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 Brackets, Other, Division, Multiplication, 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.
   

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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:

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

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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 $$\dfrac{\sqrt{(8-4)}\times15}{2^3+7} = \underline{2}$$