# Order of operations: BODMAS

## In a nutshell

BODMAS is used in multi-step calculations and when questions have a few different operations. BODMAS is an acronym for the order of operations, with the priority order of each operation.

## BODMAS

**BODMAS** stands for **B**rackets, **O**ther, **D**ivision, **M**ultiplication, **A**ddition, **S**ubtraction.

**Priority** | **BODMAS** | **Symbol** |

1 | **B**rackets | $()$ |

2 | **O**ther | $\sqrt{x},\, x^n$ |

3 | **D**ivision | $\div$ |

**M**ultiplication | $\times$ |

4 | **A**ddition | $+$ |

**S**ubtraction | $-$ |

*Note:** When there is both multiplication and division, or addition and subtraction in the question, you work from left to right.*

#### Procedure

- Calculate the value inside the brackets.

- Calculate the value of any terms raised to a certain power.

- Calculate the value of any terms being multiplied and/or divided.

- Calculate the value of any additions and/or subtractions.

##### Example 1

*Calculate the positive solution to $(26 - 18) \times \sqrt9$*

*First calculate what is inside the brackets: *

*$(26 - 18) = 8$*

*Secondly calculate the other operation, such as square root of $9$:*

*$\sqrt 9 = 3$*

*Lastly multiply the results together: *

*$8 \times 3 = 24$*

*Therefore, the answer is $(26 - 18 ) \times \sqrt9 = \underline{24}$*

**Note: **The reason the question specifies 'positive solution' is because, strictly speaking, $\sqrt{9}=\pm3$. $-3$* is also a solution to *$\sqrt{9}$* which would yield a 'negative' solution to the question also.*

##### Example 2

*Evaluate the positive solution to $\dfrac{\sqrt{(8-4)}\times15}{2^3+7}$*

*First calculate what is inside the brackets:*

*$8-4 = 4$*

*Calculate the other operations such as square root then the indices:*

*$\sqrt4 = 2\\ 2^3= 8$*

**

*Now the fraction becomes:*

*$\dfrac{2 \times 15}{8 +7}$*

*Now you may want to carry out this fraction first as it is division but in this case treat each the numerator and denominator like they have separate brackets:*

*$\dfrac{(2 \times 15)}{(8+7)} = \dfrac{30}{ 15}$*

*Calculate the final division: *

*$\dfrac{30}{15}= 2$*

*Therefore the positive solution to $\dfrac{\sqrt{(8-4)}\times15}{2^3+7} = \underline{2}$ *