Conversion of Fractions to Percentage
To convert a fraction to a percent, multiply the given fraction by 100 and simplify it further. We have two different methods for converting a fraction into a percent. The first method is the conversion of a fraction to a decimal and then converting the obtained decimal to a percent. The second method is the conversion of a fraction to a percent using proportions.
Fraction to Percent Using Decimals
Follow the steps below to convert fractions to percents using decimals:
- First, divide the numerator by the denominator.
- Now, multiply the obtained result by 100.
- Add the percent symbol to the result obtained in the above step.
Example: Convert to 4/9 percent by first converting it into decimal form.
Solution:
Step 1: Divide the numerator by the denominator, i.e., divide 4 by 9. 4 ÷ 9 = 0.444445
Step 2: Multiply the 0.444445 by 100, i.e., 0.444445 × 100 = 44.4445.
Step 3: Add the percent symbol to the result obtained in the above step.
So, 4/9 = 44.4445%
Fraction to Percent Using Proportions
Let a/b and c/d be equal ratios, so the numbers a, b, c, and d are said to be in proportion. To convert a fraction a/b into a percent, we should convert it into the form of x/100, where x is the required percentage.
- Write the given fraction in proportion format.
a/b = x/100
- Solve the above proportion using the cross-multiplication method and simplify it further to obtain the required percent.
Required percent (x) = (a/b) × 100
Example: Convert 5/11 to percent using proportions.
Solution:
Step 1: First, we have to write the given fraction in proportion format.
5/11 = x/100
Step 2: Now, let us solve the above proportion using the cross-multiplication method.
x = (5/11) × 100
Step 3: Simplify it further to obtain the required percent.
x = 45.4545%
We have different methods to convert the given fraction to percent using proportions.
Method 1
Multiply the given fraction by 100, and then solve it further.
Example: Find the percent of 5/11
Solution:
5/11
= (5/11 × 100) %
= (500/11) %
= 45.4545%
Method 2
Convert the given fraction into a decimal, and then multiply it by 100.
Example: Convert 5/11 to percentage
Solution:
5/11
= 0.45454545
= 0.45454545 × 100%
= 45.4545%
Method 3
Let x be the required percentage.
5/11 = x/100
x = (5/11) × 100 = 45.4545%
We can also convert mixed fractions into percentages using the above-mentioned methods. But first, we have to convert the mixed fraction into an improper fraction. Then, we can follow any of the above-mentioned methods.
Example: Convert 1¾ into percent.
Solution:
First, convert the mixed fraction into an improper fraction.
1¾ = 7/4
Now, convert 7/4 into a decimal, and divide the numerator by the denominator.
7/4 = 7 ÷ 4 = 1.75
Now, multiply the decimal by 100 to convert it to percent.
1.75 × 100 % = 175%
So, 7/4 = 175%
Fraction to Percent Conversion
In daily life, we quite often compare two quantities. Fractions and percents are two different ways of expressing a number and are generally used for comparing quantities. The fractions can be converted to percentages and vice versa. Let us consider that Rosy passed 5 out of 6 subjects while John passed 6 out of 8 subjects. So, can you determine who has the better pass percentage? For that, we need to calculate their pass percentage first. So, we need to convert the given fractions to percentages. We have two different methods for converting a fraction into a percent.
But before learning about the conversion of fractions to percent, let us learn the definitions of fractions and percentages.