Multi-Digit Addition and Subtraction (4th Grade)

What is it?

Adding big numbers works like adding small ones, one place at a time, starting with the ones. Whenever a place adds up to 10 or more, 10 of that place are traded for 1 of the next place to the left. This is regrouping, or carrying. Subtraction runs the other way: when the top digit is too small, 1 is borrowed from the next place to the left and traded for 10 here. Lining the digits up by place keeps every step in the right column.

Step by step: 3,478 + 865

1. Write 3,478 on top and 865 below it, with the ones under the ones, the tens under the tens, and so on. The thousands place of 865 is empty.
2. Ones: 8 + 5 = 13. Write 3 and carry 1 ten.
3. Tens: 7 + 6 + 1 (the carried ten) = 14. Write 4 and carry 1 hundred.
4. Hundreds: 4 + 8 + 1 = 13. Write 3 and carry 1 thousand.
5. Thousands: 3 + 0 + 1 = 4. Only the carried thousand is added.
6. So 3,478 + 865 = 4,343. Check by estimating: 3,500 + 900 is about 4,400, so 4,343 makes sense.

Common mistakes

• Forgetting to add the carried digit into the next place.
• Not lining up the places, so tens are added to hundreds. Add zeros as placeholders if the numbers have different lengths.
• In subtraction, taking the smaller digit from the larger in each column instead of always taking the bottom number from the top.

Your turn

Here is a problem to try. Pause and let your child work it out before you check.

What is 6,425 − 738?

Answer: 5,687. Start with the ones and regroup in the ones, tens and hundreds places: 15 − 8 = 7, 11 − 3 = 8, 13 − 7 = 6. The thousands place gave up 1, so 5 − 0 = 5. Check by adding: 5,687 + 738 = 6,425.

Practice at home

Write a 4-digit problem on graph paper with one digit per square so the places stay lined up. Have your child circle each carried or borrowed digit as they go. Afterward, check subtraction by adding the answer back to the number you took away, and check addition with a quick estimate.