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# Order of operations: BODMAS 0%

Summary

# 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 = Bracket, Other, Division, Multiplication, Addition, Subtraction

 Priority BODMAS Symbol 1 Brackets ​$()$​​​ 2 Other ​$\sqrt{x},\, x^n$​​ 3 Division ​$\div$​​ Multiplication ​$\times$​​​ 4 Addition ​$+$​​ Subtraction ​$-$​​

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

#### Procedure

 1 Calculate the value inside the brackets. 2 Calculate the value of any terms raised to a certain power. 3 Calculate the value of any terms being multiplied and/or divided. 4 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 $\dfrac{\sqrt{(8-4)}\times15}{2^3+7} = \underline{2}$