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# How to Convert Fractions to Percentages

Students can learn How to Convert Fractions to Percentages from the online expert Math Tutors. They can get elaborate explanation and solved examples to understand the concepts clearly.

## Converting Fractions to Percentages

A fraction is a number that represents part of a whole and percentage is the representation of number as a part of 100. To convert a fraction into percentage, multiply the fraction by 100 and divide the numerator by the denominator. Suppose, you have a fraction as 6/17, then multiply it by 100 as (6/17) x 100 = (6 x 100)/ 17 = 600/17 = 35. So 6/17 = 35 percent. You can get many solved examples on how to convert fractions to percentages from our online. See also the solved examples given in the following paragraph.

## Convert Fractions to Percentages Solved Examples

Here are some Convert fractions to percentages solved examples:

Example 1: In a survey of students in a school on the choice of the games, 8 out of 20 students preferred soccer. What is the percentage of students preferred soccer?

8 out of 20 means a fraction of $\frac{8}{20}$

Let ‘x’ be the percentage equivalent to the fraction $\frac{8}{20}$

‘x’ percentage is also a fraction which is equivalent to $\frac{x}{100}$

Therefore,

$\frac{x}{100}$ = $\frac{8}{20}$

By cross multiplication,

20x = 800 or, x = 40

Hence 40% of the students preferred soccer.

Example 2: In a court settlement Robert was given the rights for 1/5th of a disputed land property. If he decides to use 1/3rd of his share to build a house, what is the percentage of area of the house that will occupy the entire land?

If Robert gets 1/5th of the land and if he is building a house 1/3rd of that fraction, then the house occupies a fraction of (1/5)(1/3) = (1/15) of the entire land.

Let ‘x’ be the percentage equivalent to the fraction $\frac{1}{15}$

‘x’ percentage is also a fraction which is equivalent to $\frac{x}{100}$

Therefore,

$\frac{x}{100}$ = $\frac{1}{15}$

By cross multiplication,

15x = 100 or, x = 6.67 (approximately)

Hence approximately 6.67% of the land is occupied by the house.

Example 3: A sector subtends an angle of 220o at the center of the circle. What is the percentage of the area of occupied on the circle by this sector ?

The area of a sector occupied in a circle is the fraction of its central angle to 360o. Hence this sector occupies a fraction of (220/360 = 11/18) of the circle.

Let ‘x’ be the percentage equivalent to the fraction $\frac{11}{18}$

‘x’ percentage is also a fraction which is equivalent to $\frac{x}{100}$

Therefore,

$\frac{x}{100}$ = $\frac{11}{18}$

By cross multiplication,

18x = 1100 x = 61 (approximately)

Hence approximately 61% of the total area of the circle is occupied by this arc.