Introduction, Theory, and Practicals of BODMAS

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BODMAS

* BODMAS rule is an acronym that is used to remember the order of operations to be followed while solving expressions in mathematics. It stands for B - Brackets, O - Order of powers or roots, D - Division, M - Multiplication A - Addition, and S - Subtraction. It means that expressions having multiple operators need to be simplified from left to right in this order only. First, we solve brackets, then powers or roots, then division or multiplication (whichever comes first from the left side of the expression), and then finally, subtraction or addition, whichever comes on the left side.

* In this lesson, we will be learning about the BODMAS rule which helps to solve arithmetic expressions, containing many operations, like, addition (+), subtraction (-), multiplication (×), division (÷), and brackets

 * If you are given any such equation which is made up of more than 1 operation.  So to solve that you have to follow the rule of BODMAS

 Eg – 2+4×3-2=12 Answer

 * To solve the above question, we first did the action of multiplication.  Because according to the rule of BODMAS,

 Multiplication comes before addition and subtraction, so its action was done first.

 * Then after this the action of addition was done and finally the operation of subtraction was done.  All these have been done in exactly the same way.  The order in which they appear in BODMAS is

 * Basically now you must have understood this.  That which comes first in BODMAS is done first and what comes later is done later.

 Solving Brackets in BODMAS

 * You all must know this.  There are four types of parentheses.  The law of BODMAS tells us that first we should do parentheses.  But if all the four parentheses are available at the same place, then which parenthesis should we act first.  It doesn't tell.  So next we are going to understand the action of parentheses.

 * There is also a method to simplify parentheses which is as follows.  Their order is also taken care of while solving the brackets.  Their sequence is ViCiCuSq

 •Vi- Viniculum- Line Brackets "-'

 •Ci- Circular bracket- small bracket “( )”

 •Cu- Curly bracket- floor bracket "{}"

 •Sq- Square bracket -capital bracket "[]"

 * It is also solved in the same order as we told to do BODMAS, that means according to their order, that is, the one that comes first, and the one that comes after, has to be solved 

Maths is fun

Operations

"Operations" mean things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation.

But, when you see something like...

7 + (6 × 52 + 3)

... what part should you calculate first?

Start at the left and go to the right?

Or go from right to left?

Warning: Calculate them in the wrong order, and you can get a wrong answer !

So, long ago people agreed to follow rules when doing calculations, and they are:

Order of Operations

Do things in Brackets First

yes   4 × (5 + 3) = 4 × 8 = 

32

 

not   4 × (5 + 3) = 20 + 3 = 

23

(wrong)

Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract

yes   5 × 22 = 5 × 4 = 

20

 

not   5 × 22 = 102 = 

100

(wrong)

Multiply or Divide before you Add or Subtract

yes   2 + 5 × 3 = 2 + 15 = 

17

 

not   2 + 5 × 3 = 7 × 3 = 

21

(wrong)

Otherwise just go left to right

yes   30 ÷ 5 × 3 = 6 × 3 = 

18

 

not   30 ÷ 5 × 3 = 30 ÷ 15 = 

2

(wrong)

How Do I Remember It All ... ? BODMAS !

B

Brackets first

O

Orders (i.e. Powers and Square Roots, etc.)

DM

Division and Multiplication (left-to-right)

AS

Addition and Subtraction (left-to-right)

Divide and Multiply rank equally (and go left to right).

Add and Subtract rank equally (and go left to right)

So do it this way:

bodmas

After you have done "B" and "O", just go from left to right doing any "D" or "M" as you find them.

Then go from left to right doing any "A" or "S" as you find them.

Note: the only strange name is "Orders". "Exponents" is used in Canada, and so you might prefer "BEDMAS". There is also "Indices" which makes it "BIDMAS". In the US they say "Parentheses" instead of Brackets, so it is "PEMDAS"

Examples

Example: How do you work out 3 + 6 × 2 ?

Multiplication before Addition:

First 6 × 2 = 12, then 3 + 12 = 15

Example: How do you work out (3 + 6) × 2 ?

Brackets first:

First (3 + 6) = 9, then 9 × 2 = 18

Example: How do you work out 12 / 6 × 3 / 2 ?

Multiplication and Division rank equally, so just go left to right:

First 12 / 6 = 2, then 2 × 3 = 6, then 6 / 2 = 3

A practical example:

ball throw

Example: Sam threw a ball straight up at 20 metres per second, how far did it go in 2 seconds?

Sam uses this special formula that includes gravity:

height = velocity × time − (1/2) × 9.8 × time2

Sam puts in the velocity of 20 metres per second and time of 2 seconds:

height = 20 × 2 − (1/2) × 9.8 × 22

Now for the calculations!

Start with: 20 × 2 − (1/2) × 9.8 × 22

Brackets first: 20 × 2 − 0.5 × 9.8 × 22

Then Orders (22=4): 20 × 2 − 0.5 × 9.8 × 4

Then the Multiplies: 40 − 19.6

Subtract and DONE ! 20.4

The ball reaches 20.4 metres after 2 seconds

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