Two things happen
A school fair takes $345 in the morning and $187 more in the afternoon. Then it pays $268 for the tent. How much money does the fair have left?
Two things happen in this story. Money comes in, and then money goes out. One calculation cannot do both, so the problem takes two steps, one for each thing that happens, in the order they happen.
Step one: the total
First find how much the fair took. The morning and the afternoon are two parts of one total, so add them: 345 + 187. In columns, the ones give 5 + 7 = 12, so write 2 and carry 1. The tens give 1 + 4 + 8 = 13, so write 3 and carry 1. The hundreds give 1 + 3 + 1 = 5. The fair took $532.
The morning and the afternoon are two parts of one bar. The whole bar is 345 + 187 = 532.
The ones and the tens both carry: 345 + 187 = 532.
Step two starts from the first answer
Now the fair pays for the tent. The $268 comes out of the money the fair has at that moment, which is the $532 from step one, not the $345 it had in the morning. So step two is 532 − 268.
In columns, the ones ask for 2 − 8, so borrow a ten: 12 − 8 = 4. The tens are now 2, and 2 − 6 needs a borrow too, so borrow a hundred: 12 − 6 = 6. The hundreds are now 4, and 4 − 2 = 2. The fair has $264 left.
The same whole of 532 is now split into the 268 paid for the tent and the part that is left: 532 − 268 = 264.
A borrow for the ones and a borrow for the tens: 532 − 268 = 264.
One chain
The two steps make a chain. 345 goes in, adding 187 makes 532, and taking away 268 makes 264. Each step works on the answer the step before it made.
Check the answer by running the chain backward: 264 + 268 = 532, and 532 − 187 = 345, the amount the fair took in the morning.
The answer to step one, 532, is the number step two starts from.
Two slips
Stopping after one step is the usual mistake. $532 is the money the fair took, but the question asks for the money left, and the tent has not been paid for yet.
The other slip is to start step two from the wrong number. Taking the $268 away from the $345 of the morning leaves out the afternoon. Draw the bar first, and each step shows which number it starts from.
Worked example: Some Are Added, Then Some Are Taken Away
Question A fruit seller has 1465 apples. A lorry brings him 2378 more apples. Then he sells 1856 apples. (a) How many apples does he have after the lorry comes? (b) How many apples does he have left after selling?
1.First the apples are joined. Draw the 1465 apples and the 2378 apples as two parts of one bar. Add: 1465 + 2378.
First the apples are joined, so add. 2.(a) Ones: 5 + 8 = 13, so write 3 and carry 1. Tens: 6 + 7 + 1 = 14, so write 4 and carry 1. Hundreds: 4 + 3 + 1 = 8. Thousands: 1 + 2 = 3. He has 3843 apples.
(a) 5 + 8 = 13, 6 + 7 + 1 = 14, 4 + 3 + 1 = 8 and 1 + 2 = 3. He has 3843 apples. 3.Now 3843 is the whole. The 1856 apples sold are one part, and the apples left are the other part. Subtract: 3843 − 1856.
Now 3843 is the whole, and the 1856 apples sold are one part. Subtract. 4.Ones: 3 is less than 6, so borrow a ten: 13 − 6 = 7. Tens: 3 is less than 5, so borrow a hundred: 13 − 5 = 8.
Ones: borrow a ten, 13 − 6 = 7. Tens: borrow a hundred, 13 − 5 = 8. 5.(b) Hundreds: 7 is less than 8, so borrow a thousand: 17 − 8 = 9. Thousands: 2 − 1 = 1. He has 1987 apples left. Check: 1987 + 1856 = 3843.
(b) Hundreds: 17 − 8 = 9. Thousands: 2 − 1 = 1. He has 1987 apples left.
Answer: (a) 3843 apples; (b) 1987 apples
Common mistakes
- Subtracting 1856 from 1465, the number at the start. The apples are sold after the lorry comes, so subtract from 3843.
- Doing only one step. The story has two changes, first more apples and then fewer apples, so it needs an addition and then a subtraction.
More written addition and subtraction problems, worked step by step →
Worked example: Two Things Bought, the Money Left
Question Mrs Lim has $1000. She buys a bed for $468 and a desk for $275. (a) How much does she spend altogether? (b) How much money does she have left?
1.Draw one bar for the $1000. Two parts are spent, $468 and $275. The last part is the money left. Find the money spent first.
The $1000 is the whole. Two parts are spent and the last part is left. 2.(a) 468 + 275. Ones: 8 + 5 = 13, so write 3 and carry 1. Tens: 6 + 7 + 1 = 14, so write 4 and carry 1. Hundreds: 4 + 2 + 1 = 7. She spends $743 altogether.
(a) 8 + 5 = 13, 6 + 7 + 1 = 14 and 4 + 2 + 1 = 7. She spends $743. 3.The money left is 1000 − 743. Ones: 0 is less than 3. The tens and the hundreds are 0 too, so borrow from the thousands. The thousands become 0, the hundreds become 9, the tens become 9 and the ones become 10.
The ones, tens and hundreds of 1000 are all 0. Borrow from the thousands: 0, 9, 9 and 10. 4.(b) Ones: 10 − 3 = 7. Tens: 9 − 4 = 5. Hundreds: 9 − 7 = 2. She has $257 left. Check: 1000 − 468 = 532 and 532 − 275 = 257.
(b) 10 − 3 = 7, 9 − 4 = 5 and 9 − 7 = 2. She has $257 left.
Answer: (a) $743; (b) $257
Common mistakes
- Writing 9 above every zero. The ones column becomes 10, not 9, because it keeps the ten that it borrowed and lends nothing.
- Taking away only the bed and stopping at $532. She buys two things, so both prices come off the $1000.
More written addition and subtraction problems, worked step by step →