Table of Contents

Percentage Formula: Knowing the percentage formula is highly important in our daily lives, whether it’s for a loan payment or a wage increment. The percentage Formula is used to express the proportion or amount of something in terms of 100. There are various modes of Percentage Formulas that can be used to solve the different problems of percentages. The fundamental percentage formula is P% = **(Value/Total Value)×100**. In this article, we are going learn Several Percentage Formulas for calculating percentage growth, reduction, difference, and so on. Some solved problems are provided for a better understanding of Percentage Formulas.

## Percentage Formula

Before learning the percentage formula, we have to know the** meaning of Percentage.** The term “percentage” was derived from the Latin word “per centum,” which means “by hundred,” A percentage is a figure or ratio in mathematics that represents a fractional portion of a percent, i.e., per 100. The percentage symbol “%” is read as “percent” or “percentage” in this context. To convert this percent symbol to a fraction or decimal counterpart, simply replace it with “divided by 100” For example, if someone received 80% on his science examination, It means he received 80 out of the total 100 marks. In a percentage calculation, the total or denominator of the fraction is always 100.

## Percentage Formula Examples

A percentage formula is used to calculate the amount or proportion of a quantity in terms of a hundred. The % formula is used to calculate a percentage of a whole in terms of 100. You can use this formula to represent a number as a fraction of 100. The following formula is used for calculating the percentage:

**Percentage = (Value/Total Value)×100**

**Example: **In a 600 marks Exam, Bimal scored 540 marks. Then calculate how much percentage he gets in that exam.

**Solution:** Total marks in Exam = 600.

Bimal obtained=540 marks.

As per the percentage formula**, Percentage = (obtained Marks/Total Marks)×100**

Bimal’s mark in percentage = 540/600×100=90%

## Percentage Formula Calculation

Calculating a percentage of a given number implies determining the proportion of the total in terms of 100. When the data are supplied as fractions with a denominator of 100, the percentage can be simply determined. But in case a fraction with a denominator of 100 is not given then, we must convert the fraction to a fraction with a denominator of 100 so that it will be easily determined. Let’s now understand both methods for calculating percentages:

**Using the unitary method:**To calculate the percentage, simply multiply the fraction by 100. For example, the percentage associated with the fraction 3/20 is: 3/20×100 = 300/20 = 15%**Changing the fraction’s denominator to 100:**While calculating the percentage of a fraction, we must find the equivalent fraction of a given fraction such that the resultant denominator is 100 using this method. For example: Percentage of 3/20 = 3/20 × 5/5= 15 × 100 = 15%

## Percentage Formula for Conversion

Sometimes, we need to convert the Fraction to a Percentage or sometimes the percentage to a fractio while solving various problems based on the percentage formulas. Now let’s understand the hoe to convert a percentage to a fraction or vice versa.

### Fraction to Percentage Conversion

In some circumstances, we are given a percentage and must convert it to a fraction number. Some calculations are required to convert percentages to fractions. We can employ the formula,

**Fraction = Percentage/100**

For example,

Fraction of 10% = 10/100 = 1/10

Fraction of 20% = 20/100 = 1/5.

Fraction of 50% = 50/100 = 1/2

Fraction of 75%= 75/100 = 3/4

### Fraction to Percentage Conversion

To convert a fraction to a percentage, assume the fraction is represented by a/b, where “a” is a subset of “b.” The numerator and denominator are multiplied by 100. We can employ the formula,

**a/b × 100%.**

For example,

Percentage of 1/10 = 1/10×100= 10%

Percentage of 3/4 = 3/4×100= 75%

Percentage of 1/2 = 1/2×100= 50%

### Conversion between Percentage and Decimals

As previously we know the conversion between fractions and percentages. now Let’s Learn how to convert percentages to decimals and vice versa .whille converting percentages to decimals, we simply replace the % symbol with “divided by 100” to convert percentages to decimals. For instance, 20% = 20/100 = 0.2. on the other hand, We must multiply a decimal by 100 to convert it to a percentage. For instance, 0.2 = 0.2× 100 = 40%.

## Percentage Conversion Chart

In the below table, we have tabulated some commonly used percentage conversions.

Fraction | Percentage | Fraction | Percentage |
---|---|---|---|

1/1 | 100% | 1/11 | 9.09% |

1/2 | 50% | 1/12 | 8.33% |

1/3 | 33.33% | 1/13 | 7.69% |

1/4 | 25% | 1/14 | 7.14% |

1/5 | 20% | 1/15 | 6.66% |

1/6 | 16.66% | 1/16 | 6.25% |

1/7 | 14.28% | 1/17 | 5.88% |

1/8 | 12.5% | 1/18 | 5.55% |

1/9 | 11.11% | 1/19 | 5.26% |

1/10 | 10% | 1/20 | 5% |

## Percentage Change

Percentage changes in the value of a quantity over time are expressed as a percentage. For example, an increase in population, voting, and a reduction in poverty, among other things. There are two scenarios that may emerge when calculating percentage change:

**Percentage increase:** The percentage increase is calculated by subtracting the original number from the new number, dividing the result by the original number, and multiplying by 100. The following formula can be used to determine percentage increases:

**Percentage Increase = (Increased Value-Original Value)×100**

**Percentage Decrease: **A percentage drop is the same as subtracting a new number from the old number, dividing by the original amount, and multiplying by 100.

**Percentage Decrease= (Original Value-Decreased Value)/Original Value ×100**

## Percentage Formula Solved Examples

**Example 1: A student received 80 points out of total 100 points in an examination. Determine the student’s percentage of the marks received.**

**Solution:** The total number of marks obtained by the student is 80.

total marks of the Examination = 100

student’s percentage of the marks received = (80/ 100) = 80%

As a result, the proportion of marks obtained is 80%.

**Example 2:** **A class contains 400 Students. The percentage of total girls and boys in the Class are 40% and 60% respectively. female. Determine the total number of boys and girls in the class.**

**Solution:** Given that the total number of students in the class is 400.

Percentage of Total Girls= 40%

Number of female students in the class =(Girls pecentage× Total number of students)

= 40% x 400= 40/100 x 400= 160 girls.

Similarly, the number of boys in the class =(Boys pecentage× Total number of students)

= 60% x 400= 60/100 x 400= 240 boys

The total number of boys and girls in the class is 240 and 160 respectively.