When the top digit is too small
Work out 52 − 27 in columns. Write 27 under 52 with the ones under the ones, and start with the ones column, on the right.
The ones column asks for 2 − 7. There are only 2 ones, and 7 ones cannot be taken away from 2, so this column cannot be subtracted yet. The tens column can help, because it has 5 tens.
The ones column is 2 − 7, and 2 is smaller than 7.
Borrow one ten
Take one ten from the 5 tens. The tens drop to 4: cross out the 5 and write 4 above it. The ten you took is ten ones, and they join the 2 ones already in the ones column: 10 + 2 = 12. Write 12 above the ones column.
The number has not changed. 52 is 5 tens and 2 ones, and it is also 4 tens and 12 ones, because 40 + 12 = 52. Only the way it is split into tens and ones is different.
One ten has been broken into ten ones. 4 tens and 12 ones are still 52.
The 5 tens drop to 4, and the ones become 12.
5 tens + 2 ones = 52: breaking changes the digits, not the number
Break what the columns need to take away 27
Breaking a ten turns the 5 tens and 2 ones into 4 tens and 12 ones. The digits change, and the number is still 52.
Subtract each column
Now every column can be subtracted. The ones: 12 − 7 = 5. The tens: 4 − 2 = 2. The answer is 25.
Check it by adding: 25 + 27 = 52. The answer and the number taken away must add up to the number you started with.
12 − 7 = 5 and 4 − 2 = 2. The answer is 25.
A borrow in more than one column
Bigger numbers can need a borrow in more than one column, and each borrow is the same move. Work out 634 − 258. The ones ask for 4 − 8, so borrow a ten: the 3 tens drop to 2, and the ones become 14. 14 − 8 = 6.
The tens now ask for 2 − 5, so borrow a hundred: the 6 hundreds drop to 5, and one hundred is ten tens, so the tens become 12. 12 − 5 = 7. The hundreds: 5 − 2 = 3. So 634 − 258 = 376, and 376 + 258 = 634 checks it.
A ten is borrowed for the ones, then a hundred for the tens: 634 − 258 = 376.
Two slips
The usual mistake is to take the smaller digit from the bigger one in every column, and work out 7 − 2 in the ones. But the ones column is the top digit take away the bottom digit, 2 − 7, so it needs a borrow.
The other slip is to borrow the ten and leave the tens digit as 5. The ten has left the tens column, so only 4 tens are left. In 52 − 27 both slips give 35, and adding back catches them: 35 + 27 = 62, not 52.
Worked example: A Whole and One Part, the Other Part Missing
Question There are 5342 people at a concert. 2678 of them are adults and the rest are children. (a) How many children are at the concert? (b) 1395 of the children are girls. How many boys are at the concert?
1.Draw one bar for the 5342 people. One part is the 2678 adults. The other part is the children, so subtract: 5342 − 2678.
The people are the whole. The adults are one part, so subtract to find the children. 2.Write 2678 under 5342. Ones: 2 is less than 8, so borrow a ten. The tens become 3 and the ones become 12. 12 − 8 = 4.
Ones: 2 is less than 8. Borrow a ten: the tens become 3 and the ones become 12. 12 − 8 = 4. 3.(a) Tens: 3 is less than 7, so borrow a hundred: 13 − 7 = 6. Hundreds: 2 is less than 6, so borrow a thousand: 12 − 6 = 6. Thousands: 4 − 2 = 2. There are 2664 children.
(a) Tens: 13 − 7 = 6. Hundreds: 12 − 6 = 6. Thousands: 4 − 2 = 2. There are 2664 children. 4.The children are a whole too. The girls are one part, so the boys are 2664 − 1395. Ones: borrow a ten, 14 − 5 = 9. Tens: 5 is less than 9, so borrow a hundred: 15 − 9 = 6.
The girls are one part of the children. Ones: 14 − 5 = 9. Tens: 15 − 9 = 6. 5.(b) Hundreds: 5 − 3 = 2. Thousands: 2 − 1 = 1. There are 1269 boys. Check: 1269 + 1395 = 2664.
(b) Hundreds: 5 − 3 = 2. Thousands: 2 − 1 = 1. There are 1269 boys.
Answer: (a) 2664 children; (b) 1269 boys
Common mistakes
- Taking the smaller digit from the larger digit in every column, such as 8 − 2 in the ones. The top number is 5342, so the ones are 12 − 8 after a ten is borrowed.
- Borrowing a ten and leaving the tens digit as 4. The ten that was borrowed has left the tens column, so the 4 must be crossed out and 3 written above it.
More written addition and subtraction problems, worked step by step →