Add and subtract four-digit numbers

Exchange only equal amounts

Find 2687 + 1756. Add ones: 7 + 6 = 13, leaving three ones and one exchanged ten. Add tens: 8 + 5 + 1 = 14, leaving four tens and one exchanged hundred. Add hundreds: 6 + 7 + 1 = 14, leaving four hundreds and one exchanged thousand. Add thousands: 2 + 1 + 1 = 4.

The total is 4443. Write each exchanged amount above the next place so it is used once.

In the first row, 13 ones become three ones and one ten. The tens row includes that exchanged ten. A 1 in the last column always means one unit of the next larger place. If an exchange remains beyond the greatest written place, keep its new leading digit in the answer.

Before calculating, 2700 + 1800 = 4500 is a useful estimate. The exact result should be near it.

Subtract across more than one empty place

For 4002-1765, the two ones cannot supply five ones. Exchange one thousand for ten hundreds, then one hundred for ten tens, then one ten for ten ones.

A 1 in the last column means taking one unit from the next larger place and making ten units here. The hundreds and tens each pass one of their ten new units to the next smaller place, leaving nine. There is no exchange from above the thousands place.

This is still 4002: 3000 + 900 + 90 + 12 = 4002.

Subtract each place: 12-5 = 7, 9-6 = 3, 9-7 = 2, 3-1 = 2. The answer is 2237.

Check 2237 + 1765 = 4002. An exchange changes the way you represent the amount, not the amount itself.

Check your understanding 1 Check the exchange

Find 5004-2687. Use addition to check your result.

Difference

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2317. The place differences are 14-7 = 7, 9-8 = 1, 9-6 = 3, 4-2 = 2. Checking 2317 + 2687 gives 5004.

Mental calculations can use compensation

For 47 + 38, add 40, then remove the extra two: 47 + 40-2 = 85.

For 83-29, take away 30, then give one back: 83-30 + 1 = 54. Taking away an extra one made the result too small, so add it back.

Check your understanding 2 Choose the correction

Use a nearby multiple of ten to find 56 + 29 and 92-48. Explain why your correction is subtraction in one calculation and addition in the other.

Your answer or drawing on paper

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56 + 29 = 56 + 30-1 = 85; adding 30 added one too many. 92-48 = 92-50 + 2 = 44; subtracting 50 removed two too many. The correction restores the intended amount.

For a story, decide what is unknown before calculating. A remaining part calls for subtraction; a total of separate parts calls for addition. A word such as “more” alone does not decide the operation.