### Mixed Calculations

**Mixed calculations** have different types of sum all in one.

If you are weak on addition, subtraction, multiplication or division, now is the time to go back and learn these areas fully because they are all used here.

Mixed calculations need to be **broken down in to separate parts**.

For example the calculation 78 + 2 x 5 should **not** be attempted all at once but treated as two sums like this:

2 x 5 = 10

78 – 10 = **68**

The **order** in which you carry out the **different parts** of the calculation is very important.

With the above example, if you had first done the addition:

78 + 2 = 80

And then the multiplication:

80 x 5 = **400**

**You get the wrong answer!** This is because there is an order which you must follow when faced with mixed calculations and the word **BODMAS** helps us to remember it. We will look at this in the next section.

### BODMAS

**BODMAS** is a word you must learn.

It’s a funny word isn’t it? Well, it’s not really a word, it’s a way of remembering an order – it tells us **the order in which we carry out mixed calculations**. So you need to remember it and what it stands for.

BODMAS stands for:

Brackets, Other, Division, Multiplication, Addition, Subtraction.

BODMAS tells you the order to work out your calculations. It tells you to **start with the Brackets**, then work out

**(this means things like square numbers and cube numbers), next do**

__O__ther**Division and Multiplication (working left to right)**, finally you do

**Addition and Subtraction (working left to right)**.

What do we mean working left to right? Division and multiplication have the same value so we do not always do division before multiplication, instead we work from left to right:

2 x 6 ÷ 4 = ?

2 x 6 = 12

12 ÷ 4 = **3**

The same applies to addition and substraction, they have the same priority in BODMAS and should be worked out going from left to right.

So if you are faced with a calcultaion with several parts – **remember BODMAS**.

Let’s work through some example questions together.

Example 1

**Question**: 42 + 15 x 10 = ?

We must do the multiplication **BOD MAS** before the addition

**BODM**

__A__S15 x 10 = 150

42 + 150 = **192**

Example 2

**Question**: 50 ÷ (10 – 5) = ?

We must do the brackets ** BODMAS** before the division

**BO**.

__D__MASEven though the brackets have a subtraction sum inside them which comes after division in BODMAS, the **brackets** tell us to do that sum **first!** **Always work out the brackets first**.

(10 – 5) = 5

50 ÷ 5 = **10**

Example 3

**Question**: (11 – 3) + (8 ÷ 2) ÷ (4 – 2) = ?

Work out all the **brackets first** __B__ODMAS:

(11 – 3) = 8

(8 ÷ 2) = 4

(4 – 2) = 2

Then put these values back in to the calculation where the brackets were:

8 + 4 ÷ 2

Again think about the order – Division **BODMAS** comes before addition **BODMAS**:

4 ÷ 2 = 2

8 + 2 = **10**