BIDMAS - GCSE Maths Definition

Definition

BIDMAS is the order in which operations should be carried out in mathematical calculations.
It stands for Brackets, Indices, Division, Multiplication, Addition, and Subtraction.

Explanation

BIDMAS tells you the order in which mathematical operations should be done when you have a calculation with more than one operation. Following this order ensures you get the correct answer every time.

The letters in BIDMAS represent different mathematical operations, and should be worked through them in this order. There is some overlap between multiplication and division, and between addition and subtraction.

B stands for Brackets. These include round brackets ( ).

I stands for Indices (also called powers or exponents). These are  written in superscript to the right of the base numbers, like 3² or 5³. Calculate these after brackets but before other operations

D stands for Division. This includes the ÷ symbol and fractions. Division and multiplication have equal priority.

M stands for Multiplication. This includes the × symbol and when numbers are written next to brackets, like 3(4). Division and multiplication have equal priority, so work from left to right.

A stands for Addition. This is the + symbol. Addition and subtraction have equal priority.

S stands for Subtraction. This is the - symbol. Addition and subtraction have equal priority, so work from left to right.

When operations have equal priority (like division and multiplication, or addition and subtraction), you work from left to right across the calculation.

BIDMAS is sometimes called BODMAS, where the O stands for "Orders" instead of "Indices". Both mean exactly the same thing. Outside the UK, you may see PEMDAS, where different words are used for some operations, but the order remains the same - maths is still maths the world over!

Example

Question: Calculate 3 + 2 × (8 - 3)² ÷ 5

Solution:

Following BIDMAS order:

Step 1: Brackets first (8 - 3) = 5 So the calculation becomes: 3 + 2 × 5² ÷ 5

Step 2: Indices next 5² = 25 So the calculation becomes: 3 + 2 × 25 ÷ 5

Step 3: Division and Multiplication (left to right) First: 2 × 25 = 50 Then: 50 ÷ 5 = 10 So the calculation becomes: 3 + 10

Step 4: Addition 3 + 10 = 13

Answer: 13

Without following BIDMAS, you might get a completely different (and wrong) answer. This shows why the order of operations is so important.

Common mistakes (and how to avoid them)

Mistake 1: Working from left to right without following BIDMAS

Many students try to solve calculations by simply working from left to right, ignoring the order of operations.

For example, with 4 + 3 × 2, students might calculate:

• Wrong way: 4 + 3 = 7, then 7 × 2 = 14

• Correct way: 3 × 2 = 6, then 4 + 6 = 10

How to avoid this: Always identify which operations are in your calculation first. Write out the BIDMAS order and tick off each step as you complete it.

Mistake 2: Forgetting that multiplication and division have equal priority

Students often think multiplication always comes before division because M comes before D in BIDMAS.

For example, with 12 ÷ 3 × 2, students might incorrectly calculate:

• Wrong way: 3 × 2 = 6, then 12 ÷ 6 = 2

• Correct way: 12 ÷ 3 = 4, then 4 × 2 = 8 (working left to right)

How to avoid this: Remember that division and multiplication have equal priority. When you see both in a calculation, work from left to right. The same rule applies to addition and subtraction.

Mistake 3: Not dealing with indices properly

Students sometimes forget to calculate indices or mix them up with multiplication.

For example, 2³ means 2 × 2 × 2 = 8, not 2 × 3 = 6.

How to avoid this: Remember that an index tells you how many occurrences of the  base number need to be multiplied together. Write out the multiplication if it helps you see what's happening.

Mistake 4: Ignoring brackets completely

Some students skip over brackets or don't realise they need to be calculated first.

How to avoid this: Always look for brackets before you start any calculation. Highlight them if it helps you spot them. Solve everything inside brackets before moving to the next step.

Mistake 5: Making calculation errors within each step

Students might follow BIDMAS correctly but make simple arithmetic mistakes along the way.

How to avoid this: Take your time with each calculation step. Write down every step clearly. Double-check your basic arithmetic, especially with negative numbers or larger calculations.

Frequently asked questions

What's the difference between BIDMAS and BODMAS?

There's no difference. BIDMAS uses "Indices" while BODMAS uses "Orders", but they both refer to the same thing - powers and exponents. Both systems give you exactly the same answer.

Do I need to follow BIDMAS when using a calculator?

Most scientific calculators automatically follow the order of operations, but basic calculators might not. Know how your calculator works!

What if there are no brackets in my calculation?

You still follow BIDMAS, just skip the brackets step. Start with indices, then division and multiplication (left to right), then addition and subtraction (left to right).

Can I change the order if it seems easier?

No, you must always follow BIDMAS order. The order of operations is a mathematical rule that ensures everyone gets the same answer. Changing the order will give you the wrong result.

What happens with fractions and BIDMAS?

Treat the fraction line like brackets. Calculate the numerator (top) and denominator (bottom) separately first, then divide the results. For example, with , calculate 4 + 2 = 6 and 3 × 2 = 6, then divide = 1.

Related GCSE Mathematics glossaries

BIDMAS

Operation