Paper Together: sit a paper in a room with your friends.See how it works
This page sets out the method for calculation problems 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 Calculation problems topic page.
When you see a paragraph of information, turn it into a list of short calculations with a word label on each.
When you see money or measures, round the numbers to check your answer is the right size before you finish.
“Each”, “rows of” and “per” usually mean multiply.
“Left”, “change” and “how many more” usually mean subtract.
Find the equal groups first.
Add or subtract the loose amount afterwards.
A total of groups should be bigger than one group.
An amount left should be smaller than the start.
Write the first calculation, then use that result in the second.
Do not squash both steps into one addition.
The answer is still seats, pens or pounds.
A bare number with the wrong unit is not finished.
A rough size tells you if the answer is sensible.
48 pens cannot become 14 if you were meant to multiply.
Read for the action, not for the first number you notice. Rafi buys 7 bags with 8 apples in each bag. The bags are equal, so each means multiply: 7 × 8. Shared equally between 7 people would be a division. How many more apples than bags would be a subtraction.
Money uses the same test. A price written as £4.75 each is the cost of one item, so three items cost 3 × 4.75. How much change from £36.50 is a subtraction, but only after the full cost is known. Subtracting the price of one plant, when three plants and a pot were bought, leaves too much money.
Write one line of symbols for each action. If the story has two events, expect two operations and keep them in that order. Name what the first line counts: apples, books, or pounds.
Method: 1. Read the story for the action before you pick an operation. 2. Equal groups mean multiply, and sharing equally means divide. 3. Write the calculation in symbols, then work it out.
Do the equal groups before you add an extra or take something away. Nine shelves with 14 books on each shelf hold 9 × 14 = 126 books. Moving 23 books to the stock room happens after the shelves are filled, so the second line is 126 - 23 = 103. Adding 9 + 14, or adding the 23 onto the 126, answers a question the story did not ask.
Two different prices are two products. Four sandwiches at £2.50 and six drinks at £1.25 are 4 × 2.50 and 6 × 1.25. Add those costs at the end. Adding 4 + 6 and then multiplying by £2.50 pretends the drinks cost the same as the sandwiches. They do not.
Keep a running total you can point at. After the first line, write what the number means: 126 books on the shelves, or £10 for the sandwiches. The second line uses that meaning. A bare number with no unit is easy to drop into the wrong operation on the next line.
Method: 1. Do the equal groups first. 2. Then add the extra amount or subtract what is taken away. 3. Check the second step uses the result of the first.
A pound is 100 pence. The two digits after the decimal point are the pence. £4.75 means 4 pounds and 75 pence. Six pounds exactly, in a money answer, is written £6.00. An answer of 16.2 pounds is not finished: write £16.20 if the second digit really is zero, and £16.25 if the hundredths digit is 5.
Line the decimal points up when you add or subtract. £14.25 + £6.00 = £20.25. For £36.50 - £20.25, the pence can be done on their own when the top pence are larger: 50 pence minus 25 pence is 25 pence, and 36 pounds minus 20 pounds is 16 pounds. Joined, that is £16.25.
Multiply a price by a whole number in two pieces if you are working without a calculator. For £4.75 × 3, three lots of 4 pounds is £12, and three lots of 75 pence is 225 pence, which is £2.25. Together that is £14.25. A price ending in 75 pence, multiplied by 3, ends in 25 pence, because 75 × 3 = 225.
Method: 1. Keep pounds and pence as two decimal places. 2. Multiply or add the prices, then round money only if asked. 3. A whole number of pounds still needs the pence written as .00 when the question uses money.
Decide what a sensible answer looks like before you commit to it. Seven bags must contain more apples than one bag, so 56 can be right and 15 cannot. Money left after shopping must be less than the money at the start. A bill for sandwiches and drinks must be more than the sandwiches alone.
A rough estimate catches a wrong operation. 7 × 8 is near 7 × 10 = 70, so 56 is in range. £4.75 × 3 is near £5 × 3 = £15, so £14.25 is in range and £7.75 is not. If the exact answer is nowhere near the estimate, redo the operation. Do not change the estimate to match a suspicious answer.
The unit is part of the check. 56 is a number of apples. £16.25 is pounds left. If the question asks for a cost, do not stop at how many items were bought. A division has a check too: £18 shared by 4 people is £18 ÷ 4 = £4.50 each, and four lots of £4.50 come back to £18.
Method: 1. Decide whether the answer should be bigger or smaller than the start. 2. Compare your result with one group or one item. 3. If the size is wrong, the operation was the wrong way round.
Shopping questions in exams bring in offers and payment plans. "Three for the price of two" means you pay for only two out of every three items. Seven items at £8.50 each contain two complete groups of three, so you pay for 2 + 2 = 4 items from those, plus the single extra one, which makes 5 items in all, 5 × 8.50 = £42.50.
A payment plan has a deposit and then equal payments. A bicycle with a deposit of £60 and 12 monthly payments of £28.50 costs 60 + 12 × 28.50 = £402 altogether. The deposit is only paid once, so it is added to the total of the payments and not added to each payment. Then compare with the cash price to find how much extra the plan costs. Set out each stage on its own line so partial marks are easy to give.
Method: 1. Work out how many items are paid for after the offer. 2. Multiply the number of payments by the amount of each payment. 3. Add the deposit once, and then compare with the cash price. 4. Write the answer in pounds, with two decimal places where the money is not a whole number.
Tip: For "3 for 2", find the number of complete groups of three and count the leftover items separately.
To compare two deals you need a price for the same amount in each. Find the cost of one can, one litre or one gram, and compare. Six cans for £2.40 cost 2.40 ÷ 6 = £0.40 a can. Ten cans for £3.80 cost 3.80 ÷ 10 = £0.38 a can. The ten-pack is better value because each can costs less.
Always divide the price by the amount, not the other way round. The amount per pound is another valid way, as long as you compare like with like. Write a sentence that names the better deal and quotes both unit prices: "The ten-pack is better value because 38p per can is less than 40p per can". The final sentence is worth a mark of its own, so do not leave the working unfinished.
Method: 1. Divide each price by its quantity to get a price for one item. 2. Write both unit prices with the same units. 3. Compare them and choose the cheaper unit price as the better value. 4. Write a sentence that names the deal and quotes both prices.
Some questions give the total and ask for a quantity inside it. "Saj buys 8 rulers at 45p each and some pens at 80p each. The total cost is £10. How many pens does he buy?" First find the cost of the part you know: 8 × 0.45 = £3.60. Take it from the total: 10 - 3.60 = £6.40. That is the money spent on pens.
Now divide by the price of one pen: 6.40 ÷ 0.80 = 8 pens. Check by running the story forwards: 8 rulers cost £3.60, 8 pens cost £6.40, and the total is £10. Work in pounds throughout, or convert everything to pence, but do not mix. Writing 45p as 0.45 in pounds before multiplying prevents slips with the decimal point.
Method: 1. Work out the cost of the part that is fully known. 2. Subtract it from the total to find what is left. 3. Divide what is left by the price of one of the unknown items. 4. Check by working forwards through the story to the total.
Pay questions combine two rates. A worker is paid £11.50 an hour for 35 hours and £17 an hour for 6 hours overtime. Work out each part separately: 35 × 11.50 = £402.50 and 6 × 17 = £102. Then add them to get £504.50. Keep the pounds and pence in the right columns, and write the pound sign in the final answer.
Grouping questions bring in remainders. Eggs come in boxes of 12 and a baker needs 100 eggs. 100 ÷ 12 = 8.33ldots, but 8 boxes hold only 96 eggs, which is too few. She must buy 9 boxes, which hold 108 eggs, so 8 eggs are left over. Rounding up, when the story needs enough to cover everything, is a skill that these questions check again and again.
Method: 1. Work out each rate multiplied by its time or quantity. 2. Add the separate parts to get the total. 3. For grouping, divide and look at the remainder. 4. If the story needs everyone covered, round up to the next whole group.
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