Regrouping Made Easy

When you add and a column overflows, regrouping carries the extra to the next place. Add 28 and 15: the ones give 8 plus 5, which is 13. Thirteen is one ten and three ones, so you write the 3 and carry the ten into the tens column. Now 2 tens plus 1 ten plus the carried ten makes 4 tens. The answer is 43.

Subtraction regroups in the other direction. For 42 minus 17, you cannot take 7 ones from 2 ones, so you break one of the tens into ten ones. Now 42 becomes 3 tens and 12 ones, and 12 minus 7 is 5, 3 tens minus 1 ten is 2 tens. The answer is 25.

Regrouping is not magic or a trick - it is place value doing its job. A carried ten is just ten ones wearing a new hat, and a borrowed ten is the same hat worn in reverse. Once you see regrouping as trading between places, every column works the same way.