BODMAS Rule of Mathematical Operations

Introduction

BODMAS Rule of Mathematical Operations | BODMAS vs PEMDAS. Many a times someone might have asked you “What is 2+2÷2?”, and in haste you would have answered 2. However, the correct answer for this is 3.

We perform multiple mathematical operations in our daily life. In order to do a proper calculation, there is a rule which is called BODMAS. The other similar rule is PEMDAS. Let us know what these rules “BODMAS” and “PEMDAS”.

BODMAS Rule of Mathematical Operations | What is PEMDAS Rule | BODMAS vs PEMDAS rule | Examples of BODMAS Rule | BEDMAS

There are different mathematical operations. They are Addition, Subtraction, Multiplication, and Division. BODMAS rule provides us the sequence or order in which they need to be performed.

Abbreviation of BODMAS

BODMAS – Brackets, Orders, Divisions Multiplications, Addition and Subtraction

What is PEMDAS Rule?

PEMDAS is similar to BODMAS and only the terms used are different, it is nothing but a change of name for BODMAS.

Abbreviation of PEMDAS

PEMDAS – Parentheses First, Exponents, Multiplication, Division, Addition, and Subtraction.

BODMAS vs PEMDAS Rule

As discuss earlier, it is only a name change. Let us look further as how they are same or different.

In United States, we call it PEMDAS.
In India and The United Kingdom, the same is called BODMAS.
In Canada the same rule is call: BEDMAS – Brackets, Exponents, Division, Multiplication, Addition, and Subtraction.
These rules are different, but the order of calculation is still the same. Else, different countries would have got different results and there would have been a world war to settle this down. Nice Joke!

So, you might have noticed a difference in BODMAS and PEMDAS. The Multiplication and Division have changed places. That even does not make a difference, if we perform multiplication first or division first. But rest all should be in order.

BODMAS	PEMDAS	BEDMAS
Brackets – [], {}, (),	Parentheses- [], {}, (),	Brackets – [], {}, (),
Orders – 2², 8⁵, √24, √16	Exponents – 2², 8⁵, √24, √16	Exponents – 2², 8⁵, √24, √16
DM – Division and Multiplication (÷ and X)	MD – Multiplication and Division (÷ and x)	DM – Division and Multiplication (÷ and x)
Addition	Addition	Addition
Subtraction	Subtraction	Subtraction

BODMAS, PEMDAS, BEDMAS Table

Examples of BODMAS Rule: (PEMDAS and BEDMAS)

Example 1: Solve: 4 +2³× (5−2)

Taking the BODMAS rule into consideration. We first solve the brackets.

4+2³× (5−2) ==> 4+2³×3

Next, we solve the Exponent.

4+2³×3 ==> 4+8×3

Next, we solve the Multiplication.

4+8×3 ==> 4+24

Finally, we add.

4+24 ==> 28.

Hence, 4 + 2³ × (5−2) = 28.

Example 2:

Solve 3 × (4+2) − 10 ÷ 2 + 5.

Solving 3 × (4+2) −10 ÷2 + 5 by BODMAS rule:

Let us solve the Bracket first:

3× (4+2) −10 ÷ 2 + 5 ==> 3 × 6−10 ÷ 2 + 5

This expression does not have orders or exponents. So, we proceed with Division.

3 × 6 − 10 ÷ 2 + 5 ==> 3 × 6 − 5 + 5

Now, let us do the multiplication.

3 × 6 − 5 + 5 ==> 18 – 5 + 5

Addition and Subtraction is next.

18 – 5 + 5 ==> 18 – 0 ==> 18

Hence, 3 × (4+2) − 10 ÷ 2 + 5 = 18.

Solving 3 × (4+2) −10 ÷2 + 5 by PEMDAS rule:

Parentheses, let us first solve the parentheses.

3 × (4+2) −10 ÷2 + 5 ==> 3 x 6 – 10 ÷2 + 5

Multiplication and Division, let us do multiplication and division:

3 x 6 – 10 ÷2 + 5 = 18 – 5 + 5

Now, we perform Addition and Subtraction.

18 – 5 + 5 = 18 – 0 = 18.

The answer is 18.

Note: Most of the time, you might get confused while performing the operation on 18 – 5 + 5.

How do we solve this?

In expression: 18 – 5 + 5 = 18 – (5-5)

In the above step we need to perform the addition, however, we need to look into the signs of Integers as well.

This will give: 18 – 0 = 18.

Let us look into more examples involving signs of integers.

#1. Solve: 35 – 22 + 28.

Common mistake that we do:

35 – 22 + 28 ==> 35 – 50.

This is wrong.

Correct method is:

35 – 22 +28 ==> 35 – (22 – 28).

35 – (22 – 28) ==> 35 – (-6)

35 – (-6) ==> 35 + 6 = 41.

Now, let us see few more examples:

#2. Solve: 48 + 92 -69

In this example, we can do Addition or Subtraction at the same time.

48 + 92 – 69 ==> 140 – 69

140 – 69 = 71

#3. Solve: 67 – 22 + 11

Either you can start from the left-hand side and perform operations.

==> 67 – 22 + 11 ==> 45 + 11

45 + 11 = 56.

Or you can group the numbers to be operated:

67 – 22 + 11 = 67 – (22 – 11)

==> 67 – (22 – 11) = 67 – 11

==> 67 – 11 = 56.

So now that we learned different methods to solve the equation, we can answer few questions.

Solve these using BODMAS rule, Solve, these using PEMDAS rule.

Expression	Result
13 + 12 – 12	13
95 – 22 -23 + 27	77
– 48 + 45 – 90	-93
22 + 89 – 108	3
90 – 90 + 20 – 10	10
10 – 22 + 27	15
78 – 90 – 22	-34