## Table of Contents

## Definition of Percentage

Percentage is one of the many ways to look at or measure quantities in relation to a base value. In the simplest terms, a percentage value is basically a number that can be looked at as a fraction of 100 since 100 percent is taken as the total value. With percentages, we can ascertain how small or big a value is relative to another value (base value).

For instance, if you want to express how your current salary compares with your salary last year, you can express the same in terms of the percentage hike you got in your salary this year. Let us take another example to add to this understanding.

Let’s say you want to figure out what part of the overall population of the United States does the population of New York account for. So, here you are trying to express the population of New York relative to the overall population of the US which you are referring to as the base value. One of the most effective and convenient ways to express the same can be in terms of percentage.

Besides, let us consider one more example from a different approach. Let’s say in a classroom, the percentage of female students is 45 percent. This implies that female students account for 45 percent of the total population of the class. So, if there are 100 students in total in the classroom, 45 percent implies that 45 of them are female students.

Besides, using percentages, you can even compare the top economies of the world based on their inflation rates, percentage of exports and imports etcetera.

## Definition of Fraction

Like percentage values, fractions also express the parts of the total value in the form of a ratio where the total value is in the denominator and the portion is represented by the numerator. The only difference is that in percentages, the whole value is taken as hundred while in the case of fractions, 1 is taken as the total value. In either case, you can simply convert percentages into fractions and vice versa.

For instance, a fraction value of ½ represents half the total value. Now if we convert the fraction into a percentage, ½ comes out to be 50 percent (½ x 100).

## Calculation of Percentage

### a. To find what is A% of B

Let’s say you have to find 25 percent of 200

Here, A is 25 while B is 200

The formula to compute what is A% of B is given below

( A/100 ) X B |

So, if we take our example forward, 25 percent of 200 will be

( 25/100 ) X 200= | 50 |

### b. To find A is what percent of B

Let’s say you need to find 50 is what percentage of 750

Here A is 50 and B is 750

The calculation can be made using the following formula :

( A /B ) X 100 |

Taking our example into consideration

( 50/750 ) X 100= | 6.66 % |

### c. To find A is B% of what

Let’s say we need to find out 70 is 20 percent of what (say )

Here A is 70 while B is 20

The following formula can be used to find the answer

= | ( A x 100 )/ B |

### d. To find B is what percent of A

Let’s say we need to find 35 is what percent of 800

Here A is 800, B is 35

You can apply the following formula to carry out this calculation

( B/A )X 100 |

So, as per the example

( 35/800 ) X 100 = | 4.37% |

### e. To find C when A % is C of B

Let’s say we need to find C when 10 % is C of 150

Here A is 10 % and B is 150

The value of C can be computed using the following formula

C = | A X B |

100 |

So, as per example, the value of C will come out to be 15

### f. To find C when A% is B of C

Let’s say we need to find C when 50 percent of C is 700

Here A is 50 and B is 700

The value of C can be calculated using the formula given below

C = | B X A |

100 |

### g. To find what is A plus B% of A is equal to

Let’s say we need to find the value of 2000 plus 25 percent of 2000

Here A is 2000

B is 25

The formula to calculate the value of A plus B% (of A) is given below

A + ( ( B/100 ) X A ) |

So, our answer in the context of our example will come out to be

2500

### h. To find what percent of A plus A is equal to B

Let’s say you need to find what percent of 3000 when added to 3000 is equal to 3300

Here A = 3000

B = 3300

To find what percentage of A when added to A yields 3300, the following formula can be used

( ( 3300 - 3000 ) /3000 ) X 100 | =10 percent |

### i. To find the the value of C when A% of C plus C is equal to B

Let’s say you need to find C when 25 percent of C plus C is equal to 250

ou can use the following formula to find out the value of C

C = | ( ( B/100 ) + A ) X 100 |

So, in the context of our example, the value of C will be 200

### j. To find A - B% of A

Let’s say you need to find the value of 4000 - 40% of A

Here A = 4000

B = 40

The value of A - B% of A can be computed using the following formula

A - | ( B/100 ) X A |

So, in our example,

The value of A - B/100 X A will be 2400

### k. What percent of A when subtracted from A is equal to B

Let’s say you want to calculate what percentage of 10000 when subtracted from it yields 8000.

Here A is 10000 while B is 8000

The calculation can be made using the following formula given below

( ( 10000- 8000 ) /10000 ) X 100 |

As per our example, the percentage value will come out to be 20 percent

### l. To find the value of C when C minus A % of C is B

Let’s say we need to find C when C- 20 percent of C =1000

Here A is 20 and B is 1000

The calculation can be made using the following formula

C= | B |

1- A/100 |

As per the formula, the value of C as per our example will be 1250

### m. To find percentage increase or percentage decrease

Let’s say your salary has increased from 20000 per month to 25000 per month and you want to calculate the percentage increase

The formula to calculate the percentage increase is given below

New value - Old Value X 100 |

Old value |

As per our example, the percentage increase will be 25 percent