# Simplification & Approximation

**GETTING STARTED**

** ☛ BODMAS rule:**

The long mathematical expressions are always solved using BODMAS rule.

It gives the sequence in which expressions are solved.

B – Bracket

O – Of

D-Division

M-Multiplication

A-Addition

S-Subtraction

☛ First the brackets are solved. Within brackets also there is an order to solve – (), then {} and then [ ].

☛ After brackets, Division operation is to be carried out followed by Multiplication.

☛ After multiplication, addition and subtraction are carried out.

☛ **Virnaculum:**

Some questions may have a bar over a few terms indicating that they are to be solved even before starting off with brackets

☛ Modulus of a number:

This **expression always returns a non-negative value** irrespective of the input.

Y= f (x) =|x|

**Eg. Let x = 50**

Y= |50| = 50

**Let x = -50**

Y = |-50| = 50

**Approximation:**

☛It helps in quickening the process of arriving at an answer. It is one of the most important topics to be continuously practiced for MCQ type exams.

☛ Approximation helps in eliminating incorrect answer choices quickly.

☛The best way to approximate is to reduce the numbers to its nearest integer which can be easily used for calculation.

Let us consider an example:

A) 302

B) 502

C)202

D)102

**Soln:**

Approximating, we get,

Solving Further,

**=(60 + 140 -230 +230)/2**

**=100**

Of the given options, the alternatives are too apart the closest number is 102.

**Therefore D is the right answer.**