Percent and fractions are usually used in our daily life to relate and compare quantity. For example, we use percentage or percent to rank in class, comparing marks and performance. In simple words, the percent is a way of expressing a fraction of 100 by number.

Percent refers to the fractions of a whole and can be remembered easily than the fraction. It is how much of a whole thing contains. For example, \( \small 50 \% \) can be written as \( \small \frac{1}{2} \), and \( \small 25 \% \) means \( \small \frac{1}{4} \). In the same way you can convert vice versa: fraction to percent conversion.

You often need to find out what percent of something in your daily life. To understand how to convert percent to fraction, consider an example. If a school has 865 students out of which 389 are female, then what percent of students are female. To solve this you need to divide both the numbers. It is 389 out of 865 or \( \small \frac{389}{865} = 0.44971 \). To simplify this you need to convert it into percent, which is \( \small 44.9711 \% \). Now, let’s discuss how to convert percent and fraction in detail.

What is a Percent?

In a simple word, the percentage actually means “out of a hundred”. The word is derived from Latin word – ‘per centum’, which means thoroughly a hundred. It is number that is being used to express a fraction of 100. It is denoted by a sign \(\small \left ( \% \right )\) called percentage. In this sense, \( \small 64 \% \) can be written in a fraction as \( \small \frac{64}{100} \). Another example, in a school \( \small 80 \% \) of students are female, which means out of 100 students 80 are female.

What is a Fraction?

Fraction is a number of part of a whole thing. It represents how many parts of a certain size is divided into a whole thing. A fraction consists of a numerator and a denominator: \( \small \frac{1}{2} \), where the number which is written above the line is called numerator, and the number below the line is called denominator.

The numerator represents a number of parts of a whole thing, while the denominator indicates how many parts make up a whole thing, which can’t be a zero. For instance, an apple is equally sliced into four pieces and you are using only three pieces, then as a fraction it can be written as \( \small \frac{3}{4} \), here, the numerator: 3 represents parts of the apple and the denominator: 4 indicates there are four equal parts of the apple.

How to Convert Percent to Fraction?

Percent to fraction conversion is very simple using the formula provided in this page. As we already know, percent means “out of a hundred”. We need to first convert a percent into a decimal and then convert the decimal to fraction.

Check: Use Online Percent Calculator to convert a fraction to percent.

Steps to Convert Percent to Fraction

Method One

Step 1: Divide the given percent by 100. This will give a decimal number.

Step 2: Count number of digits after a decimal point. The digit is represented as \( \small d \).

The decimal number 2.56 has two digits after the decimal point, so \(\small d = 2\).

Step 3: Now, calculate the factor \(\small (f)\). This will convert the decimal number as an integer using a formula \(\small f = 10^{d}\)

\(\small f = 10^{2} = 100\)

Step 4: The decimal number should be multiplied and divided by the factor

\( \small \frac{2.56 \times 100}{100} = \frac{256}{100} \)

Step 5: Find Greatest Common Divisor (GCD) of the fraction: \( \small \frac{256}{100} \)

GCD \(\small (256, 100) = 4\)

Step 6: Simply the fraction by dividing the numerator and denominator by the GCD value:

\(\frac{256}{100} = \frac{\left ( \frac{256}{4} \right )}{\left ( \frac{100}{4}\right )} = \frac{64}{25}\)

Method Two

Step 1: Divide the given percent by 100 to get the decimal number \( \frac{percent}{100} \).

Step 2: If the percent is not a whole number, then multiply every number by 10 after the decimal point.

Step 3: Simplify the fraction.

Mixed Number Percent to Fraction

To convert simple percentages to fractions, we have already learned. Here we will see how to convert a mixed number or mixed fraction percent into an equivalent fraction. Follow the below-given steps:

• Convert the mixed fraction percent into a proper fraction
• Now multiply the 1/100 to remove the percent symbol
• Reduce to the simplified fraction

Examples:

1. Find the equivalent fraction of 11¹/₂ %.

Given, the mixed fraction is 11 ¹/₂ %

Now converting into a proper fraction

11 ¹/₂ % = 23/2 %

Now multiply by 1/100 to remove the % symbol.

23/2 x 1/100 = 23/200

Since we cannot further solve 23/200, therefore, it is the equivalent fraction.

2. Convert 2 ¹/₂ % into fraction.

Given,

2 ¹/₂ %

Converting the mixed fraction percentage into proper fraction.

⇒ 2 ¹/₂ % = 5/2 %

Now multiply by 1/100 to remove the % symbol.

⇒ 5/2 x 1/100 

⇒ 5/200

⇒ 1/40

Percent to Fraction Table

Problems and Solutions

Example 1: Convert \( \small 11 \% \) to fraction.

Solution:

Step 1: Divide the percent by 100 to get the decimal number.

\( \small \frac{11}{100} \)

Step 2: The given percent is a whole number, so go to step 3.

Step 3: The fraction \( \small \frac{11}{100} \) can’t be simplified further

The answer is \( \small \frac{11}{100} \).

Example 2: Convert \( \small 75 \% \)  to a fraction.

Solution:

Step 1: Divide the percent by 100 to get the decimal number.

\( \small \frac{75}{100} \)

Step 2: The given percent is a whole number, so go to step 3.

Step 3: Simply the fraction \( \small \frac{75}{100} \).

The answer is \( \small \frac{3}{4} \).

Example 3: Convert \( \small 62.5 \% \)  to a fraction.

Solution:

Step 1: Write down the given percent as: \( \small \frac{62.5 }{100} \)

Step 2: The given percent is not a whole number, so multiply both the numerator and denominator by 10, because there is one digit after the decimal point.

Step 3: \( \small \frac{62.5 \times 10}{100 \times 10} \)

\( \small = \frac{625}{1000} \)

Step 4: Simply the fraction: \( \small = \frac{625}{1000} \)

The answer is \( \small \frac{5}{8} \).

Percentage to Decimal

Converting a value in percentage to an equivalent decimal value, follow the below steps:

• Divide the given percentage value by 100 and remove the percent symbol
• Now cancel the common factors from numerator and denominator
• Simplify to get the decimal equivalent

Examples

1. Convert 10% to decimal.

Dividing 10% by 100, we get;

10/100 = 1/10 = 0.1

Thus, 0.1 is the decimal equivalent of 10%

2. Convert 77.5% into decimal

Dividing 77.5% by 100, we get;

77.5% = 77.5/100 = 7.75/10 = 0.775

Thus, 0.775 is the decimal equivalent of 77.5%.

Decimal to Fraction

To convert a decimal value into its equivalent fraction, we need to follow the given steps:

• Multiply and divide the decimal value by 10n, where n is the number of digits to the right of the decimal places. 
• Now, find the HCF of numerator and denominator. 
• Divide the numerator and denominator by the GCF
• Once, there is no common factor left for numerator and denominator, then the fraction is in the simplest form

Examples:

1. Convert 1.5 into fraction.

We can write, 1.5 as 1.5/1

Now, there is only one digit to the right of the decimal, therefore, multiplying and dividing, the numerator and denominator by 10, we get;

⇒ (1.5/1) x (10/10)

⇒ 15/10

GCF of 15 and 10 = 5

Therefore, 

⇒ (15÷5)/(10÷5) 

⇒ 3/2

2. Convert 2.25 into fraction.

⇒ 2.25/1 

Multiply and divide by 10² = 100, to remove the decimal up to two places.

⇒ (2.25/1) x (100/100)

⇒ 225/100

GCF of 225 and 100 = 25

Therefore,

⇒ (225÷25)/(100÷25)

⇒ 9/4

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