Number & Operations in Base Ten

Multi-Digit Addition & Subtraction

Fluently adding and subtracting within 1,000.

Foundational15 min lesson3 min readUpdated August 12, 2026Author not yet attributed

Adding and Subtracting with Confidence

Grade 2 introduced carrying and borrowing for numbers up to 1,000. This lesson builds real fluency with those same strategies — accurate, reasonably fast, and checked using the rounding skill from the last lesson.

Rounding both numbers in a problem before solving gives a quick estimate of what the exact answer should be close to. If the exact answer is far from that estimate, it's a strong signal that a mistake happened somewhere in the carrying or borrowing.

Worked Example — Adding and Estimating to Check

Add 486 + 375. Carrying through each place value: ones 6 + 5 = 11 (write 1, carry 1), tens 8 + 7 + 1 = 16 (write 6, carry 1), hundreds 4 + 3 + 1 = 8. The sum is 861. Checking with rounding: 486 rounds to 500 and 375 rounds to 400, and 500 + 400 = 900 — close to 861, so the exact answer is reasonable.

Worked Example — Subtracting and Estimating to Check

Subtract 703 − 258. Borrowing through each place value: ones 3 − 8 needs borrowing, tens 0 − 5 needs borrowing again, hundreds 7 becomes 6 after lending. Working through it carefully gives 445. Checking with rounding: 703 rounds to 700 and 258 rounds to 300, and 700 − 300 = 400 — close to 445, so the exact answer is reasonable.

Tip

When borrowing crosses a zero, like in 703 − 258, borrow from the hundreds place into the tens place first, and then from that borrowed ten into the ones place — working one place value at a time keeps the borrowing organized.

Common Mistakes

Getting stuck when a digit to borrow from is 0, such as not knowing how to borrow into the tens place of 703 when the tens digit is already 0.
Borrow from the next place value over instead — reduce the hundreds digit by 1 and treat the 0 tens as 10 tens, then continue borrowing from there into the ones place.
Skipping the estimate check and not noticing when an exact answer is clearly unreasonable.
Round both numbers first and estimate the answer before calculating exactly — if the final answer isn't close to the estimate, recheck the carrying or borrowing.

Key Takeaways

Multi-digit addition and subtraction use the same carrying and borrowing strategies from Grade 2, applied with more fluency.
Borrowing across a zero means borrowing from the next place value over, one step at a time.
Rounding both numbers first gives a quick estimate to check whether an exact answer is reasonable.

Summary

Fluent multi-digit addition and subtraction, checked by estimation, completes this unit's number work. The next unit introduces a new kind of number entirely — fractions — starting with what a fraction actually represents.

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