When subtracting three-digit numbers and a digit in the minuend is smaller than the digit below it, regroup by trading one ten for ten ones (or one hundred for ten tens). This allows you to solve problems like 325 - 148.
Model with base-ten blocks the trading process: breaking a ten into ones when needed. Use guided practice with problems that require regrouping in different places.
You already know two important skills from your prerequisites: how to subtract three-digit numbers when no regrouping is needed, and how to regroup when subtracting two-digit numbers — trading a ten for ten ones. Three-digit subtraction with regrouping combines these skills and extends them: now you may need to trade across two columns instead of one.
Regrouping (sometimes called borrowing) is the key operation. When the digit you're subtracting is larger than the digit above it, you can't subtract directly — you need to trade from the next column to get enough to work with. In 325 − 148: the ones column shows 5 − 8, which is impossible as-is. So you trade — take one ten from the tens column (turning 2 tens into 1 ten) and add those ten ones to the ones column (turning 5 ones into 15 ones). Now 15 − 8 = 7. Moving left: the tens column now shows 1 − 4, also impossible. Trade from the hundreds: turn 3 hundreds into 2 hundreds, and give 10 tens to the tens column (1 + 10 = 11 tens). Now 11 − 4 = 7. Finally, 2 − 1 = 1. The answer is 177.
The trickiest case is regrouping through a zero. If the tens digit is 0, you can't borrow a ten from there — it's empty. Instead, borrow from the hundreds column first: trade 1 hundred for 10 tens, then immediately trade 1 of those tens for 10 ones. This is a two-step trade across two columns. Base-ten blocks make this concrete: you physically exchange one hundreds flat for ten tens rods, then one rod for ten ones cubes, and see that the total quantity hasn't changed — only the form.
The important thing to understand is that regrouping doesn't change the value of the numbers — it only changes how they're written. 3 hundreds + 2 tens + 5 ones is the same quantity as 2 hundreds + 12 tens + 5 ones, or 2 hundreds + 11 tens + 15 ones. You're re-packaging the quantity into forms that make column subtraction possible. Once you see regrouping as renaming rather than "borrowing" (nothing is actually paid back), the whole procedure makes logical sense.
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