Subtracting three-digit numbers extends borrowing to three columns: subtract ones (borrow from tens if needed), subtract tens (borrow from hundreds if needed), then subtract hundreds. Some problems require borrowing across a zero — for example, 400 − 163 requires borrowing from the hundreds when the tens digit is zero. Checking answers by adding (result + subtrahend = minuend) reinforces the addition-subtraction relationship.
Spend extra time on the 'borrowing across zero' case using base-ten blocks. Have students use addition to check every subtraction answer. Estimation before computing ('about 240') helps catch large errors.
Three-digit subtraction builds directly on what you already know about subtracting two-digit numbers. You start at the ones column, move to the tens, and finish with the hundreds — and whenever a column's top digit is smaller than the bottom digit, you borrow (also called regrouping) from the column to the left. The new piece is simply that you now have three columns instead of two.
The ordinary case — no borrowing needed — is straightforward. For 785 − 342, subtract each column: 5 − 2 = 3, 8 − 4 = 4, 7 − 3 = 4, giving 443. One-column borrowing works just like you practiced with two-digit numbers: if you can't subtract ones, borrow a ten from the tens place, making the ones digit 10 bigger and the tens digit 1 smaller. Then move left and finish the subtraction.
The genuinely new challenge in three-digit subtraction is borrowing across a zero. Consider 400 − 163. You need to subtract 3 from 0, so you want to borrow from the tens place — but the tens digit is also 0. There's nothing to borrow there. You have to go all the way to the hundreds first: borrow one hundred from the 4, making the hundreds 3 and giving 10 tens to the tens place. Now borrow one of those tens for the ones place: the tens digit drops from 10 to 9, and the ones become 10. Now you can subtract: 10 − 3 = 7, 9 − 6 = 3, 3 − 1 = 2, giving 237.
The most reliable way to check any subtraction is to add your answer back to the number you subtracted: 237 + 163 should equal 400. If it does, your subtraction was correct. This inverse relationship — subtraction undone by addition — is one of the most useful checking strategies in arithmetic, and it works for numbers of any size.