Hierarchy Of Operations

A hierarchy is any system of people or things ranked one above another. The word comes from “hiero-” which means priest or sacred and “-archy” which means rule or government. It comes from something like “sacred rule”.

A good example of a hierarchy is the British army. People’s jobs are ranked in a hierarchy. These are called ranks. Here are some, including the top and the bottom:

Field-Marshal
General

Colonel

Major
Captain
Lieutenant

Sergeant

Private

In mathematics, the operations are organised in a hierarchy

x and ÷ rank higher than

+ and –

So you do those operations first.

To solve this equation

5 + 3 x 2 = ?

we must do the higher ranking operation first.

If we do the addition first we get 5 + 3 = 8 and we substitute the 5 + 3 with 8 to get

5 + 3 x 2 = 8 x 2 = 16

This is the wrong answer because we didn’t do the operations in accordance with the hierarchy

We need to do the multiplication before the addition. 3 x 2 = 6

5 + 3 x 2 = 5 + 6 = 11

So, it is essential to do the operations in the correct order according to the hierarchy.