## Shortcuts for finding Percentages

Percentage is nothing but a fraction, whose denominator is 100. The actual meaning of Per-Cent is per every 100. It is usually denoted by the sign **%** and sometimes shortened as P.C.

Eg. 5/100 is called 5 per cent (or 5%)

**Here 5, which is the numerator is called the rate per cent.**

In the same way 18% means 18/100 (18 out of 100)

Percentage is the the standard way to compare two quantities. Suppose we want to compare to fractions (4/50) and (9/25), make the denominator 100 for both the fractions.

So,

4/50 = 8/100 => means 8 out of 100

9/25 = 36/100 => means 36 out of 100

so, (4/50) < (9/25)

Have a look at some important points about Percentages.

- 5% of Rs. 200 means (5/100)X(200/1) = 10 (remember guys, ‘Of’ means multiplication).
- 75% is equivalent to 75/100 = 3/4
- Increase % = (increase/original) X (100)

#### Have a look at some short forms of percentages before doing some problems (better try to remember these)

**5 % = 5/100 = 1/20 = 0.05**

**6 1/4 % = 25/400 = 1/16 = 0.0625**

**10 % = 10/100 = 1/10 = 0.1**

**12 1/2 % = 25/200 = 1/8 = 0.125**

**16 2/3 % = 50/300 = 1/6 = 0.166**

**20% = 20/100 = 1/5 = 0.2**

**25% = 25/100 = 1/4 = 0.25**

**33 1/3 % = 100 / 300 = 1/3 = 0.33**

**40 % = 40 / 100 = 2 / 5 = 0.4**

**50 % = 50 / 100 = 1/2 = 0.5**

**60 % = 60 / 100 = 3/5 = 0.6**

**66 2/3 % = 200/300 = 2/3 = 0.66**

**75 % = 75 / 100 = 3/4 = 0.75**

**80 % = 80 / 100 = 4 / 5 = 0.8**

**90 % = 90 / 100 = 9/10 = 0.9**

**100% = 100 / 100 = 1**

**125 % = 125 / 100 = 5 / 4 = 1.25**

**150 % = 150 / 100 = 3/2 = 1.5**