Percents and Fractions

In mathematics and everyday life, the term "percent" represents a fraction of 100 or "per hundred." Specifically, when we say that a number is a certain percent of another number, we mean that it is that number divided by 100 times the other number. The percent symbol ( $%$ ), which dates back to the early $15^{th}$ century, is a shorthand way to express this idea.

For example, if we say that $28 %$ of a quantity is a particular value, we mean that this value is equal to 28 hundredths or 0.28 of the quantity. In other words, it is equal to $\frac{28}{100}$ of the quantity.

Convert a percent to a fraction in lowest terms

As the previous explanation shows, any number expressed as a percent can also be expressed as a fraction where 100 is the denominator. But In many cases, that fraction is not expressed in the lowest terms.

This is how you convert a percent to a fraction in the lowest terms:

Example 1:

$5 % = \frac{5}{100}$

The easiest way to find the lowest terms for this fraction is to divide the numerator and denominator by 5, the greatest common factor of 5 and 100. 100 divided by 5 is 20, so 20 is the denominator. Because dividing 5 by 5 gives you 1, the resulting answer is $\frac{1}{20}$ .

$5 % = \frac{5}{100} = \frac{1}{20}$

Converting higher percents into fractions

This works the same for higher percentages.

Example 2:

$40 % = \frac{40}{100}$

This time, you divide the numerator and denominator by 20, the greatest common factor, so when you reduce to the lowest terms, you get $\frac{2}{5}$ .

$40 % = \frac{40}{100} = \frac{2}{5}$

Converting percents over 100 into fractions

Sometimes you run into a percentage that is larger than 100. For example, a company may experience 125% growth in one year. This can also be expressed as a fraction in the lowest terms, only you will get a mixed number as an answer.

Example 3:

$125 % = \frac{125}{100}$

Here, you will start by dividing the numerator and denominator into the largest common factor, which is 25. The result is $\frac{5}{4}$ . Then you simply lower this further into a mixed number, or $1 \frac{1}{4}$ .

$125 % = \frac{125}{100} = 1 \frac{1}{4}$

Converting percents that contain fractions in the percent

If a percent is not a whole number, you may end up with a denominator that is greater than 100. For example, sometimes you have a percent that is written as a mixed number like $4 \frac{1}{2} %$ . You can easily convert this to a fraction. Start by converting the percent to a decimal, which is $4.5 %$ , or $\frac{4.5}{100}$ .

To remove the decimal, move it one place to the right on both the numerator and the denominator, so you have $\frac{45}{1000}$ . The greatest common factor for 45 and 1000 is 5, so reduce the fraction to the lowest terms:

$4.5 % = \frac{45}{1000} = \frac{9}{200}$

Practice questions on learning percents and fractions

a. Express $23 %$ as a fraction.

$\frac{23}{100}$

b. Express $25 %$ as a fraction in the lowest terms.

$\frac{25}{100} = \frac{1}{4}$

c. Express $60 %$ as a fraction in the lowest terms.

$\frac{60}{100} = \frac{3}{5}$

d. Express $150 %$ as a fraction in the lowest terms.

$\frac{150}{100} = \frac{3}{2} = 1 \frac{1}{2}$

e. Express $5.5 %$ as a fraction in the lowest terms.

$\frac{5.5}{100} = \frac{55}{1000} = \frac{11}{200}$

f. Express $\frac{1}{3} %$ as a fraction in the lowest terms.

$\frac{\frac{1}{3}}{100} = \frac{1}{3 \times 100} = \frac{1}{300}$

Topics related to the Percents and Fractions

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Reciprocals

Percent

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Practice tests covering the Percents and Fractions

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Get help learning about percents and fractions

It can be incredibly confusing to make sense of percentages, fractions, and how the two relate to each other. There are a lot of things to remember and a number of functions to perform for different problems. Working with a qualified tutor can help your student understand how percentages relate to fractions and vice versa. Tutors work with your student until they understand the concepts and can easily perform the problems each time. To find out more about how tutoring can help your student, get in touch with the Educational Directors at Varsity Tutors today.