Add and Subtract 3- and 4-Digit Numbers
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Learning Objectives
- 1Add two 3-digit or 4-digit numbers using the column method, regrouping where needed
- 2Subtract two 3-digit or 4-digit numbers using the column method, borrowing where needed
- 3Check a sum or difference by using the inverse operation
Mini Lesson
The column method lines up digits by place value so we can add or subtract one column at a time, starting from the ones. When the ones column adds up to 10 or more, we regroup (carry) the extra ten into the tens column. When we cannot subtract, we borrow (regroup) from the next column.
Column Addition with Regrouping
- Line up the digits by place value: ones under ones, tens under tens, hundreds under hundreds.
- Add the ones column: 6 + 8 = 14. Write 4 in the ones; carry 1 to the tens.
- Add the tens column: 5 + 7 + 1 (carry) = 13. Write 3; carry 1 to the hundreds.
- Add the hundreds: 4 + 2 + 1 (carry) = 7. Write 7.
- 456 + 278 = 734.
Column Subtraction with Borrowing
- Start from the ones. Can we subtract 7 from 4? No. Borrow 1 ten from the tens column.
- 14 - 7 = 7. The tens column is now 1 (was 2, lent 1).
- Can we subtract 6 from 1? No. Borrow 1 hundred. 11 - 6 = 5. Hundreds becomes 4.
- 4 - 1 = 3. So 524 - 167 = 357.
Check addition by subtracting your answer from one addend — you should get the other addend. Check subtraction by adding the difference to the subtrahend.
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