Calculation Problems
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Revision notes for Edexcel GCSE Maths Calculation Problems. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Maths (1MA1) specification, so the content matches what's examinable rather than general Maths background.

Calculation Problems

What you'll learn

  • Choose whether to add, subtract, multiply or divide.
  • Work accurately with pounds and pence.
  • Deal with “as many as possible” and “enough for” questions.
  • Check your answer makes sense in a real-life situation.

The basic routine

Definition

Calculation problem and operation

A calculation problem is a word question where you decide what maths to do from the information given. An operation is a maths action: add, subtract, multiply, or divide.

Most Grade 2 calculation problems are about everyday situations: shopping, payments, items in packs, lengths, mass, or liquid.

Definition

Unit

A unit is the label for an amount, such as p, £, cm, ml, g, or litres. Units tell you what the number means.

Key Idea

Main routine

Make the units match first, then calculate, then answer in the units asked for.

Money questions: total cost and change

Definition

Change

Change is the money you get back when you pay more than the total cost.

In money questions, it is often easiest to work in pence. Remember: 100p makes £1.

Example

Buying items and finding change

Aisha buys 7 cakes. Each cake costs 62p. She pays with a £10 note.

Seven cakes at 62p each are paid for with £10, so the change is the part of the £10 left after the total cost.

  1. Convert £10 into pence: £10 is 1000p.

  2. Find the total cost of 7 cakes:

    7×62=4347 \times 62 = 4347×62=434

  3. Subtract the cost from the amount paid:

    1000−434=5661000 - 434 = 5661000−434=566

  4. Convert 566p back into pounds and pence. The change is £5.66.

  5. If the price of each cake goes up, the total cost goes up, so the change goes down.

Common Mistake

Mixing pounds and pence

Do not subtract pence from pounds directly. Convert everything to pence first, or everything to pounds first.

“As many as possible”: divide and look at what is left

Sometimes a question asks how many items someone can buy, make, or cut. You can only use whole items in these questions.

Definition

Remainder

A remainder is the amount left over when you divide but cannot make another full group.

Example

Buying as many bars as possible

Ben has £4 to spend. Each snack bar costs 35p. Work out his change if he buys as many as possible.

The £4 budget is divided into as many full 35p snack bars as possible, with the leftover amount as change.

  1. Convert £4 into pence: £4 is 400p.

  2. Divide 400p by 35p to see how many full bars he can buy:

    400÷35=11 remainder 15400 \div 35 = 11 \text{ remainder } 15400÷35=11 remainder 15

  3. So Ben can buy 11 bars, with 15p left over.

  4. His change is 15p.

Tip

As many as possible

If buying one more item would cost too much, stop. The leftover amount is the change.

Several items and grouped prices

A question may give prices like “5 for 80p” or “10 for £2.40”.

Definition

Group price and pack

A group price tells you the cost for several items together. A pack is a group of items sold together.

Work out how many groups are needed, then multiply by the group price.

Example

Using a price list

A teacher buys 20 pens, 30 rulers, and 5 calculators. Pens cost 5 for 80p, rulers cost 10 for £2.40, and calculators cost £4.50 each. Find the total cost.

The items are organised into price groups before adding the three separate costs.

  1. Pens: 20 pens means 4 groups of 5. The pen cost in pence is:

    4×80=3204 \times 80 = 3204×80=320

  2. Rulers: £2.40 is 240p, and 30 rulers means 3 groups of 10. The ruler cost is:

    3×240=7203 \times 240 = 7203×240=720

  3. Calculators: £4.50 is 450p each. The calculator cost is:

    5×450=22505 \times 450 = 22505×450=2250

  4. Add the costs in pence:

    320+720+2250=3290320 + 720 + 2250 = 3290320+720+2250=3290

  5. 3290p is £32.90, so the teacher spends £32.90.

Paying some now and the rest later

Definition

Deposit and instalment

A deposit is money paid at the start. An instalment is one of the equal payments made later.

To find each equal payment, subtract the deposit first, then divide what is left.

Example

Deposit and monthly payments

A bike costs £540. Priya pays a deposit of £120, then pays the rest in 12 equal monthly payments.

The total bike cost is split into the deposit and 12 equal instalments for the remaining amount.

  1. Work in pounds. Subtract the deposit:

    540−120=420540 - 120 = 420540−120=420

  2. Divide the remaining amount by 12:

    420÷12=35420 \div 12 = 35420÷12=35

  3. Each monthly payment is £35.

Finding the cost of one item

Definition

Unit cost

The unit cost is the cost of one item.

If you know the cost of several identical items, divide to find the cost of one.

Example

Pens and pencils

Tom buys 2 pens and 3 pencils for £1.05. Raj buys 4 pens for £1.20. Work out the cost of 1 pen and 2 pencils.

Raj's purchase finds the cost of one pen, then Tom's purchase can be used to find the pencil cost.

  1. Convert £1.20 to 120p. Find the cost of 1 pen:

    120÷4=30120 \div 4 = 30120÷4=30

  2. So 1 pen costs 30p. Find the cost of 2 pens:

    2×30=602 \times 30 = 602×30=60

  3. Convert £1.05 to 105p. Subtract the cost of 2 pens to find the cost of 3 pencils:

    105−60=45105 - 60 = 45105−60=45

  4. Find the cost of 1 pencil:

    45÷3=1545 \div 3 = 1545÷3=15

  5. Find the cost of 1 pen and 2 pencils:

    30+2×15=6030 + 2 \times 15 = 6030+2×15=60

  6. The cost is 60p.

Checking if there is enough money

Definition

Budget

A budget is the amount of money available to spend.

To decide if someone has enough money, find the total cost first, then compare it with the budget.

Example

Does he have enough?

Owen wants to buy 20 calculators and 20 folders. 2 calculators cost £9.80. 3 folders cost £2.40. Owen has £110.

Owen's total calculator and folder cost must be compared with his £110 budget.

  1. Convert £9.80 to 980p. Find the cost of 1 calculator:

    980÷2=490980 \div 2 = 490980÷2=490

  2. Find the cost of 20 calculators:

    20×490=980020 \times 490 = 980020×490=9800

  3. Convert £2.40 to 240p. Find the cost of 1 folder:

    240÷3=80240 \div 3 = 80240÷3=80

  4. Find the cost of 20 folders:

    20×80=160020 \times 80 = 160020×80=1600

  5. Add the costs:

    9800+1600=114009800 + 1600 = 114009800+1600=11400

  6. 11400p is £114, so Owen does not have enough money. He is short by £4.

Tip

Show your answer

If the question says “show that” or “does he have enough?”, you need a calculation and a final sentence.

Measures: litres, millilitres, grams, and packs

Definition

Convert

To convert means to change an amount into an equal amount using a different unit, such as litres to millilitres.

Useful facts:

  • 1 litre is 1000 ml.
  • 100 cm is 1 m.
  • 1000 g is 1 kg.
Example

Making full cups

A jug contains 1.6 litres of water. Each cup needs 180 ml. Work out how many full cups can be made.

The jug amount must be converted to millilitres and divided into full 180 ml cups, leaving any extra water unused.

  1. Convert 1.6 litres to millilitres: 1.6 litres is 1600 ml.

  2. Check how many full cups fit:

    1600÷180=8 remainder 1601600 \div 180 = 8 \text{ remainder } 1601600÷180=8 remainder 160

  3. There is not enough water for a 9th cup, so 8 full cups can be made.

Example

Buying enough packs

A washing powder pack contains 600g. Sam uses 45g for each wash and does 2 washes each week. He wants enough for 10 weeks.

Sam needs enough powder for all 10 weeks, so the required amount is compared with 600g packs.

  1. Find how much powder is used each week:

    2×45=902 \times 45 = 902×45=90

  2. Find how much powder is needed for 10 weeks:

    10×90=90010 \times 90 = 90010×90=900

  3. One pack gives 600g, which is not enough for 900g.

  4. Two packs give 1200g, so Sam needs 2 packs.

Common Mistake

Round the right way

To round down means choose the lower whole number; to round up means choose the higher whole number. For full cups or cut lengths, round down. For buying enough packs, round up.

Exam technique

In the exam

  1. Underline the important numbers and units before calculating.

  2. Convert units early, especially pounds to pence or litres to millilitres.

  3. Write a final sentence, such as “She gets £4.20 change” or “He does not have enough money.”

Self review

Check yourself

  • Can you explain when to multiply and when to divide in a shopping question?

  • If you have a remainder, should you always round up?

  • Have you checked that your final answer uses the correct unit?

Recap questions

Test yourself with 5 quick questions on this guide. Answer them all correctly to complete it.

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