Order of Operations and Calculator Methods
The order of operations, often remembered by the acronym BIDMAS or BODMAS, is the internationally agreed set of rules deciding which part of a calculation is worked out first: Brackets, then Indices, then Division and Multiplication, then Addition and Subtraction, without which the same calculation could give more than one answer. Entering a multi-step calculation correctly on a scientific calculator uses bracket keys to group a fraction's numerator and denominator, or the terms under a root, so it applies the intended order of operations.
Before you start
Make sure you're comfortable with these topics first:
Method
- Learn the order BIDMAS follows: Brackets first, then Indices, then Division and Multiplication (left to right), then Addition and Subtraction (left to right).
- Always work out everything inside brackets completely before doing anything outside them, including a fraction's numerator or denominator, which counts as being in an invisible bracket.
- Division and multiplication have equal priority, so when both appear with no brackets separating them, work through the expression from left to right rather than always doing multiplication first.
- The same rule applies to addition and subtraction: with no brackets separating them, work left to right rather than automatically adding before subtracting.
- On a calculator, use the bracket keys to enter an expression exactly as it is written, especially for a fraction (put the whole numerator in brackets, then divide by the whole denominator in brackets).
- Use the calculator's power key for indices and its square root key for roots, rather than working these out by repeated multiplication when the numbers are large.
- Use the 'Ans' key to carry an unrounded answer into the next line of a multi-step calculation, instead of retyping a rounded version, which avoids losing accuracy.
- After calculating, check the answer is a sensible size by estimating with rounded numbers; an answer wildly different from the estimate usually means a bracket or operation was entered in the wrong order.
Worked example
Work out the value of (7 + 5)^2 - 3 x 8, showing each step in the correct order.
- Work out the bracket first: 7 + 5 = 12.
- Apply the index: 12^2 = 144.
- Work out the multiplication: 3 x 8 = 24.
- Subtract: 144 - 24 = 120.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Work out 5 + 3 x 6.Show answer
Answer: 23 (3 x 6 = 18 first, then 5 + 18 = 23)
Q2Work out (9 - 4) x (2 + 6).Show answer
Answer: 40 (5 x 8)
Q3Work out 20 - 12 / 4.Show answer
Answer: 17 (12 / 4 = 3 first, then 20 - 3 = 17)
Q4Work out 2^3 + 5 x 2.Show answer
Answer: 18 (2^3 = 8, 5 x 2 = 10, then 8 + 10 = 18)
Q5Describe, in order, the four stages of BIDMAS.Show answer
Answer: Brackets, then Indices, then Division and Multiplication (left to right), then Addition and Subtraction (left to right).
Q6Priya types 15 + 9 / 3 into her calculator without using any brackets and gets an answer of 18. Explain why this is correct, even though working out 15 + 9 first would give a different result.Show answer
Answer: Division has a higher priority than addition in the order of operations, so the calculator works out 9 / 3 = 3 first, then 15 + 3 = 18; doing 15 + 9 first breaks the correct order and gives the wrong answer.
Q7To work out (18 + 6) / (2 x 4) on a calculator, explain which two things must be placed in brackets and why.Show answer
Answer: Both the numerator (18 + 6) and the denominator (2 x 4) must be placed in their own brackets; without them, the calculator would divide 6 by 2 first and then carry out the addition and multiplication in the wrong order, rather than treating the top and bottom of the fraction as complete groups.
Q8Work out 30 / (1 + 4) x 2.Show answer
Answer: 12 (1 + 4 = 5 first, then 30 / 5 = 6, then 6 x 2 = 12)
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
Work out the value of 4 x (11 - 3) + 2^3, showing your working.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
Amir wants to work out (23 + 17) / (5^2 - 15) using his calculator. (a) Write down the two calculations that must each be placed inside their own bracket. (b) Work out the value of the full expression.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
Work out the value of (6 - 9)^2 x 2 - 10 / 5, showing each step of your working in the correct order.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Free printable worksheet
Want more practice on paper? Download the order of operations and calculator methods worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 8 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
Other cuts of this worksheet:
Next topics
Not quite what you needed?
Tell us what is missing on order of operations and calculator methods, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.