ways find the correct answer of 244.
Cardel's way works because adding or subtracting the same number to both numbers does not change the difference between them. By adding 4 to both numbers, Cardel adjusted the original numbers, but the difference between them remains the same.
Malia's way also works because subtracting the same number from both numbers does not change the difference between them. By subtracting 2 from both numbers, Malia adjusted the original numbers, but the difference between them remains the same.
Therefore, both Cardel's and Malia's ways are valid and will find the correct answer of 244.
Cardel:
Adding 4 to both numbers: (456 + 4) - (212 + 4) = 460 - 216 = 244
Malia:
Subtracting 2 from both numbers: (456 - 2) - (212 - 2) = 454 - 210 = 244
Both Cardel's and Malia's ways find the correct answer of 244.
Cardel's way works because adding or subtracting the same number to both numbers does not change the difference between them. By adding 4 to both numbers, Cardel adjusted the original numbers, but the difference between them remains the same.
Malia's way also works because subtracting the same number from both numbers does not change the difference between them. By subtracting 2 from both numbers, Malia adjusted the original numbers, but the difference between them remains the same.
Therefore, both Cardel's and Malia's ways are valid and will find the correct answer of 244.