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Order of operations: BODMAS

Order of operations: BODMAS

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Order of operations: BODMAS

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Explainer Video

Tutor: Alice

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

BODMAS stands for Brackets, Other, Division, Multiplication, Addition, Subtraction.


Priority 
BODMAS
Symbol
1
Brackets
​()()()​​​
2
Other
​x, xn\sqrt{x},\, x^nx​,xn​​
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)×9(26 - 18) \times \sqrt9(26−18)×9​


First calculate what is inside the brackets: 

(26−18)=8(26 - 18) = 8 (26−18)=8​​


Secondly calculate the other operation, such as square root of 999:

9=3\sqrt 9 = 39​=3


Lastly multiply the results together: 

8×3=248 \times 3 = 248×3=24​​


Therefore, the answer is (26−18)×9=24‾(26 - 18 ) \times \sqrt9 = \underline{24}(26−18)×9​=24​​


Note: ​The reason the question specifies 'positive solution' is because, strictly speaking, 9=±3\sqrt{9}=\pm39​=±3.  −3-3−3 is also a solution to 9\sqrt{9}9​ which would yield a 'negative' solution to the question also.


Example 2

Evaluate the positive solution to (8−4)×1523+7\dfrac{\sqrt{(8-4)}\times15}{2^3+7}23+7(8−4)​×15​


First calculate what is inside the brackets:

8−4=48-4 = 48−4=4


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

4=223=8\sqrt4 = 2\\ 2^3= 84​=223=8

​

Now the fraction becomes:

2×158+7\dfrac{2 \times 15}{8 +7}8+72×15​


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:

(2×15)(8+7)=3015\dfrac{(2 \times 15)}{(8+7)} = \dfrac{30}{ 15} (8+7)(2×15)​=1530​​​


Calculate the final division: 

3015=2\dfrac{30}{15}= 2 1530​=2


Therefore the positive solution to (8−4)×1523+7=2‾\dfrac{\sqrt{(8-4)}\times15}{2^3+7} = \underline{2}23+7(8−4)​×15​=2​ 


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Order of operations: BIDMAS

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Order of operations: BIDMAS

Order of operations: BIDMAS

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Order of operations: BIDMAS

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Order of operations: BODMAS

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Order of operations: BODMAS

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FAQs - Frequently Asked Questions

When should BODMAS be used?

When you complete a mathematical number sentence involving several different operations then BODMAS helps you to know which order to complete them in.

How does BODMAS rule work?

The BODMAS rule states that mathematical expressions with multiple operators need to be solved from left to right in the order of BODMAS.

Does BODMAS rule apply if there are no brackets?

Yes, use the BODMAS rule to get the correct answer even if there are no brackets.

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