Lesson 3.2 · Adding and Subtracting Within 100
Adding with regrouping
What is 37 + 25? The ones make 7 + 5 = 12. But 12 is too big for the ones place! When you get 10 or more ones, you trade 10 ones for 1 ten. This is called regrouping.
Trade 10 ones for 1 ten
37 is 3 tens and 7 ones. 25 is 2 tens and 5 ones.
Ones: 7 + 5 = 12 ones.
12 ones is 1 ten and 2 ones. Keep the 2 ones. Move the 1 ten over to the tens.
Tens: 3 + 2 = 5 tens. Plus the 1 new ten makes 6 tens.
6 tens and 2 ones is 62. So 37 + 25 = 62.
Definition
Regrouping
Regrouping means trading 10 ones for 1 ten. You do it when the ones add up to 10 or more.
Stack them up
When you stack, write the new ten as a small 1 above the tens.
Ones: 7 + 5 = 12. Write 2, carry the 1. Tens: 1 + 3 + 2 = 6.
Adding with regrouping
- Add the ones.
- If you get 10 or more, keep the ones and move 1 ten to the tens.
- Add the tens, and don't forget the new ten.
Worked example: 48 + 26
Ones: 8 + 6 = 14. That is 1 ten and 4 ones. Write 4.
Tens: 4 + 2 = 6, plus the new ten is 7 tens.
So 48 + 26 = 74.
Worked example: Make a ten on a number line
Find 47 + 8.
47 needs 3 more to make 50. Split 8 into 3 and 5. Hop 3 to 50. Then hop 5 to 55.
So 47 + 8 = 55.
Worked example: 65 + 35
Ones: 5 + 5 = 10. That is 1 ten and 0 ones. Write 0.
Tens: 6 + 3 = 9, plus the new ten is 10 tens.
10 tens is 100. So 65 + 35 = 100.
Common mistake
Don't write 12 in the ones place! For 37 + 25, some kids write 3 + 2 = 5 and 7 + 5 = 12, and get 512. That is way too big. Only one digit fits in the ones place. Move the ten.
Tip
Estimate first. 37 + 25 is close to 40 + 25 = 65. So 62 makes sense.
Practice
What is 18 + 7?
Type a number.
What is 36 + 28?
Type a number.
What is 29 + 29?
Type a number.
What is 47 + 45?
Type a number.
What is 55 + 38?
Type a number.
Which problem needs regrouping?
Mia read 46 pages last week. She read 37 pages this week. How many pages did she read in all?
Type a number.
Fill in the blank: 64 + ___ = 100.
Type a number.