Video: Estimating Differences of Decimals and Using Estimates to Check Reasonableness

Consider this subtraction problem. 75.43 − 32.19 = _. Estimate the difference by rounding each number to the nearest whole number. Calculate the difference. Check that your answer is reasonable using your estimate.

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Video Transcript

Consider this subtraction problem. 75.43 minus 32.19. Estimate the difference by rounding each number to the nearest whole number. Calculate the difference. Check that your answer is reasonable using your estimate.

The first part of the question asked us to estimate the difference by rounding to the nearest whole number. We need to round 75.43 and 32.19 to the nearest whole number. When rounding to the nearest whole number, the deciding number is in the tenths column. If this number is five or greater, we round up. If it is less than five, we will round down.

As four is less than five, 75.43, to the nearest whole number, is equal to 75. One is also less than five, so 32.19, to the nearest whole number, is equal to 32. This means that we need to subtract 32 from 75. Five minus two is equal to three. And seven minus three is equal to four. This means that our estimated answer is 43, as 75 minus 32 is equal to 43.

The second part of our question asked us to calculate the difference. We need to subtract 32.19 from 75.43. We can calculate this using column subtraction, working from right to left. Nine is greater than three, so we can’t subtract nine from three without getting a negative number. We need to go next door and borrow from the four. This leaves us with three tenths and 13 hundredths.

13 minus nine is equal to four, so we have four in the hundredths column. Three minus one is equal to two, so we have two in the tenths column. The decimal point must stay in the same place. Five minus two is equal to three, so we have three in the units, or the ones, column. Finally, seven minus three is equal to four, so we have four in the tens column. This means that the actual answer to the calculation 75.43 minus 32.19 is 43.24.

The last part of the question asked us to check if the answer was reasonable. As 43.24 is very close to our estimated answer of 43, then we know that our answer is reasonable.

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