Addition and subtraction with regrouping

Addition and subtraction with regrouping

Addition and subtraction with regrouping

This is the most important trick of 2nd grade. When the ones spill over ten, we have to move one ten across to the tens place.

When it happens

In addition:

  • 27 + 18 → ones 7 + 8 = 15. That's more than 9 — we have a new ten!
  • 56 + 27 → ones 6 + 7 = 13. Another new ten.

In subtraction (this is called borrowing):

  • 52 − 27 → ones 2 − 7 doesn't work (2 is less than 7) — we have to borrow one ten.

How a new ten is born

Ten unit cubes being gathered into a single tens rod

Picture ten cubes. When you gather them all together, you get one tens rod — exactly like the ones you saw in the hundred chart.

That's the whole secret: 10 ones = 1 ten. When adding with regrouping, you bundle ten ones and move them up.

Adding example: 27 + 18

Step 1 — ones. 7 + 8 = 15.

15 is "ten and five". So we have:

  • 5 ones (these stay in the ones place).
  • 1 extra ten (this moves up to the tens).
Step 2 — tens. Tens of the numbers: 2 + 1 = 3. Plus the carried ten: 3 + 1 = 4. Together: 4 tens and 5 ones = 45. 27 + 18 = 45.

Adding example: 56 + 27

  • Ones: 6 + 7 = 13 → 3 ones, 1 extra ten.
  • Tens: 5 + 2 + 1 = 8.
  • 56 + 27 = 83.
A ten-frame overflows past ten and a new ten begins

Subtracting example: 52 − 27

In subtraction we borrow a ten.

Step 1 — ones. 2 − 7 doesn't work — 2 is too few. I take one ten from the top number and trade it for 10 ones.

After borrowing the top is:

  • Instead of 5 tens and 2 ones I have 4 tens and 12 ones.
  • Now 12 − 7 = 5.
Step 2 — tens. Tens on top (after borrowing) are 4, on the bottom 2. 4 − 2 = 2. Together: 2 tens and 5 ones = 25. 52 − 27 = 25.

The most common mistake

Forgetting to add the carried ten to the tens column. The result then comes out ten short of the right one.

  • 27 + 18 — wrong way: ones 5, tens 2+1=3. Result would be 35. But that's ten less than the correct 45.

Always remind yourself: "I'm adding the carried ten too."

Summary

  • When the ones spill past 9, a new ten is born.
  • 10 ones = 1 ten. We move this ten over to the other tens.
  • In subtraction we do the opposite — we borrow a ten from the higher place and trade it for 10 ones.
  • Most common mistake: forgetting to add the carried ten.