IGCSE Maths / Working with algebra

Order of operations

Edexcel International GCSE Maths (4MA1), chapter 4: Working with algebra, specification point 1.1f. Free lesson.

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The order of operations tells you which calculation to do first when an expression has several operations. Applying it correctly gives one reliable answer and helps you avoid common errors.

The order of operations

Use the hierarchy of operations to decide what to calculate first. Operations in the same group have equal rank, so work through them from left to right. Do brackets first, then powers. Next do multiplication and division, then addition and subtraction. Multiplication and division have equal rank. Addition and subtraction also have equal rank.

Multiplication before addition

In 4 + 3 × 5, multiplication has a higher rank than addition, so calculate 3 × 5 first. Working left to right across the whole line would change the question and give the wrong answer.

Brackets and powers

Calculate the bracket first, then the power, then multiplication. In 2 × (3 + 1)², the square applies to the bracket's value, 4. It does not apply to the whole expression 2 × 4.

Equal rank means left to right

Multiplication does not outrank division. Since they have equal rank, calculate whichever is furthest left first. The same left-to-right rule applies to addition and subtraction. For 12 ÷ 2 × 3, divide first because ÷ is on the left. 12 ÷ 2 = 6, then 6 × 3 = 18.

A fraction bar acts like a bracket

A fraction bar groups the whole expression above it and the whole expression below it. Finish the top and bottom before dividing, just as you would work inside brackets. For (6 + 4)/5, add the top first: 6 + 4 = 10. Then divide: 10/5 = 2.

Use the full order in one expression

In 20 − 2 × 3², follow the hierarchy one stage at a time. The power comes before multiplication, and multiplication comes before subtraction.

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