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Order of operations: BIDMAS

Order of operations: BIDMAS

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Summary

Order of operations: BIDMAS

​​In a nutshell

The order of operations is a rule that states which operation must be performed first. It is very helpful when having to solve multi-step equations.



Order of operations: BIDMAS

BIDMAS is the acronym for the order of equations. It stands for:

  • Brackets
  • Indices
  • Division/Multiplication
  • Addition/Subtraction


Note: Division/Multiplication and Addition/Subtraction are written on the same line because it depends what comes first when reading the equation from left to right.



Example 1

What is 303×(81)30-3\times(8 -1)?


First, using BIDMAS, simplify any Brackets:

81=78-1=7​​


The equation is now:

303×730-3\times7​​


There are no Indices, so move on to Division/Multiplication:

3×7=213\times7=21​​


The equation is now:

302130-21​​


Finally, go through any Addition/Subtraction:

3021=930-21=9​​


303×(81)=9\underline{30-3\times(8-1)=9}


Example 2

Two variables yy and xx are connected through the formula y=3x2x+5y=3x^2-x+5. What is yy when x=4x=4?


Substituting in x=4x=4 into the equation gives:

y=3(4)24+5y=3(4)^2-4+5​​


Going through BIDMAS, there are no Brackets to simplify. So, move onto ​Indices:

42=164^2=16​​


The equation then becomes:

y=3×164+5y=3\times16-4+5​​


Now, move onto Division/Multiplication:

3×16=483\times16=48​​


The equation then becomes:

y=484+5y=48-4+5​​


Finally, move onto Addition/Subtraction:

Note that even though the addition comes first in BIDMAS, you perform the subtraction first as it comes first when reading the equation from left to right.

484=4448-4=44​​

44+5=4944+5=49​​


y=49\underline{y=49}


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