Number & Operations in Base Ten

Adding & Subtracting Within 1,000

Using models and place-value strategies to add and subtract three-digit numbers.

Intermediate20 min lesson3 min readUpdated August 12, 2026Author not yet attributed

Prerequisites

Adding Two-Digit Numbers

Adding and Subtracting Three-Digit Numbers

The same place-value strategy used for two-digit numbers — working with hundreds, tens, and ones separately — extends naturally to three-digit numbers. The numbers are bigger, but the method is the same one already practiced.

For addition, work through ones, then tens, then hundreds, carrying an extra ten or extra hundred forward whenever a column adds up to 10 or more. For subtraction, when a digit being subtracted is larger than the digit above it, borrow one unit from the next place value over.

Worked Example — Adding Two Three-Digit Numbers

Add 348 + 275. Ones: 8 + 5 = 13, write 3 and carry 1 ten. Tens: 4 + 7 + 1 (carried) = 12 tens, write 2 and carry 1 hundred. Hundreds: 3 + 2 + 1 (carried) = 6 hundreds. The sum is 623.

Worked Example — Subtracting Two Three-Digit Numbers

Subtract 512 − 236. Ones: 2 is less than 6, so borrow 1 ten from the tens place, making it 12 − 6 = 6. Tens: after lending 1 ten, the tens digit 1 becomes 0, which is less than 3, so borrow 1 hundred, making it 10 − 3 = 7. Hundreds: after lending 1 hundred, 5 becomes 4, and 4 − 2 = 2. The difference is 276.

Tip

After borrowing, double check the digit you borrowed from was reduced by exactly 1 — a common slip is forgetting to actually lower that digit after taking from it.

Common Mistakes

Adding a column and writing the full two-digit sum in one place instead of carrying the extra ten forward, such as writing '13' directly in the ones place.
When a column's sum is 10 or more, write only the ones digit of that sum in the column, and carry the tens digit into the next column over.
Subtracting the smaller digit from the larger one regardless of which number it belongs to, instead of borrowing when the top digit is smaller.
If the digit on top is smaller than the digit being subtracted, borrow 1 from the next place value over rather than swapping which digit gets subtracted from which.

Key Takeaways

Adding and subtracting three-digit numbers uses the same place-value strategy as two-digit numbers, one more column at a time.
Carrying moves an extra ten or hundred into the next column during addition.
Borrowing takes one unit from the next place value over during subtraction, when needed.

Summary

Adding and subtracting within 1,000 completes the place-value strategies started with two-digit numbers. The next unit turns to measurement, starting with measuring length using standard, universally recognized units.

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