Introduction – Percentage 

Definition: 

A Percent is a number or ratio expressed as a fraction of 100. In other words, Percent is a fraction of denominator 100.

Percent is denoted by the symbol %. ‘Per’ ‘cent’ means out of 100.

The percent symbol is written to the right side of the number, like this 15%.

Example: 25% (read as twenty five percent) 

                 equal to  25% = 25/100

means 25/100 that is 25 part from 100, this can also be written as 0.25.

                or  25% = 25/100 = 0.25

                     1% = 1/100 = 0.01

                     10/100 = 1/10 = 0.1

                     100/100 = 1/1 = 1

                     50/100 = 5/10 = 0.5

                     25 /100 = 1/4  = 0.25

         Calculation Tricks for percent

If we calculate a% of b, use the formula

                   (a/100)b = (a x b)/100…..1

If we calculate b% of a, use the formula

                    (b/100)a = (b x a)/100…..2

From eq. 1 and eq. 2 we have,

      a % of b = b % of a

we can see by below example,

Example: Prove that 60% of 90, is equal to 90% of 60?

Solution:         60% of 90 = (60/100)x 90

                        60% of 90 = 54

         and          90% of 60 = (90/100)x 60

                         90% of 60 = 54

we get the value of 60% of 90 is 54 and also the value of 90% of 60 is 54 so, 

                      a % of b = b % of a

Example: 40% of a number is 200, what is the number?

Solution: Let the number be a,

Given that  (40/100)x a = 200

                            ∴ 4a = 200 x 10

                              ∴ a = 2000/4

                              ∴ a = 500

 Solution: the number is 500

Example: 60% of a number is 300, what is the number?

Solution: Let the number be a,

Given that  (60/100)x a = 300

                            ∴ 6a = 300 x 10

                              ∴ a = 3000/6

                              ∴ a = 500

                    Solution – the number is 500

Example: Find 25% of 500

                             = (25 x 500)/100

                             = 125

Example: Find 30% of 1500

                            = (30 x 1500)/100

                            = 45000/100

                            = 450

Example: John’s monthly income is $1500, he spent $500 per month on clothes. find the percent of monthly income saved by john. 

Solution: John’s monthly income = $1500

              john’s saving per month = $1500 – $500

              john’s saving per month = $1000

percent of saving income = (1000/1500) x100

                                     = 1000/15

      percent of saving income = 66.6%