Percent (%) means per hundred is called ‘Percentage’. For example: 22% means 22 per 100, and can also be written as a fraction ($latex \frac{22}{100}$) or a decimal (0.22).

It is quite straightforward to convert a percent into a fraction or decimal (and vice versa) using the following rules.

Question: Write 42% as a fraction and a decimal.

42% = $latex \frac{42}{100}$  = $latex \frac{21}{50}$ (as a fraction)

42% = 42 ÷ 100 = 0.42 (as a decimal)

Question: Write 0.05 as a percentage.

0.05 x 100 = 5%

Question: Find 25% of 320.

25% is the same as $latex \frac{1}{4}$,  so divide by 4.

$latex \frac{320}{4}$ or  320 ÷ 4 = 80

Percentage Increase or Decrease:

Add (+) it on for an increase and Subtract (-) it for a decrease

Question: The price of a book increases by 12%. If the original price is Rs. 4.70 what is the new price?

Find 12% at first, $latex \frac{12}{100}$ ×$latex \frac{470}{1}$ = 56.4

Therefore, add it on: Rs 4.70 + 56 will be Rs 5.26. This is the new price.

Writing One Number as a Percentage of another:

To write one number as a percentage of another make a fraction (using the two numbers) then multiply by 100 to turn it into a percent.

$latex \frac{Amount}{out of}$ × $latex \frac{100}{1}$

Question: Out of a class of 20 children, 17 are going on a school trip. What percentage is this?

$latex \frac{17}{20}$ × $latex \frac{100}{1}$ = 85%.      (Make 17 out of 20 into a fraction then × 100)

Percentage Profit or Loss:

If you are asked what percentage something has increased or decreased by, work out the increase or decrease as a percentage of the original.

$latex \frac{increase / decrease}{original price}$ × $latex \frac{100}{1}$

The denominator (bottom) of the fraction is always the original amount. Make the fraction then x 100 to make into a percentage.

Question: Shahid bought a lamp for Rs 45 then sold it a year later for Rs 28. What was her percentage loss (decrease)?

Loss = 45 – 28 = Rs 17 and the original price = Rs 45

Using the formula,

$latex \frac{17}{45}$ × $latex \frac{100}{1}$ = 37.8 % (this is in loss percentage)