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 1/5^{th} of a disputed land property. If he decides to use 1/3^{rd} 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 1/5^{th} of the land and if he is building a house 1/3^{rd} 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 220^{o} 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 360^{o}. 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.