Lesson 3.4 · Adding and Subtracting Within 100
Subtracting with regrouping
What is 52 − 27? Start with the ones: 2 − 7. You can't take 7 from 2! So you break 1 ten into 10 ones. This is regrouping for subtraction.
Break a ten into 10 ones
52 is 5 tens and 2 ones. You need more ones.
Break 1 ten into 10 ones. Now you have 4 tens and 12 ones. It is still 52.
Ones: 12 − 7 = 5.
Tens: 4 − 2 = 2 tens.
2 tens and 5 ones is 25. So 52 − 27 = 25.
Subtracting with regrouping
- Look at the ones. Is the top digit smaller than the bottom digit?
- If yes, break 1 ten into 10 ones. Now the top has 1 fewer ten and 10 more ones.
- Subtract the ones. Then subtract the tens.
Worked example: 63 − 38
Ones: 3 − 8? Not enough ones. Break a ten.
63 becomes 5 tens and 13 ones.
Ones: 13 − 8 = 5. Tens: 5 − 3 = 2.
So 63 − 38 = 25.
Worked example: 80 − 46
Ones: 0 − 6? Not enough ones. Break a ten.
80 becomes 7 tens and 10 ones.
Ones: 10 − 6 = 4. Tens: 7 − 4 = 3.
So 80 − 46 = 34. Check: 34 + 46 = 80.
Worked example: Count up on a number line
Find 62 − 47 by counting up from 47.
Hop from 47 to 50. That is 3. Hop from 50 to 62. That is 12.
3 + 12 = 15. So 62 − 47 = 15.
Common mistake
Don't flip the digits! For 52 − 27, some kids do 7 − 2 = 5 in the ones and get 35. But the top number has only 2 ones. You must break a ten. The right answer is 25.
Tip
Check by adding: 25 + 27 = 52. If you get back the top number, you are right.
Practice
What is 34 − 8?
Type a number.
What is 45 − 19?
Type a number.
What is 72 − 35?
Type a number.
What is 90 − 54?
Type a number.
What is 61 − 28?
Type a number.
Which problem needs regrouping?
A class has 83 crayons. They use up 47 crayons. How many crayons are left?
Type a number.
What is 100 − 63?
Type a number.