A zero has nothing to lend
Work out 304 − 127. The ones column asks for 4 − 7, and 4 is smaller than 7, so you need to borrow a ten from the tens column.
But the tens digit of 304 is 0. There are no tens in the tens column, so there is no ten to take.
The ones column is 4 − 7, and the tens column above it holds a 0.
Go one column further
So go one more column to the left, to the hundreds. Take one of the 3 hundreds: cross out the 3 and write 2 above it. One hundred is ten tens, so the tens column, which had none, now has 10 tens. Cross out the 0 and write 10 above it.
The 3 hundreds drop to 2, and the 0 tens become 10 tens.
Now the tens can lend
Now the tens column has something to lend. Take one ten: the 10 tens drop to 9, and the ten ones join the 4 ones, so the ones become 14.
The number is still 304. 2 hundreds, 9 tens and 14 ones make 200 + 90 + 14 = 304. That is why a 9 appears where the 0 was: one hundred has been broken into 9 tens and 10 ones.
2 hundreds, 9 tens and 14 ones are still 304.
The 10 tens drop to 9, and the ones become 14.
3 hundreds + 0 tens + 4 ones = 304: breaking changes the digits, not the number
Break what the columns need to take away 127
With 0 tens there is no ten to break, so the hundred goes first. Its 10 tens can then lend one ten to the ones, and the number is still 304.
Subtract each column
Every column can be subtracted now. The ones: 14 − 7 = 7. The tens: 9 − 2 = 7. The hundreds: 2 − 1 = 1. The answer is 177.
Check by adding: 177 + 127 = 304.
14 − 7 = 7, 9 − 2 = 7 and 2 − 1 = 1. The answer is 177.
Two zeros
Work out 500 − 238. The ones ask for 0 − 8, and the tens digit is 0 too, so the borrow goes to the hundreds. The 5 hundreds drop to 4, and the tens become 10. Then the tens lend one ten: they drop to 9, and the ones become 10.
The ones column becomes 10, not 9. It keeps the ten it borrowed and lends nothing. Now subtract: 10 − 8 = 2, 9 − 3 = 6 and 4 − 2 = 2, so 500 − 238 = 262.
The hundred breaks into 9 tens and 10 ones: 500 − 238 = 262.
Cross off what was lent
Every column that lends goes down by one. If the 3 hundreds of 304 are not crossed out and changed to 2, the answer comes out as 277, a hundred too big. And the 10 tens lend just one ten, so they become 9, not 8. Writing 8 in the tens gives 167, ten too small.
Worked example: Two Amounts Compared: How Many More
Question A zoo had 4052 visitors on Saturday and 2786 visitors on Sunday. (a) How many more visitors came on Saturday than on Sunday? (b) On Monday there were 1895 visitors. How many fewer visitors came on Monday than on Sunday?
1.Draw a bar for Saturday and a shorter bar for Sunday under it. The part of the Saturday bar that goes past the Sunday bar is the difference, so subtract: 4052 − 2786.
The dotted part is how much longer the Saturday bar is. It is the difference, so subtract. 2.Ones: 2 is less than 6, so borrow a ten. The tens become 4 and the ones become 12. 12 − 6 = 6.
Ones: 2 is less than 6. Borrow a ten: the tens become 4 and the ones become 12. 12 − 6 = 6. 3.(a) Tens: 4 is less than 8, and the hundreds digit is 0, so borrow from the thousands. The thousands become 3, the hundreds become 9 and the tens become 14. 14 − 8 = 6. Hundreds: 9 − 7 = 2. Thousands: 3 − 2 = 1. 1266 more visitors came on Saturday.
(a) The hundreds digit is 0, so borrow from the thousands: 3, 9 and 14. 14 − 8 = 6, 9 − 7 = 2, 3 − 2 = 1. The answer is 1266. 4.Now compare Monday with Sunday. Draw the Monday bar under the Sunday bar and subtract: 2786 − 1895. Ones: 6 − 5 = 1. Tens: 8 is less than 9, so borrow a hundred: 18 − 9 = 9.
Monday is compared with Sunday. Ones: 6 − 5 = 1. Tens: borrow a hundred, 18 − 9 = 9. 5.(b) Hundreds: 6 is less than 8, so borrow a thousand: 16 − 8 = 8. Thousands: 1 − 1 = 0. 891 fewer visitors came on Monday. Check: 1895 + 891 = 2786.
(b) Hundreds: 16 − 8 = 8. Thousands: 1 − 1 = 0. 891 fewer visitors came on Monday.
Answer: (a) 1266 visitors; (b) 891 visitors
Common mistakes
- Adding the two numbers because the question says "more". "How many more" asks for the difference between the two bars, and a difference is found by subtracting.
- Trying to borrow from the 0 in the hundreds of 4052 and stopping there. A zero has nothing to lend, so borrow from the thousands first. The 0 becomes 10, and then it lends one hundred to the tens and becomes 9.
More written addition and subtraction problems, worked step by step →