(Online Course) CSAT Paper – II : Basic Numeracy: Simplification

In simplification of an expression there are certain laws which should be
strictly adhered to. These laws are as follows:

‘VBODMAS’ Rule

This rule gives the correct sequence in which the mathematical operation are
to be executed so as to find out the value of a given expression.

Here, ‘V’ stands for Vicnaculum (or Bar), ‘B’ stands for ‘Brcket’, ‘O’ stands
for ‘Of’, ‘D’ stands for ‘Division’, ‘M’ stands for ‘Multiplication’, ‘A’ stands
for ‘Addition’ and ‘S’ stand for ‘Subtraction’.

1. Here, ‘VBODMAS’ gives the order of simplification. Thus, the order of
   performing the mathematical operations in a given expression are
   
   First : Virnaculum or line bracket or bar
   Second: Bracket
   Third: Of
   Fourth: Division
   Fifth: Multiplication
   Sixth: Addition &
   Seventh: Subtraction
   The above order should strictly be followed.
    
2. There are four types of brackets.

   (i) Square brackets [ ](ii) Curly brackets { }
   (iii) Circular brackets ( )
   (iv) Bar or Virnaculum –

   Thus, in simplifying an expression all the brackets must be removed in the
   order ‘–’, ‘( )’, ‘{ }’ and ‘[ ]’.

Modulus of a Real Number

The modulus of a real number x is defined as
                                                               
= x, if a > 0
                                                                      |x|
                                                               
= x, if a < 0

Basic Formulae

Example 1: Simplify 1005 + 500 – 10 – 80.

Solution. 1005 + 500 – 10 – 80 = 1005 + 490 – 80 = 1495 – 80 = 1415

Example 2: If a * b = 2(a + b), then what is the value of 5 * 2?

Solution. 5 * 2 = 2(5 + 2) = 2 × 7 = 14

Example 4: 2/5 part of the students in a class are the girls and
remaining are the boys. If 2/9 part of the girls and 1/4 part of the boys are
absent, then what part of total students is present.

Solution. Let total number of students = x