Subtraction with borrowing
By the end of this lesson a child subtracts when the ones digit is not large enough. One ten is then exchanged for 10 ones. That step is called borrowing.
What the child can do at the end
- For 23 − 7, see that 7 cannot be taken from 3.
- Exchange one ten: 13 − 7 = 6, and one ten remains.
- Get 16, not 24.
Why we borrow
In 23, the digit 2 is two tens and the digit 3 is three ones. Seven is greater than three, so the ones are filled first. One ten is worth 10 ones. After the exchange, one ten remains and the ones become 13.
One problem, step by step
A box has 23 sweets. 7 are taken out. How many are left?
- Ones: 3 − 7 does not work, because 7 is greater than 3.
- Exchange one ten. Of the two tens, one remains.
- The ten ones just exchanged, plus the old 3, make 13 ones.
- 13 − 7 = 6. The remaining ten and 6 ones make 16.
- Check: 16 + 7 = 23. The sum brings back the number you started with.
A common mistake
The child cannot do 3 − 7, so they flip the digits and compute 7 − 3 = 4. They then keep the tens and write 24. The smaller digit is not subtracted from the larger one just because that “works”. Borrowing gives 13 − 7 = 6, and the answer is 16.
The other mistake is exchanging a ten and still counting two tens. The exchanged ten is gone. In 23, one ten remains after the borrow.
Practice
- 21 − 5 = ___
- 30 − 4 = ___
- 42 − 8 = ___
- 15 − 9 = ___
- 50 − 6 = ___
Answers
- 16
- 26
- 34
- 6
- 44
30 − 4: zero ones cannot give 4. Exchange one ten, 2 tens remain, and the ones become 10. 10 − 4 = 6, so the answer is 26.
After the lesson, the quiz
Open the subtraction quiz. If the child gets a number larger than the one they started from, they subtracted the digits backwards. Go back to the borrow.
Subtraction quiz Subtraction table
For a parent
Tie ten sticks with a rubber band. When the ones are not enough, the child takes the band off and counts those ten sticks as ones. A band that is still tied is a ten that remains.