Precedence in Mathematical Operators

What comes first?

We are going to introduce a simple set of rules here that can be remembered to solve that age old problem.

Which do we do first?

Prerequisites:

  • none

Terminology

BODMAS: Brackets first then Other then Division then Multiplication then Addition and finally Subtraction

Formulae: A group of mathematical symbols that make a result

Infix: The notation commonly used in mathematical formulae

The Problem

What is the answer to

3 + 2 x 4?

There are two possible solutions. You can either calculate the 3 + 2 part first (which we can show in by forcing this with brackets as brackets go first)

(3 + 2) x 4 = (5) x 4 = 20

But, if we calculate the 2 x 4 part first we would calculate the following

3 + (2 x 4) = 3 + (12) = 15

now (don’t be too confused); 20 is not the same as 15. Shocking.

Now brackets have been used above to make it clear which order the calculation should be taken in.

This is clearly not acceptable as we need to have brackets all over the place. Wouldn’t it be better if we had a set of rules to see what should be calculated first? That is where BODMAS comes in.

BODMAS

BODMAS tells us which order to perform a calculation in. Brackets first then Other then Division then Multiplication then Addition and finally Subtraction.

Since multiplication is ahead of addition in the order of BODMAS,

3 + 2 x 4

this is therefore calculated as

15

Problem solved

Conclusion:

When you perform a calculation you need to know which order of precedence a calculation might have. In order to do so, people have developed an anacronym to help them out. BODMAS is an easy to remember order, meaning Brackets first then Other then Division then Multiplication then Addition and finally Subtraction and stopping eternal confusion when calculating answers.

Not bad. Not bad at all.

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