Adding and subtracting by regrouping — Mathematics, 7–10 years
Learn how tens and ones can be exchanged so that larger additions and subtractions stay organised.
Tens and ones can trade places
A number is built from groups of ten and single ones. When an addition makes ten or more ones, trade ten ones for one ten; when a subtraction needs more ones, trade one ten for ten ones. The value stays the same, but the calculation becomes possible.
Why do we regroup?
Small numbers can be counted directly, but larger numbers quickly become hard to track. People needed a reliable way to count collections, prices and amounts without starting again each time. Place-value notation solves this by recording ten ones as one ten, so the written method follows real groups.
47 + 28, step by step
First add the ones: 7 + 8 = 15. Write 5 ones and carry the 1 ten. Then add the tens: 4 + 2 + 1 = 7 tens. So 47 + 28 = 75. You can check it by splitting 28 into 20 and 8: 47 + 20 = 67, then 67 + 8 = 75.
The columns must match
A common mistake is to add a ten to the ones column, or to line up 47 and 28 by their left edges. This is understandable because the digits look like separate marks on a page. But each column has a job: ones belong under ones and tens under tens, so the carried ten must join the tens.
Where it helps
This appears when you total prices, compare scores or count objects in several boxes. If a shop item costs 47 cents and another costs 28 cents, the total is 75 cents. The same regrouping works whether the numbers describe money, points, stickers or people.
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