GCSE Maths / Edexcel

Four operations with integers

Add, subtract, multiply, and divide whole numbers accurately, choosing a reliable written method when mental methods are not enough.

Number and Place ValueFoundationGrades 1 to 4Skill

Curriculum path: GCSE Maths > Edexcel > Number > Four operations with integers

Pearson Edexcel GCSE Maths number: use the four operations with integers and apply arithmetic fluently.

Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

The four operations are addition, subtraction, multiplication, and division. GCSE questions often mix them with money, measures, averages, ratio, and problem solving.

For addition and subtraction, line up the place value columns. Ones go under ones, tens under tens, hundreds under hundreds.

For multiplication, break the calculation into parts or use a written method. For example, 24 x 13 means 24 x 10 plus 24 x 3.

For division, think about equal groups. In short division, divide each place value column and carry remainders carefully.

Always estimate first when the numbers are large. An estimate helps you spot impossible answers, such as a multiplication answer that is too small.

In Edexcel Foundation papers, method marks are often available even if the final answer is wrong. Show your written method clearly, especially for multi-step questions.

Key ruleLine up place values for add and subtract; split or use a written method for multiply and divide.

Worked examples

Column addition

Work out 378 + 546.

  1. Add the ones: 8 + 6 = 14, write 4 and carry 1 ten.
  2. Add the tens: 7 + 4 + 1 = 12, write 2 and carry 1 hundred.
  3. Add the hundreds: 3 + 5 + 1 = 9.

Answer: 924

Subtraction with exchanging

Work out 503 - 278.

  1. You cannot do 3 - 8, so exchange from the tens. The tens column is 0, so exchange from the hundreds first.
  2. 503 becomes 4 hundreds, 9 tens, and 13 ones.
  3. 13 - 8 = 5, 9 - 7 = 2, and 4 - 2 = 2.

Answer: 225

Multiplication by partitioning

Work out 36 x 14.

  1. Split 14 into 10 and 4.
  2. 36 x 10 = 360.
  3. 36 x 4 = 144.
  4. 360 + 144 = 504.

Answer: 504

Common mistakes

  • Not lining up place values in column addition or subtraction.
  • Forgetting to carry or exchange.
  • Multiplying by only one digit in a two-digit multiplication.
  • Dividing in the wrong direction, such as doing 6 divided by 84 instead of 84 divided by 6.
  • Not checking whether the answer is sensible.

Quick exercise

Try these before moving to the exam-style questions.

  1. Work out 247 + 386.
  2. Work out 900 - 458.
  3. Work out 28 x 6.
  4. Work out 84 divided by 7.
  5. Work out 35 x 12.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator2 marks

Work out 406 + 287.

additioncolumn methodintegers
Standard exam styleFoundationNon-calculator3 marks

A school buys 24 packs of exercise books. Each pack contains 18 books. How many books are bought altogether?

multiplicationword problemfoundation arithmetic
ChallengeFoundationNon-calculator4 marks

Tickets cost 7 pounds each. A group pays with a 50 pound note for 6 tickets. How much change should they receive?

multi-step arithmeticmoneymultiplicationsubtraction