**BIDMAS/BODMAS/Orders of Operations** *GCSE Revision and Worksheets*

## What you need to know

BIDMAS (sometimes BODMAS) is an acronym that helps us remember which order to perform operations in. The letters stand for:

**B**rackets**I**ndices (or as they can be called, p**O**wers)**D**ivision**M**ultiplication**A**ddition**S**ubtraction

These rules apply to calculations involving numbers as well as algebra so it’s important to make sure you’re super comfortable with it.

**Example: **What is the value of 3 \times (3^2 + 4) - 8?

The first letter of BIDMAS is B, meaning the first thing we should do is look to what’s inside the brackets. In there we have two operations happening: a power/index, and an addition. The letter I comes before the letter A in BIDMAS which means we first work out the result of 3^2 and then add 4 to it.

3^2 + 4 = 9 + 4 = 13

Then, our calculation becomes

3 \times 13 - 8

Here, there is a multiplication and a subtraction, so because M comes before S in our trusty acronym, we do the multiplication first and the subtraction second. We get

3 \times 13 - 8 = 39 - 8 = 31

This is the result of our BIDMAS-applied calculation.

One potential exception to this rule is when calculations are expressed like fractions. In these cases, we work out what the values of the top and bottom are (using the rules of BIDMAS), and then lastly, we look at the fraction we have and see if it can be simplified. We’ll look at an example of this now.

**Example: **Simplify the fraction \dfrac{3 \times 4 - 5}{11 + (9 \div 3)}.

First, we’ll sort out the numerator. There’s a multiplication and an addition, so we do the multiplication first and the addition second.

3 \times 4 - 5 = 12 - 5 = 7

Now, the denominator. That contains a division inside brackets, so that will be the first bit of the calculation, and then the addition will be the second.

11 + (9 \div 3) = 11 + (3) = 14

Therefore, our fraction is \frac{7}{14}. Both top and bottom have a factor of 7, so the simplified answer is

\dfrac{7}{14} = \dfrac{1}{2},

which cannot be simplified further.

**Example: **Write the expression 4xy \times 9y - 13 \times xy^2 in its simplest form.

There are two multiplications in this expression, so it doesn’t matter which order we do them in providing we do them both before the subtraction. The first one becomes:

4xy \times 9y = 4 \times 9 \times x \times y \times y = 36xy^2

The second multiplication becomes:

13 \times xy^2 = 13xy^2

So, now we subtract the second from the first one, to get the expression in its simplest form.

36xy^2 - 13xy^2 = 23xy^2

## Example Questions

1) Use the rules of BIDMAS to work out the result of (2 \times 3^3) \div (15 - 9).

BIDMAS tells us to look to the brackets first, and we’ll start with the first bracket. Inside, there is one power (or index), which is the next part of the acronym so it’s the next thing we do. After then, we do the multiplication, meaning the inside of the first bracket becomes

2 \times 3^3 = 2 \times 27 = 54

Next up, the inside of the second bracket becomes

15 - 9 = 6

Then, there is one more operation that remains, the division. So, the result of the calculation is

54 \div 6 = 9

2) Write the expression (y^2 + 5y^2) - 3y \times 7y in its simplest form.

BODMAS tells us to look to the bracket first, so in the first bracket

y^2 + 5y^2 = 6y^2

There are no indices or divisions in this expression, but there is a multiplication:

3y \times 7y = 21y^2

So, the last operation of the expression is a subtraction, and we get

6y^2 - 21y^2 = -15y^2

3) **HIGHER ONLY**. Use BIDMAS to fully simplify the fraction \dfrac{42q^2 \times pq}{28p^3 \div (9p - 5p)}.

We should deal with the numerator and denominator separately. First, the numerator – there’s only one operation (multiplication), so we go right ahead with it.

42q^2 \times pq = 42q^2 \times q \times p = 42q^{3}p

Next up, the denominator. B is the first letter of BIDMAS, so we’ll do the brackets first, and there’s only one operation inside the brackets.

9p - 5p = 4p

Then, the only other operation is the division, which leaves the denominator as

28p^3 \div 4p = 7p^2

So, the fraction becomes

\dfrac{42q^{3}p}{7p^2}

There is a p on the top and bottom, as well as a factor of 7. Both of these cancel, and leave us with

\dfrac{6q^3}{p}

There are no more common factors, so this is fully simplified.

## BIDMAS/BODMAS Revision and Worksheets

## BIDMAS/BODMAS Teaching Resources

For those who are looking to revise BIDMAS/BODMAS for KS3 Maths or GCSE Maths then the worksheets and online tests above are great. For Maths tutors looking for BIDMAS resources you are welcome to use these revision materials and you can find much more on our GCSE Maths revision page.