# BODMAS Rules

BODMAS is an acronym used to represent the order of operations when working out a mathematical expression. Thus,

B stands for brackets. All operations within the brackets must be done first. The priority of brackets when there are more than one type of brackets in a mathematical expression is: ( ), than [ ] and at last, { }.

O means other. It may represent a power or more difficult mathematical operations such as logaritms (which you don’t know yet) etc.

D stands for division.

M stands for multiplication.

Although D is before M in the acronym, they have the same level of priority. This means the operation that is more on the left is done first.

S stands for subtraction.

Addition and subtraction have also the same level of priority.

### Example

Calculate the value of the expression:

$24 - \left[ 3 + 6 \cdot \left( 14 - 2 ^ { 3 } + 8 \div 4 \right) \right]$

### Solution

We have two kinds of brackets and therefore, we start with the round ones ( ). Thus, as there is a power inside them that enters into the category of “others”, we start with it:

\begin{aligned} 24 - \left[ 3 + 6 \cdot \left( 14 - 2 ^ { 3 } + 8 \div 4 \right) \right] & \text { Brack } - E x p o \\ & = 24 - [ 3 + 6 \cdot ( 14 - 8 + 8 \div 4 ) ] \end{aligned}

Then ,we have a subtraction, an addition and a division remained. Thus, we do the division:

\begin{aligned} = 24 - [ 3 + 6 \cdot ( 14 - 8 + 8 \div 4 ) ] & \text { Brack } - D i v \\ & = 24 - [ 3 + 6 \cdot ( 14 - 8 + 2 ) ] \end{aligned}

Now we do the subtraction and the addition inside the round brackets:

\begin{aligned} = 24 - [ 3 + 6 \cdot ( 14 - 8 + 2 ) ] & \text { Brack } - S u b \\ = & 24 - [ 3 + 6 \cdot ( 6 + 2 ) ] \quad \text { Brack } - A d d \\ = & 24 - [ 3 + 6 \cdot 8 ] \end{aligned}

Now that the round braces are gone, we continue with the square ones using the same procedure. Thus,

$\begin{array} { l } { = 24 - [ 3 + 6 \cdot 8 ] } & { \text { Brack } - M u l t } \\ { = 24 - [ 3 + 48 ] } & { \text { Brack } - A d d } \\ { = } & { 24 - 51 } \\ { = } & { - 27 } \end{array}$