BIDMAS

What you'll learn

What the letters in BIDMAS mean.
Which part of a calculation to do first.
How brackets and powers can change an answer.
How to place brackets to make a statement correct.

The basic idea

Sometimes a calculation has more than one operation, such as adding, multiplying, or subtracting. BIDMAS tells you the order to do them in.

Definition

Expression and operation

An expression is a calculation, such as 6 + 3 × 2. An operation is something you do to numbers, like add, subtract, multiply, divide, or square.

If there is only one operation

If a calculation only has one operation, just work it out normally.

Example

One operation

Work out:

15 - 8

There is only one operation: subtraction.
Subtract 8 from 15.
$15 - 8 = 7$
The answer is 7.

What BIDMAS stands for

BIDMAS is a memory word:

A priority ladder showing the BIDMAS order, with division/multiplication tied and addition/subtraction tied.

Brackets
Indices
Division and Multiplication
Addition and Subtraction

Key Idea

The BIDMAS order

Do brackets first, then indices, then multiplication or division, then addition or subtraction.

BIDMAS priority order from first to last, showing the equal-priority pairs.

Multiplication before addition

Example

Multiplication before addition

Work out:

\times 4 ![The multiplication part of 3 + 6 × 4 is highlighted to show it must be done before the addition.](https://assets.mathsgenie.co.uk/notes/diagrams/fe720786-56ce-4c15-895d-9a4e8c7373e1.png)

There are two operations: addition and multiplication.
Multiplication comes before addition, so work out 6 multiplied by 4 first.

The multiplication part of 3 + 6 × 4 is identified as the first step before adding 3.

\times 4 = 24

Now add 3.
$3 + 24 = 27$
The answer is 27.

Common Mistake

Going left to right too soon

A common mistake is to do 3 + 6 first just because it is on the left. BIDMAS says multiplication must be done before addition.

Brackets come first

Definition

Brackets

Brackets show a part of the calculation that must be done first. They look like this: ( ).

Anything inside brackets gets worked out before the rest of the calculation.

The bracketed part of (9 − 4) × 3 is shown as the first part to calculate before multiplying by 3.

Example

Brackets first

Work out:

\times 3 ![The brackets around 9 − 4 show the part to calculate first before multiplying by 3.](https://assets.mathsgenie.co.uk/notes/diagrams/37f59220-d272-4096-bae3-f62d59c6014c.png)

The brackets tell you to work out 9 minus 4 first.
$9 - 4 = 5$
Replace the bracket part with 5.
$\times 3$
Multiply.
$\times 3 = 15$
The answer is 15.

Tip

Spot the brackets

When you see brackets, circle or underline the part inside them. That reminds you to do that part first.

Indices come next

Definition

Index

An index tells you how many times to multiply a number by itself. For example, $4^2$ means 4 multiplied by 4. We say “4 squared”.

An index is shown as a small number telling how many equal factors to multiply.

Indices are done after brackets, but before multiplication, division, addition, and subtraction.

Example

Squaring before adding

Work out:

4^2 ![The index applies only to the 4, so 4² is calculated before adding 7.](https://assets.mathsgenie.co.uk/notes/diagrams/f25edfd7-90d5-4759-bac0-bbc77407c0d4.png)

The index is on 4, so work out 4 squared first.
$42=4×4=164^2 = 4 \times 4 = 16$
Now add 7.
$7 + 16 = 23$
The answer is 23.

Brackets before indices

If the brackets are squared, work out inside the brackets first, then square the answer.

For (6 + 2)², the bracket calculation happens before the squaring.

Example

Brackets then square

Work out:

6 + 2)^2 ![For a squared bracket, the calculation inside the brackets is done first, then the result is squared.](https://assets.mathsgenie.co.uk/notes/diagrams/c545b490-6dfe-4f80-b251-e09d5c6ea00d.png)

Work out the brackets first.
$6 + 2 = 8$
Now square 8.
$82=8×8=648^2 = 8 \times 8 = 64$
The answer is 64.

Multiplication and division before addition and subtraction

Multiplication and division have higher priority than addition and subtraction.

Example

Division before addition

Work out:

\div 3

Division comes before addition, so work out 18 divided by 3 first.
$18 \div 3 = 6$
Now add 5.
$5 + 6 = 11$
The answer is 11.

When multiplication and division both appear

Multiplication and division are equal priority. Do them from left to right.

Multiplication and division are tied in priority, so the operations are tackled from left to right.

Example

Multiplication and division left to right

Work out:

\times 3 \div 6 ![Multiplication and division have equal priority, so the × and ÷ steps are taken from left to right before adding 4.](https://assets.mathsgenie.co.uk/notes/diagrams/28908beb-5b83-47df-8be3-60ddade92e16.png)

Multiplication and division come before addition.
Work from left to right: first do 8 multiplied by 3.
$\times 3 = 24$
Now divide by 6.
$24 \div 6 = 4$
Now add 4.
$4 + 4 = 8$
The answer is 8.

Common Mistake

Division is not always before multiplication

The D and M in BIDMAS are a tie. If both appear, work from left to right.

Addition and subtraction are also left to right

Addition and subtraction have equal priority too. Once the brackets, indices, multiplication, and division are finished, work left to right.

Addition and subtraction are tied in priority, so 10 − 6 + 3 is worked from left to right.

Example

Subtraction and addition left to right

Work out:

10 - 6 + 3! [A dd i t i o nan d s u b t r a c t i o nha v ee q u a l p r i or i t y, so t hi se x p r ess i o ni s w or k e df r o m l e f tt or i g h t .] (h ttp s : // a sse t s . ma t h s g e ni e . co . u k / n o t es / d ia g r am s / e 2728 e 13 - 02 e 0 - 4 dd 7 - 986 d - 1 c 6 b 000967 c 4. p n g)

Addition and subtraction are equal priority, so start on the left.
First do 10 minus 6.
$10 - 6 = 4$
Now add 3.
$4 + 3 = 7$
The answer is 7.

Putting BIDMAS together

Now you can handle calculations with several operations.

Example

Full BIDMAS calculation

Work out:

\times 2^3

There are no brackets, so look for indices.
Work out 2 cubed.
$23=2×2×2=82^3 = 2 \times 2 \times 2 = 8$
Now do the multiplication.
$\times 8 = 32$
Now do the addition.
$5 + 32 = 37$
The answer is 37.

Adding brackets to make a statement correct

Sometimes you are asked to put brackets into a calculation so the answer becomes correct. Brackets change the order, so they can change the answer.

Adding brackets around 4 + 2 changes the first operation and makes the target statement possible.

Example

Choosing where to put brackets

Add brackets to make this statement correct:

\times 4 + 2 = 30 ![Putting brackets around 4 + 2 forces the addition to happen first, making the target statement possible.](https://assets.mathsgenie.co.uk/notes/diagrams/da951685-164a-4459-8d7c-30bc881a573a.png)

Without brackets, multiplication happens first.
$\times 4 + 2 = 22$
To make 30, try grouping 4 plus 2.
$4 + 2 = 6$
Now multiply by 5.
$\times 6 = 30$
So the correct statement is:
$\times (4 + 2) = 30$

Example

Using two pairs of brackets

Add brackets to make this statement correct:

\times 4 + 5 = 45

Notice that 45 can be made by 5 multiplied by 9.
Put brackets around 3 plus 2 to make 5.
$3 + 2 = 5$
Put brackets around 4 plus 5 to make 9.
$4 + 5 = 9$
Multiply the two bracket answers.
$\times 9 = 45$
So the correct statement is:
$\times (4 + 5) = 45$

Tip

Bracket questions

Try the calculation without brackets first. If the answer is too small or too big, use brackets to force an addition or subtraction to happen earlier.

Exam technique

In the exam

Write BIDMAS at the side if you need a reminder.
Work out one part at a time, replacing it with the answer.
For bracket questions, check your final statement actually gives the target answer.

Self review

Check yourself

In BIDMAS, what should you do before multiplying?
Why is 6 + 2 × 5 not the same as (6 + 2) × 5?
If multiplication and division are both in a calculation, what direction do you work in?

What you'll learn

What the letters in BIDMAS mean.
Which part of a calculation to do first.
How brackets and powers can change an answer.
How to place brackets to make a statement correct.

The basic idea

Sometimes a calculation has more than one operation, such as adding, multiplying, or subtracting. BIDMAS tells you the order to do them in.

Definition

Expression and operation

An expression is a calculation, such as 6 + 3 × 2. An operation is something you do to numbers, like add, subtract, multiply, divide, or square.

If there is only one operation

If a calculation only has one operation, just work it out normally.

Example

One operation

Work out:

15 - 8

There is only one operation: subtraction.
Subtract 8 from 15.
$15 - 8 = 7$
The answer is 7.

What BIDMAS stands for

BIDMAS is a memory word:

A priority ladder showing the BIDMAS order, with division/multiplication tied and addition/subtraction tied.

Brackets
Indices
Division and Multiplication
Addition and Subtraction

Key Idea

The BIDMAS order

Do brackets first, then indices, then multiplication or division, then addition or subtraction.

BIDMAS priority order from first to last, showing the equal-priority pairs.

Multiplication before addition

Example

Multiplication before addition

Work out:

\times 4 ![The multiplication part of 3 + 6 × 4 is highlighted to show it must be done before the addition.](https://assets.mathsgenie.co.uk/notes/diagrams/fe720786-56ce-4c15-895d-9a4e8c7373e1.png)

There are two operations: addition and multiplication.
Multiplication comes before addition, so work out 6 multiplied by 4 first.

The multiplication part of 3 + 6 × 4 is identified as the first step before adding 3.

\times 4 = 24

Now add 3.
$3 + 24 = 27$
The answer is 27.

Common Mistake

Going left to right too soon

A common mistake is to do 3 + 6 first just because it is on the left. BIDMAS says multiplication must be done before addition.

Brackets come first

Definition

Brackets

Brackets show a part of the calculation that must be done first. They look like this: ( ).

Anything inside brackets gets worked out before the rest of the calculation.

The bracketed part of (9 − 4) × 3 is shown as the first part to calculate before multiplying by 3.

Example

Brackets first

Work out:

\times 3 ![The brackets around 9 − 4 show the part to calculate first before multiplying by 3.](https://assets.mathsgenie.co.uk/notes/diagrams/37f59220-d272-4096-bae3-f62d59c6014c.png)

The brackets tell you to work out 9 minus 4 first.
$9 - 4 = 5$
Replace the bracket part with 5.
$\times 3$
Multiply.
$\times 3 = 15$
The answer is 15.

Tip

Spot the brackets

When you see brackets, circle or underline the part inside them. That reminds you to do that part first.

Indices come next

Definition

Index

An index tells you how many times to multiply a number by itself. For example, $4^2$ means 4 multiplied by 4. We say “4 squared”.

An index is shown as a small number telling how many equal factors to multiply.

Indices are done after brackets, but before multiplication, division, addition, and subtraction.

Example

Squaring before adding

Work out:

4^2 ![The index applies only to the 4, so 4² is calculated before adding 7.](https://assets.mathsgenie.co.uk/notes/diagrams/f25edfd7-90d5-4759-bac0-bbc77407c0d4.png)

The index is on 4, so work out 4 squared first.
$42=4×4=164^2 = 4 \times 4 = 16$
Now add 7.
$7 + 16 = 23$
The answer is 23.

Brackets before indices

If the brackets are squared, work out inside the brackets first, then square the answer.

For (6 + 2)², the bracket calculation happens before the squaring.

Example

Brackets then square

Work out:

6 + 2)^2 ![For a squared bracket, the calculation inside the brackets is done first, then the result is squared.](https://assets.mathsgenie.co.uk/notes/diagrams/c545b490-6dfe-4f80-b251-e09d5c6ea00d.png)

Work out the brackets first.
$6 + 2 = 8$
Now square 8.
$82=8×8=648^2 = 8 \times 8 = 64$
The answer is 64.

Multiplication and division before addition and subtraction

Multiplication and division have higher priority than addition and subtraction.

Example

Division before addition

Work out:

\div 3

Division comes before addition, so work out 18 divided by 3 first.
$18 \div 3 = 6$
Now add 5.
$5 + 6 = 11$
The answer is 11.

When multiplication and division both appear

Multiplication and division are equal priority. Do them from left to right.

Multiplication and division are tied in priority, so the operations are tackled from left to right.

Example

Multiplication and division left to right

Work out:

\times 3 \div 6 ![Multiplication and division have equal priority, so the × and ÷ steps are taken from left to right before adding 4.](https://assets.mathsgenie.co.uk/notes/diagrams/28908beb-5b83-47df-8be3-60ddade92e16.png)

Multiplication and division come before addition.
Work from left to right: first do 8 multiplied by 3.
$\times 3 = 24$
Now divide by 6.
$24 \div 6 = 4$
Now add 4.
$4 + 4 = 8$
The answer is 8.

Common Mistake

Division is not always before multiplication

The D and M in BIDMAS are a tie. If both appear, work from left to right.

Addition and subtraction are also left to right

Addition and subtraction have equal priority too. Once the brackets, indices, multiplication, and division are finished, work left to right.

Addition and subtraction are tied in priority, so 10 − 6 + 3 is worked from left to right.

Example

Subtraction and addition left to right

Work out:

10 - 6 + 3! [A dd i t i o nan d s u b t r a c t i o nha v ee q u a l p r i or i t y, so t hi se x p r ess i o ni s w or k e df r o m l e f tt or i g h t .] (h ttp s : // a sse t s . ma t h s g e ni e . co . u k / n o t es / d ia g r am s / e 2728 e 13 - 02 e 0 - 4 dd 7 - 986 d - 1 c 6 b 000967 c 4. p n g)

Addition and subtraction are equal priority, so start on the left.
First do 10 minus 6.
$10 - 6 = 4$
Now add 3.
$4 + 3 = 7$
The answer is 7.

Putting BIDMAS together

Now you can handle calculations with several operations.

Example

Full BIDMAS calculation

Work out:

\times 2^3

There are no brackets, so look for indices.
Work out 2 cubed.
$23=2×2×2=82^3 = 2 \times 2 \times 2 = 8$
Now do the multiplication.
$\times 8 = 32$
Now do the addition.
$5 + 32 = 37$
The answer is 37.

Adding brackets to make a statement correct

Sometimes you are asked to put brackets into a calculation so the answer becomes correct. Brackets change the order, so they can change the answer.

Adding brackets around 4 + 2 changes the first operation and makes the target statement possible.

Example

Choosing where to put brackets

Add brackets to make this statement correct:

\times 4 + 2 = 30 ![Putting brackets around 4 + 2 forces the addition to happen first, making the target statement possible.](https://assets.mathsgenie.co.uk/notes/diagrams/da951685-164a-4459-8d7c-30bc881a573a.png)

Without brackets, multiplication happens first.
$\times 4 + 2 = 22$
To make 30, try grouping 4 plus 2.
$4 + 2 = 6$
Now multiply by 5.
$\times 6 = 30$
So the correct statement is:
$\times (4 + 2) = 30$

Example

Using two pairs of brackets

Add brackets to make this statement correct:

\times 4 + 5 = 45

Notice that 45 can be made by 5 multiplied by 9.
Put brackets around 3 plus 2 to make 5.
$3 + 2 = 5$
Put brackets around 4 plus 5 to make 9.
$4 + 5 = 9$
Multiply the two bracket answers.
$\times 9 = 45$
So the correct statement is:
$\times (4 + 5) = 45$

Tip

Bracket questions

Try the calculation without brackets first. If the answer is too small or too big, use brackets to force an addition or subtraction to happen earlier.

Exam technique

In the exam

Write BIDMAS at the side if you need a reminder.
Work out one part at a time, replacing it with the answer.
For bracket questions, check your final statement actually gives the target answer.

Self review

Check yourself

In BIDMAS, what should you do before multiplying?
Why is 6 + 2 × 5 not the same as (6 + 2) × 5?
If multiplication and division are both in a calculation, what direction do you work in?

What you'll learn

The basic idea

If there is only one operation

What BIDMAS stands for

Multiplication before addition

Brackets come first

Indices come next

Brackets before indices

Multiplication and division before addition and subtraction

When multiplication and division both appear

Addition and subtraction are also left to right

Putting BIDMAS together

Adding brackets to make a statement correct

Recap questions

Review BIDMAS by teaching Genie

Remember key concepts with flashcards

BIDMAS

What you'll learn

The basic idea

If there is only one operation

What BIDMAS stands for

Multiplication before addition

Brackets come first

Indices come next

Brackets before indices

Multiplication and division before addition and subtraction

When multiplication and division both appear

Addition and subtraction are also left to right

Putting BIDMAS together

Adding brackets to make a statement correct

Recap questions

Review BIDMAS by teaching Genie

Remember key concepts with flashcards

BIDMAS

What you'll learn

The basic idea

If there is only one operation

What BIDMAS stands for

Multiplication before addition

Brackets come first

Indices come next

Brackets before indices

Multiplication and division before addition and subtraction

When multiplication and division both appear

Addition and subtraction are also left to right

Putting BIDMAS together

Adding brackets to make a statement correct

Recap questions

Review BIDMAS by teaching Genie

Remember key concepts with flashcards

BIDMAS Revision Guide

BIDMAS

What you'll learn

The basic idea

If there is only one operation

What BIDMAS stands for

Multiplication before addition

Brackets come first

Indices come next

Brackets before indices

Multiplication and division before addition and subtraction

When multiplication and division both appear

Addition and subtraction are also left to right

Putting BIDMAS together

Adding brackets to make a statement correct

Recap questions

Review BIDMAS by teaching Genie

Remember key concepts with flashcards

BIDMAS Revision Guide