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.
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.
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.
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.
To find the difference of 748−431 by estimating, we can round both numbers to the nearest ten and then to the nearest hundred.
1. Rounding to the nearest ten:
Rounding 748 to the nearest ten gives us 750.
Rounding 431 to the nearest ten gives us 430.
Now, subtracting 430 from 750 gives us an estimate of 320.
2. Rounding to the nearest hundred:
Rounding 748 to the nearest hundred gives us 800.
Rounding 431 to the nearest hundred gives us 400.
Now, subtracting 400 from 800 gives us an estimate of 400.
Comparing the two estimates, we can see that rounding to the nearest hundred gives a closer estimate. In this case, rounding to the nearest hundred is more accurate because it eliminates the smaller rounding errors introduced by rounding to the nearest ten.