When ones sum to 10 or more, regroup 10 ones as 1 ten. In 27 + 15: ones sum to 12 (regroup as 1 ten + 2 ones), then add tens (2 + 1 + 1 = 4 tens), yielding 42. Regrouping preserves place value.
You already know how to add two-digit numbers when the ones column stays under 10 — add ones to ones, tens to tens, and you're done. But what happens when the ones column produces a sum of 10 or more? That's exactly what regrouping solves.
Think of it using what you know about place value: the ones place can only hold a single digit (0–9). When your ones sum reaches 10, you've actually made a brand-new ten — so you trade those 10 ones for 1 ten and carry it over to the tens column. This is sometimes called carrying, and it's just another way of saying: "I've accumulated enough ones to fill a tens cup, so I'll move it over."
Take 27 + 15 as an example. Start with the ones: 7 + 5 = 12. Since 12 is bigger than 9, you can't write "12" in the ones column — there's only room for one digit. Instead, you write the 2 in the ones place and carry the 1 (which stands for 1 ten) up to the tens column. Now the tens column reads 2 + 1 + 1 (the carried ten) = 4. So the answer is 42.
The key insight is that regrouping doesn't change the total — it just reorganizes how the total is expressed. 12 ones is exactly the same amount as 1 ten and 2 ones; you're not adding or removing anything. Every time you carry, you're simply converting between equivalent forms. This same idea — trading 10 of a smaller unit for 1 of the next unit up — will power every column of addition you'll ever do, from three-digit numbers all the way to millions.