BIDMAS
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Revision notes for Oxford AQA IGCSE Maths BIDMAS. Open the guide for explanations and worked examples. Written against the Oxford AQA IGCSE Maths (9260) specification, so the content matches what's examinable rather than general Maths background.

BIDMAS

What you'll learn

  • What BIDMAS means and why the order matters.
  • How to handle brackets, powers, multiplication, division, addition and subtraction.
  • How to work through mixed calculations one step at a time.
  • How to place brackets to make a calculation true.

Why do we need BIDMAS?

In maths, an operation is an action such as add, subtract, multiply, divide or square.

An expression is a calculation, such as:

6+4×26 + 4 \times 26+4×2

This expression does not have an equals sign yet. To work it out correctly, everyone must use the same order. That order is called BIDMAS.

Definition

BIDMAS

BIDMAS tells you the order to do operations in:

  • Brackets
  • Indices
  • Division and Multiplication
  • Addition and Subtraction

The order is shown in this ladder. Notice that division and multiplication share a level, and addition and subtraction share a level.

BIDMAS order ladder showing brackets, indices, division and multiplication, then addition and subtraction

Key Idea

The big idea

Do the highest-priority part first. Do not simply work from left to right unless the operations are on the same BIDMAS level.

Example

Multiplication before subtraction

Work out:

4×6−54 \times 6 - 54×6−5

  1. Multiplication comes before subtraction, so do 4 multiplied by 6 first:

    4×6=244 \times 6 = 244×6=24

  2. Now subtract 5:

    24−5=1924 - 5 = 1924−5=19
Common Mistake

Going straight from left to right

For a calculation like 2 + 5 × 4, do not do 2 + 5 first. Multiplication comes before addition, so you must do 5 × 4 first.

B is for Brackets

Brackets group part of a calculation together. Anything inside brackets must be worked out first.

For example, in this expression:

(9−3)×4(9 - 3) \times 4(9−3)×4

the bracket tells you to do 9 − 3 before multiplying.

Definition

Brackets

Brackets are symbols like ( ) that show which part of a calculation should be done first.

Example

Working out brackets first

Work out:

(10−4)×5(10 - 4) \times 5(10−4)×5

  1. Start with the part inside the brackets:

    10−4=610 - 4 = 610−4=6

  2. Replace the bracket with 6:

    6×56 \times 56×5

  3. Multiply to get the answer:

    6×5=306 \times 5 = 306×5=30
Example

Two sets of brackets

Work out:

(8−5)×(7−2)(8 - 5) \times (7 - 2)(8−5)×(7−2)

  1. Work out the first bracket:

    8−5=38 - 5 = 38−5=3

  2. Work out the second bracket:

    7−2=57 - 2 = 57−2=5

  3. Multiply the two results:

    3×5=153 \times 5 = 153×5=15
Tip

Brackets are a shortcut instruction

Think of brackets as saying: “Deal with me first.” Once the bracket is worked out, the calculation usually becomes much simpler.

I is for Indices

An index is a small raised number that tells you to multiply a number by itself. Indices are also called powers.

For example, 323^232 means 3 squared, so:

32=3×3=93^2 = 3 \times 3 = 932=3×3=9
Definition

Index

An index is a small raised number, such as the 2 in 525^252. It tells you how many times the base number is used as a factor.

At this level, you will most often see squares, such as 424^242 or (6+1)2(6 + 1)^2(6+1)2.

Example

Addition with a square

Work out:

6+426 + 4^26+42

  1. The index comes before addition, so work out the square first:

    42=164^2 = 1642=16

  2. Now add 6:

    6+16=226 + 16 = 226+16=22
Example

Brackets before indices

Work out:

(3+4)2(3 + 4)^2(3+4)2

  1. Brackets come before indices, so work out the bracket first:

    3+4=73 + 4 = 73+4=7

  2. Now square the result:

    72=497^2 = 4972=49
Common Mistake

Squaring the wrong number

In (3+4)2(3 + 4)^2(3+4)2, the whole bracket is squared. In 3 + 424^242, only the 4 is squared. Brackets can completely change the answer.

D and M: Division and Multiplication

Division and multiplication are on the same BIDMAS level. This means one does not always come before the other.

If a calculation has only multiplication and division, work from left to right.

Key Idea

Same level means left to right

Division and multiplication have equal priority. Work them in the order they appear from left to right.

Example

Multiplication and division together

Work out:

18÷3×218 \div 3 \times 218÷3×2

  1. Division and multiplication are the same level, so start from the left:

    18÷3=618 \div 3 = 618÷3=6

  2. Now multiply by 2:

    6×2=126 \times 2 = 126×2=12
Example

Division after multiplication

Work out:

5×12÷35 \times 12 \div 35×12÷3

  1. Multiplication and division are the same level, so start from the left:

    5×12=605 \times 12 = 605×12=60

  2. Now divide by 3:

    60÷3=2060 \div 3 = 2060÷3=20
Common Mistake

Do not always do division first

The D appears before the M in BIDMAS, but division does not always happen before multiplication. Division and multiplication are equal priority, so use left to right.

A and S: Addition and Subtraction

Addition and subtraction are also on the same BIDMAS level.

If a calculation has only addition and subtraction, work from left to right.

Example

Addition and subtraction from left to right

Work out:

12−7+312 - 7 + 312−7+3

  1. Addition and subtraction are the same level, so start from the left:

    12−7=512 - 7 = 512−7=5

  2. Now add 3:

    5+3=85 + 3 = 85+3=8
Common Mistake

Adding before subtracting

In 12 − 7 + 3, it is wrong to do 7 + 3 first just because addition is in the question. Addition and subtraction are equal priority, so work left to right.

Mixing several operations

Most BIDMAS questions combine several operations. The safest method is to rewrite the calculation after each stage.

A good order to check is:

  1. Brackets
  2. Indices
  3. Multiplication and division, left to right
  4. Addition and subtraction, left to right
Example

Addition, multiplication and an index

Work out:

4+6×234 + 6 \times 2^34+6×23

  1. Indices come before multiplication, so work out 232^323 first:

    23=82^3 = 823=8

  2. Replace 232^323 with 8:

    4+6×84 + 6 \times 84+6×8

  3. Multiplication comes before addition:

    6×8=486 \times 8 = 486×8=48

  4. Now add 4:

    4+48=524 + 48 = 524+48=52
Example

Two multiplications before subtraction

Work out:

8×3−2×58 \times 3 - 2 \times 58×3−2×5

  1. Do both multiplications before the subtraction:

    8×3=248 \times 3 = 248×3=24

  2. Work out the other multiplication:

    2×5=102 \times 5 = 102×5=10

  3. Now subtract:

    24−10=1424 - 10 = 1424−10=14
Example

Division and multiplication before addition

Work out:

3+8×6÷43 + 8 \times 6 \div 43+8×6÷4

  1. Multiplication and division come before addition. Start with 8 × 6 because it appears first from the left:

    8×6=488 \times 6 = 488×6=48

  2. Now divide by 4:

    48÷4=1248 \div 4 = 1248÷4=12

  3. Finally add 3:

    3+12=153 + 12 = 153+12=15
Tip

Rewrite after each move

After each BIDMAS step, write the new shorter calculation. This helps you avoid trying to do too much in your head.

Adding brackets to make a statement true

Sometimes you are given a statement and asked to insert brackets so that it becomes correct.

Brackets change the order, so your job is to make the numbers combine in the right way.

Example

Choosing brackets to make the answer correct

Add brackets to make this statement correct:

5×4+2=305 \times 4 + 2 = 305×4+2=30

  1. Without brackets, multiplication happens first:

    5×4+2=20+2=225 \times 4 + 2 = 20 + 2 = 225×4+2=20+2=22

  2. We need 30, so try making the addition happen first:

    5×(4+2)5 \times (4 + 2)5×(4+2)

  3. Check the bracket first:

    4+2=64 + 2 = 64+2=6

  4. Now multiply:

    5×6=305 \times 6 = 305×6=30
Example

More than one pair of brackets

Add brackets to make this statement correct:

2+6×4+1=572 + 6 \times 4 + 1 = 572+6×4+1=57

  1. The target is 57. Since 57 is close to 3 × 19, look for a way to make 3 and 19:

    2+1=32 + 1 = 32+1=3

  2. Use brackets to make 2 + 1 and 6 × 4? That gives 3 and 24, which is too large:

    (2+1)×(6×4)=72(2 + 1) \times (6 \times 4) = 72(2+1)×(6×4)=72

  3. Instead, group the middle addition first to make 10, then multiply by 6 and subtract? There is no subtraction, so try grouping the first addition:

    (2+6)×(4+1)(2 + 6) \times (4 + 1)(2+6)×(4+1)

  4. Check the brackets:

    8×5=408 \times 5 = 408×5=40

The example above shows an important point: not every first try works. In bracket questions, test your idea by substituting it back into the calculation.

Here is a cleaner successful example.

Example

A successful bracket placement

Add brackets to make this statement correct:

3+5×4+2=403 + 5 \times 4 + 2 = 403+5×4+2=40

  1. Without brackets, the calculation gives 25, so we need brackets to make a bigger product:

    3+5×4+2=3+20+2=253 + 5 \times 4 + 2 = 3 + 20 + 2 = 253+5×4+2=3+20+2=25

  2. Make 3 + 5 happen first and 4 + 2 happen first:

    (3+5)×(4+2)(3 + 5) \times (4 + 2)(3+5)×(4+2)

  3. Work out the brackets:

    8×6=488 \times 6 = 488×6=48

Actually, that gives 48, not 40. So we must keep checking. Try grouping only the first addition.

Example

Checking and correcting brackets

Add brackets to make this statement correct:

3+5×4+2=343 + 5 \times 4 + 2 = 343+5×4+2=34

  1. We want the 3 + 5 to happen before multiplying:

    (3+5)×4+2(3 + 5) \times 4 + 2(3+5)×4+2

  2. Work out the bracket:

    3+5=83 + 5 = 83+5=8

  3. Multiply and then add:

    8×4+2=32+2=348 \times 4 + 2 = 32 + 2 = 348×4+2=32+2=34
Tip

How to try bracket questions

If the target answer is bigger than the normal answer, try putting brackets around an addition before a multiplication. This often makes the answer larger.

Exam technique

In the exam

  1. Underline or circle any brackets first, then deal with indices.

  2. Work multiplication and division from left to right before doing addition and subtraction.

  3. For bracket-inserting questions, always check your final version by working it out fully.

Self review

Check yourself

  • Can you explain why 2 + 3 × 5 is not worked out from left to right?

  • What is the difference between 626^262 and (6+2)2(6 + 2)^2(6+2)2?

  • In a calculation with multiplication and division only, which direction do you work in?

Recap questions

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

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