Paper Together: sit a paper in a room with your friends.See how it works
This page sets out the method for addition & subtraction in the order you would use it, then walks through the full lesson explanation. For three complete worked examples with the slips that cost marks, see the Addition & subtraction topic page.
When you see 'total', 'altogether', 'sum' or 'add', set out a column addition.
When you see 'difference', 'how many more', 'change' or 'left over', set out a column subtraction with the larger number on top.
A two-digit number is tens plus ones. 48 is 4 tens and 8 ones, which is 40 + 8.
Keep the tens together when you add. It is easier than counting on in ones.
To add 48 + 27, add the tens first: 48 + 20 = 68. Then add the ones: 68 + 7 = 75.
If the ones go past 9, that extra ten has to join the tens. 68 + 7 is 70 + 5 = 75, not 615.
Subtraction can mean “how many from here to there”. From 40 to 70 is 30, so 70 − 40 = 30.
You do not need to count back in ones when the gap is whole tens.
For 83 − 25, take away 20 first: 83 − 20 = 63. Then take away 5: 63 − 5 = 58.
If you cannot take the ones away, break a ten first. 63 − 5 uses one of the tens.
“Altogether”, “total” and “sum” mean add. “Left”, “difference” and “how many more” mean subtract.
Write the calculation before you work it out, so the operation matches the story.
Addition and subtraction undo each other. If 48 + 27 = 75, then 75 − 27 should come back to 48.
A check that does not return the start means a digit slipped.
The order of an addition does not change the total. The columns do. In 407 + 58 the 5 is tens, so it sits under the 0, and the 8 sits under the 7. An empty hundreds place on the second number is a blank, which you treat as zero.
Add the units first. In 407 + 58 the units are 7 + 8 = 15. Write 5 and carry 1 ten. The tens column is then 0 + 5 + 1 = 6. The hundreds column is 4. The total is 465.
If two carries happen in a row, keep going. 699 + 46: units 9 + 6 = 15, write 5 carry 1; tens 9 + 4 + 1 = 14, write 4 carry 1; hundreds 6 + 1 = 7. The total is 745. If the answer has an extra digit glued on, such as 6915, the carry was written in the answer instead of moved.
Method: 1. Line the units up, then add each column from the right. 2. If a column totals 10 or more, write the units digit and carry the tens. 3. Read the answer back, including any final carry.
Work out 500 - 168. Put the starting number on top. Begin at the units. The top units digit is 0 and you need to take away 8, so exchange. The tens digit is also 0, so the exchange has to come from the hundreds. The 5 becomes 4. One hundred is 10 tens, so the tens column becomes 10, then you still need units.
Exchange one of those tens into the units. Tens fall from 10 to 9, and units become 10. Now subtract: units 10 - 8 = 2, tens 9 - 6 = 3, hundreds 4 - 1 = 3. The difference is 332. Check by adding: 332 + 168 returns 500, so the subtraction stands.
Never swap the digits inside a column to avoid an exchange. In the units of 500 - 168, doing 8 - 0 = 8 because 8 is bigger is a different calculation. That gives 468, and adding 168 back does not return 500. If a whole column is zero, keep exchanging from the first column to the left that has something to give.
Method: 1. Put the larger number on top and line the columns up. 2. If the top digit is smaller, exchange one ten from the column on its left. 3. Subtract each column from the right and write the digits underneath.
A decimal point marks where the units column ends. Tenths sit immediately to its right, then hundredths. Line the points up before you add or subtract. In 3.45 + 1.28 the hundredths are 5 + 8 = 13, so write 3 and carry 1 tenth. The total is 4.73.
Money in pounds is a two-place decimal. 45 pence is £0.45. If one amount is a whole number of pounds, write the missing pence as zeros: £20 is £20.00 when it sits above £7.64. The zeros hold the tenths and hundredths so the 7 stays in the units.
Keep two decimal places in a money answer. 4.7 pounds is 4 pounds and 70 pence, written £4.70 when the answer is money. Do not round a shop total to the nearest pound unless the question asks for an estimate. The hundredths are the pence.
Method: 1. Line the decimal points up before you add or subtract. 2. Fill empty places with zeros so every column has a digit. 3. Keep two decimal places for money, and check the pounds are sensible.
Change asks what is left from a payment. Add the costs first if there is more than one item, then subtract that total from the money handed over. Maya pays with a £20 note for something costing £7.64. The calculation is 20.00 - 7.64. It is not 7.64 - 20 and it is not 20 - 7 = 13 with the 64 pence copied on the end.
The subtraction crosses several zeros. Exchange from the left until the hundredths column has 10. After the exchanges you have 1 ten, 9 units, 9 tenths and 10 hundredths. Then 10 - 4 = 6, 9 - 6 = 3 and 9 - 7 = 2. The change is £12.36.
Check a change answer by adding the change back onto the cost. 12.36 + 7.64 lands on 20.00, the note she paid with. If the check misses the payment, an exchange was dropped. Altogether and total mean add. Left, difference, how much more and change mean subtract.
Method: 1. Add the prices first if more than one item was bought. 2. Subtract that total from the amount paid. 3. Check the change plus the bill comes back to the note.
Exam questions on adding and subtracting often finish with a number that is easy to get wrong by one column. Two quick checks catch nearly every slip. First estimate: round each number to the nearest ten or hundred and add or subtract those. Your exact answer must be close to the estimate.
Second, use the inverse. If a + b = c then c - b must give a back. If a - b = c then c + b must give a back. A check takes ten seconds and is worth doing on every question with more than one step.
Method: 1. Round each number to something easy, such as the nearest ten. 2. Add or subtract the rounded numbers to get an estimate. 3. Do the exact calculation using columns. 4. Compare with the estimate, then undo the calculation with the inverse operation.
Tip: If your exact answer and your estimate are more than a ten apart, find the slip before moving on.
In a worded question the arithmetic is rarely the hard part. The skill is deciding what to add and what to take away. Underline the amounts, then ask what the question wants: a total, a difference, an amount left, or change.
"How much more" and "difference" both mean subtract the smaller from the larger. "Total", "altogether" and "in all" mean add. "Change" means payment minus cost. Write a short line such as change = 20 - 13.40 before you calculate, so the method mark is safe even if the subtraction slips.
Method: 1. Underline every amount and note the units. 2. Decide whether the question needs a total, a difference or a change. 3. Write the calculation as a line of working. 4. Work it out in columns and write the units in the answer.
AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.