In mathematics, a percentage is a method of representing numbers as a fraction of 100 (percent meaning “per hundred”). Percentage is represented as percent sign, **%**. For example, 30% (read as “thirty percent”) is equal to \frac{30}{100} or 0.3.

## Percentage Calculator

**Following are the steps to use percentage calculator:**

- Enter values in input fields.
- Click on calculate button.
- You will get answer with step by step solution

**We typically use percentage calculator in three ways:**

- To compare a quantity to the whole.
- To compare one quantity to another.
- To compare a quantity to an increased or decreased amount of the same quantity.

## Percentage Definition

Percent is an abbreviation for the Latin word Percentum. The meaning is per hundred or hundredths and denoted by “%” sign or simply “percent”.

Percentage is applied to various calculations in the practical concerns of life. Among the most of these are rise and fall of stocks, discount, interest, insurance, profit and loss, duties and taxes.

- Percentage is a fraction in which the denominator never changes and is always equal to 100.
- Percentage is a fraction and fraction being a ratio, percent is also considered as a ratio.

**Examples:**

- 10% is equal to \frac{1}{10} or 0.1
- 25% is equal to \frac{1}{4} or 0.25
- 50% is equal to \frac{1}{2} or 0.5
- 75% is equal to \frac{3}{4} or 0.75
- 90% is equal to \frac{9}{10} or 0.9

**Percentage Examples**

Solution:

Cost price = $50

Profit = 10 %

so first of all we have to find profit

so, profit = 50×10/100 = $5

Sale price is cost price + profit = (50+5)= 55

The sale price of book is $55

Solution:

Sale price = $25

Cost price = $20

Now, profit = sale price – cost price = $25 – $20 = $5

So percentage profit = 5/20 x 100 = 25%

so answer is 25%

## Percentage Formula

Percent simply means ‘per hundred’. The symbol 20% is read as ‘twenty per cent’and simply means 20 out of 100. Percentage formula is algebraic equation that has percentage, value and total value.

Percentage = \frac{Value}{Total Value} × 100

**Application of percentage:**

- Profit calculation
- Loss calculation

It is useful to be able to understand that a per cent can be converted to a fraction and a decimal.

\frac{A}{B} = P × 100

Where, A and B are the first and second values, and P is Percentage.

**Steps for converting fractions to percentage:**

- Step 1: Find a number you can multiply the bottom of the fraction by to get 100.
- Step 2: Multiply both top and bottom of the fraction by that number.
- Step 3: Then write down just the top number with the “%” sign.

## How to find Percentage?

Below are some rules which you need to follow to find percentage.

**Some Rules to find percentage:**

- When we compare two quantities of the same kind by division, we have a ratio of those two quantities.
- The ratio should be in the lowest form.
- The order in the ratio is very important. It cannot be interchanged.
- Ratio has no unit.
- Two or more ratios can be compared.
- Proportion is an equality of two ratios.

**Example:**

Question: Express 2/5 as a Percent.

Solution:

Step 1: We can multiply 5 by 20 to become 100

Step 2: Multiply top and bottom by 20

2/5 x 20/20 = 40/100

Step 3: Write down 40 with the percent sign

2/5 = 40 %.

## Percentage to Decimal and Fraction Table

The following percentage table shows the conversion of percentage to decimal and fraction that can be used to speed up solving math problems.

Fraction | Decimal | Percent |

1/2 | 0.5 | 50% |

1/3 | 0.333… | 33.333…% |

2/3 | 0.666… | 66.666…% |

1/4 | 0.25 | 25% |

3/4 | 0.75 | 75% |

1/5 | 0.2 | 20% |

2/5 | 0.4 | 40% |

3/5 | 0.6 | 60% |

4/5 | 0.8 | 80% |

1/6 | 0.1666… | 16.666…% |

5/6 | 0.8333… | 83.333…% |

1/8 | 0.125 | 12.5% |

3/8 | 0.375 | 37.5% |

5/8 | 0.625 | 62.5% |

7/8 | 0.875 | 87.5% |

1/9 | 0.111… | 11.111…% |

2/9 | 0.222… | 22.222…% |

4/9 | 0.444… | 44.444…% |

5/9 | 0.555… | 55.555…% |

7/9 | 0.777… | 77.777…% |

8/9 | 0.888… | 88.888…% |

1/10 | 0.1 | 10% |

1/12 | 0.08333… | 8.333…% |

1/16 | 0.0625 | 6.25% |

1/32 | 0.03125 | 3.125% |

## Percentage Word Problems

Solution:

Speed of car = 60 km

Increased percentage =10 % of 60 km

= (10/100) × (60) = 6 km

New speed = 60 + 6 = 66 km

Solution:

In a mathematics examination 20 students out of 25 cleared test.

Percentage calculation = (20/25) = 80%

Solution:

Emma gets 95% marks, maximum mark is 500

Emma marks out of 500 = 500 × ( 95/100 ) = 475

Solution:

Cost price of an article = $450

Selling of an article = $500

Selling price is greater than cost price so there is a profit.

Profit = Selling price – Cost price

= 500 – 450 = $50

### Percentage FAQ

What is percentage really means?

Percentage means per 100 or for every hundred and denoted by symbol % or simply percent.

What is 20% of 150?

20% of 150 is 30. Use our percentage calculator to find percentage and percentage change between two numbers.

What is the percentage formula?

The formula to calculate percentage of a value out of total value can be written as, Percentage = (Value/Total value) x 100.

What is percentage change formula?

The formula to calculate Percentage change is: (Old Value – New value)/Old Value × 100