Percent and Fraction Relation Formulas | List of Percent and Fraction Relation Formulas You Should Know - BYJUS

Percent and Fraction Relation Formulas

We use percent to express statistical quantities like scores, growth, profits, losses, discounts, statistics related to demographics and economics, and so on. Percent is basically an alternate method for expressing fractions. Here we will discuss the formula that is used to convert a percent into a fraction and vice versa.     ...Read MoreRead Less

What is the meaning of the word Percent?

The word ‘percent’ is derived from the Latin phrase “per centum”, which means “by the hundred”. Percents are basically fractions represented in an alternate way that is easier to use. As it can sometimes be difficult to understand and compare complex fractions, we can standardize any fraction to get the percent form. This makes it easy for us to compare two quantities.

Even though percentages are easier to use for comparison of two quantities, we usually have to convert them back to fractions for performing math operations. Additionally, we get an idea of the actual quantity by looking at the numerator and the denominator of the fraction. On the contrary, it is not possible to determine the actual quantities when they are expressed as percentages. So, it is important to learn the formula and the steps involved in the conversion of percents to fractions.

List of Formulas

There are two formulas associated with percentages and fractions. The first formula is used to convert fractions into percentages, and the second formula is used to convert percentages into fractions. The two formulas are inverse of each other.

1. Fraction to percent conversion formula:

$$\text{Percent}=\text{Fraction}\times 100$$

2. Percent to fraction formula:

$$\text{Fraction} = \text{Percent} \div 100$$

As the name suggests, a percent is a fraction in which the denominator is 100. To convert a fraction into a percent, we usually divide the numerator by the denominator and multiply the result by 100. Another way is to find the equivalent fraction in which the denominator is 100 and take the new numerator as the percent value.

To convert a percent into a fraction, we can use the inverse of equation 1. We can drop the ‘%’ symbol by dividing the percent value by 100 and reducing or simplifying the result to get the simplest form of the fraction.

Solved Examples

Example 1: Express $$\frac{28}{112}$$

Solution:

$$\text{Percent}=\text{Fraction}\times 100$$

$$=\frac{28}{112}\times 100$$

$$=\frac{1}{4}\times 100$$

$$=\frac{100}{4}$$

$$=25$$%

So, $$\frac{28}{112}$$ is the same as 25%.

Example 2: Convert 35% into a fraction.

Solution:

$$\text{Fraction} = \text{Percent} \div 100$$

= $$\frac{35}{100}$$

= $$\frac{35~\div~5}{100~ \div~5}$$

= $$\frac{7}{20}$$

So, 35% is the same as $$\frac{7}{20}$$.

Example 3: While walking from home to school, Sam takes 70 steps per minute. He increased his walking pace by 10% on the way back. What was his walking pace while heading home?

Solution:

The walking pace from home to school = 70 steps per minute

The percentage increase in his walking pace from school to home = 10%

Increase in the walking pace = 10% of 70

$$=\frac{10}{100} \times 70$$    [Write 10% as a fraction, that is, $$\frac{10}{100}$$ ]

= 7

Hence, Sam’s walking pace on his way home = 70 + 7 = 77 steps per minute.

Example 4: A minimum score of 580 out of 650 is required to get an A grade for an examination. John scored 92% of the total marks. Did he get an A grade for the exam?

Solution:

Marks required to get an A grade = 580

Total marks = 650

Percentage of marks scored by John = 92%

Marks scored by John (out of 650) = 92% of 650

$$=\frac{92}{100} \times 650$$      [Write 92% as a fraction, that is, $$\frac{92}{100}$$

$$=23 \times 26$$

= 598

John scored 598 marks.

Hence, John has secured an A grade for the subject as he has scored more than 580 marks.

Example 5: Shop A sells a TV at $$\frac{18}{20}$$ of its original price. Shop B sells the same type of TV at 85% of the original price. Which shop makes more money by selling the TV?

Solution:

The fraction of the original price at which shop A sells the TV  $$=\frac{18}{20}$$

The percentage of the original price at which shop B sells the TV = 85%

We can either convert the percentage into a fraction or the fraction into a percentage to compare the selling prices of the TV in both shops. Since it is easier to compare two quantities using percentages, we will convert the fraction of the price of the TV sold by shop A into a percentage.

$$\text{Percent}=\text{Fraction}\times 100$$

The percentage of the original price at which shop A sells the TV $$=\frac{18}{20}\times 100$$

$$=\frac{18 \times 10}{2}$$

= 90%

Therefore, shop A sells the TV at 90% of the original price, and shop B sells it for 85% of the original price.

Since shop A sells it at a higher percentage of the original price, they make more money than shop B by selling the TVs.

The word ‘cent’ denotes 100. So, ‘percent’ means “for every hundred”. A cent is also $$\frac{1}{100}^{th}$$ of a dollar.