Add and Subtract 3- and 4-Digit Numbers
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What you will learn
- 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 of 456 + 278: 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 in 524 - 167. 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.
Words to know
Addend
A number that is added in an addition problem
e.g. In 235 + 412, both 235 and 412 are addends.
Sum
The answer to an addition problem
e.g. The sum of 235 + 412 is 647.
Difference
The answer to a subtraction problem
e.g. The difference of 800 - 350 is 450.
Regroup
To carry or borrow between place values
e.g. I regrouped the tens to subtract 624 - 287.
Carry
To move a 1 to the next place value when a column is over 9
e.g. I carried the 1 from the ones to the tens.
Borrow
To take from the next place value to subtract
e.g. I had to borrow from the tens to subtract.
Use the inverse (opposite) operation to check. Check addition by subtracting one addend from your answer — you should get the other addend. Check subtraction by adding the difference to the number you took away.
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