What is BODMAS?

Suppose we want to calculate

    2 × 4 + 3 – (8 – 1)

How do we do it?

Do we multiply first?

Or Subtract?

We use BODMAS rule

BODMAS stands for B racket, O rder, D ivision, M ultiplication, A ddition and S ubtraction

Let’s get back to our question

  2 × 4 + 3 – (8 – 1)

In BODMAS

• We first solve B racket
• Then O rder
• Then D ivision & M ultiplication are at the same level, so we go from left to right and solve them.
• A ddition and S ubtraction are at the same level, so we go from left to right and solve them

2 × 4 + 3 – (8 – 1)

2 × 4 + 3 – (8 – 1)

  = 2 × 4 + 3 – 7

  = 8 + 3 – 7

  = 11 – 7

  = 4

Note :

Here we first solve B racket – (8 – 1)

Then there is no O rder,

So, we solve D ivision & M ultiplication left to right – 2 × 4

And then, we solve A ddition and S ubtraction left to right – 8 + 3 and 11 – 7

Let’s take some more examples

15 ÷ 3 × 1 ÷ 5

15 ÷ 3 × 1 ÷ 5

  = 15 ÷ 3 × 1 ÷ 5

  = 15/3 × 1 ÷ 5

  = 5 × 1  ÷ 5

  = 5 ÷ 5

  = 5/5

  = 1

Note :

Here we have no B racket, or O rder

So, we solve D ivision & M ultiplication left to right – first 15 ÷ 3 , then 5 × 1 and then 5 ÷ 5

And then, A ddition and S ubtraction are not there

48 ÷ 2 (9 + 3)

48 ÷ 2 (9 + 3)

  = 48 ÷ 2 × (9 + 3)

  = 48 ÷ 2 × 12

  = 48/2 × 12

  = 24 × 12

  = 288

Note :

Here we first solve B racket – (9 + 3)

Then there is no O rder,

So, we solve D ivision & M ultiplication left to right – First 48 ÷ 2, then 24 ×  12

And then, A ddition and S ubtraction are not there

10² – 4 ÷ 2

10² – 4 ÷ 2

  = 10²  – 4 ÷ 2

  = 100 –  4 ÷  2

  = 100 – 4/2

  = 100 – 2

  = 98

Note :

Here, there is no B racket

Then, we solve O rder – 10 ² ,

Then, we solve D ivision & M ultiplication left to right – 4 ÷ 2

And then, A ddition and S ubtraction left to right – 100 – 2

14 ÷ 7  + 4 × 8 – 2 ³

14 ÷ 7  + 4 × 8 – 2 ³

  = 14 ÷ 7  + 4 × 8 – 8

  = 2 + 4 × 8 – 8

  = 2 + 32 – 8

  = 34 – 8

  = 26

Note :

Here, there is no B racket

Then, we solve O rder – 2 ³ ,

Then, we solve D ivision & M ultiplication left to right – first 14 ÷ 7, then 4 × 8

And then, A ddition and S ubtraction left to right – first 7 + 32, then 39 – 8

(4 × 3 ² – 2 ³ ÷ 4) + 10 – 5

(4 × 3 ² – 2 ³ ÷ 4) + 10 – 5

  = (4 × 9 – 8 ÷ 4) + 10 – 5

  = (36 – 8 ÷ 4 ) + 10 – 5

  = (36 – 8/4) + 10 – 5

  = (36 – 2) + 10 – 5

  = (34) + 10 – 5

  = 34 + 10 – 5

  = 44 – 5

  = 39

Note :

Here, there is a B racket, so we solve it first

In bracket,

We first solve O rder – 3 ² , 2 ³ ,

Then, we solve D ivision & M ultiplication left to right – first 4 × 9, then 8 ÷ 4

And then, A ddition and S ubtraction left to right – first 36 – 4 in bracket, then 32 + 10, 42 – 5

PEMDAS

BODMAS in some Regions is called PEMDAS

PEMDAS stands for P arenthesis, E xponents, M ultiplication, D ivision, A ddition, S ubtraction

In PEMDAS

• We first solve P arenthesis
• Then E xponents
• Then M ultiplication & D ivision are at the same level, so we go from left to right and solve them
• A ddition and S ubtraction are at the same level, so we go from left to right and solve them

You can remember it by saying

  P lease  E xcuse  M y  D ear  A unt  S ally