# What are BODMAS, BEDMAS & PEMDAS?

Simplification is a very common question which comes in Quantitative Aptitude asked in various entrance exams. The simplification can be done by doing Operation.

Here operation means mathematical operations like addition, subtraction, multiplication, division and many more. It seems simple as we all know how to apply these operations from our childhood.

But when you go through an expression like

8 x 3 – 2 x 4 + 2 ÷ 2

Then if we solve this expression without knowing any specific method, we will calculate it as:

Case 1: Going Left to right

24 – 2 x 4 + 2 ÷ 2

= 22 x 4 + 2 ÷ 2

= 88 + 2 ÷ 2

= 84 ÷ 2

= 42

Case 2: Going Right to left

8 x 3 – 2 x 4 + 1

= 8 x 3 – 2 x 5

= 8 x 3 – 10

= 8 x (-7)

= – 48

This will never lead to a correct answer. Applying various methods leads us to various answers but wrong one, thus long time ago Mathematicians agreed to follow a common Rule to solve these problems. This Rule is BODMAS.

**BODMAS specifies the Order of Operations as**

**B : B**rackets first

**O : O**f/**O**rders (i.e. powers, square root etc.)

**DM : D**ivision and **M**ultiplication (left-to-right)

**AS : A**ddition and **S**ubtraction (left-to-right)

NOTE:

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

But there is some confusion because from the past the concept of BODMAS in our mind is like:

Brackets / Of or Orders (powers, square root etc)/ Division / Multiplication / Addition / Subtraction.

Means Brackets are followed by Of or Orders, and Of or Orders are followed by Division, Division are followed by Multiplication and so on in the given order.

But the fact is after going through B and O, just go from Left to right and apply operation “D” or “M”, whichever is coming first.

Then operate “A” or “S”, whichever is coming first.

Considering an example 24 / 6 x 3 / 2

We go through the right way of BODMAS, The **M**ultiplication and **D**ivision having equal rank, so we just go left to right and we got

24 / 6 x 3 / 2 = 4 x 3 / 2 = 12 / 2 = 6

Now we can solve the above expression 8 x 3 – 2 x 4 + 2 ÷ 2

= 24 – 8 + 1

= 17

It becomes so simple by Using BODMAS

Now there is one thing to remember sometimes 24 – 8 + 1 can be wrongly evaluated as 15 by those who misunderstood BODMAS, and fail to get 17 which is correct answer.

Now we under stood how BODMAS works, then the question arises what are these BEDMAS and PEMDAS are?

These are nothing but the various names of BODMAS, in Canada “Exponents” is used in place of “Orders” thus BODMAS becomes BEDMAS. Sometimes “Indices” is also used in place of “Exponents” so BODMAS also called BIDMAS.

Similarly in US, “Parentheses” is used in place of “Brackets” thus it is also known as “PEMDAS”.

At last I want to tell you an interesting thing, you see there are several scientific calculators available in the market, sometimes duplicate calculators are also available so we can check rather the calculator is mathematical or not by just typing a question based on BODMAS, if its answer is correct that means calculator is mathematical and its worth buying.

Look how maths can help you out in your daily life also in purchasing stuffs.

Enjoy learning.

All the best.

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