Class 5 - Fraction to Percent

Fractions and percent are the two terms we generally use in comparing quantities. Percentage or percent refers to the fractions of a whole, while percent is how much of the whole thing and is easier to remember than a fraction.

Table of Contents

• What is a Fraction?
• What is Percent?
• Percentage Formula
• How to Convert Fraction to Percent?
• Fraction to Percent Conversion Table
• Solved Problems on Fraction to Percent

What is a Fraction?

A fraction is a way of showing a part of a whole. When something is divided into equal parts and you take some of those parts, you use a fraction to describe how much you have taken.

A fraction has two parts. The number written on top is called the numerator it tells you how many parts you are talking about. The number written at the bottom is called the denominator it tells you how many equal parts the whole is divided into.

For example, if a pizza is cut into 8 equal slices and you eat 3 of them, you have eaten 3/8 of the pizza. Here, 3 is the numerator and 8 is the denominator.

Fractions come in different types:

A proper fraction is one where the numerator is smaller than the denominator, like 3/5 or 2/7. The value of a proper fraction is always less than 1.

An improper fraction is one where the numerator is greater than or equal to the denominator, like 9/4 or 7/7. Its value is 1 or more.

A mixed fraction combines a whole number and a proper fraction, like 2½ or 3¾. It is just another way of writing an improper fraction.

Fractions are used everywhere in real life — splitting a bill, measuring ingredients while cooking, reading a ruler, or understanding discounts in a shop.

What is Percent?

The word percent comes from the Latin phrase "per centum," which simply means "out of 100." So when you say a number as a percent, you are saying how many parts out of every 100 parts something makes up.

The symbol used for percent is %.

For example, if you scored 80% on a test, it means you got 80 marks out of every 100 marks. If a fruit drink is 25% juice, it means 25 out of every 100 ml is actual juice.

Percent is just a special kind of fraction where the denominator is always 100. So 40% is the same as 40/100, and 75% is the same as 75/100.

Percentages are extremely useful in daily life. You see them when a shop offers a 20% discount, when a bank gives 6% interest, when a report shows 95% attendance, or when a phone battery is at 15%. Understanding percent helps you make sense of all these situations quickly and clearly.

Percentage Formula

The basic formula to find the percentage of a part out of a whole is:

Percentage = (Part / Whole) × 100

Let us understand this with a simple example.

Suppose a student scored 45 marks out of 60 in an exam. To find the percentage:

Percentage = (45 / 60) × 100 Percentage = 0.75 × 100 Percentage = 75%

So the student scored 75%.

This formula works in all situations where you want to express one quantity as a percentage of another. You just divide the part by the whole and then multiply by 100.

How to Convert Fraction to Percent?

Converting a fraction to a percent is a very simple process. There are two methods you can use, and both give the same answer.

Method 1: Multiply the Fraction by 100

This is the most direct method. Simply multiply the given fraction by 100 and add the % symbol.

Percent = (Numerator / Denominator) × 100

Example: Convert 3/4 to a percent.

(3/4) × 100 = 300/4 = 75

So 3/4 = 75%

Example: Convert 7/20 to a percent.

(7/20) × 100 = 700/20 = 35

So 7/20 = 35%

Method 2: Convert the Denominator to 100

In this method, you change the fraction so that the denominator becomes 100. Once the denominator is 100, the numerator directly gives you the percentage.

Example: Convert 3/5 to a percent.

To make the denominator 100, multiply both numerator and denominator by 20 (since 5 × 20 = 100):

(3 × 20) / (5 × 20) = 60/100

So 3/5 = 60%

Example: Convert 9/25 to a percent.

Multiply both parts by 4 (since 25 × 4 = 100):

(9 × 4) / (25 × 4) = 36/100

So 9/25 = 36%

This method works neatly when 100 is exactly divisible by the denominator. For other cases, Method 1 is easier and works universally.

Fraction to Percent Conversion Table

Here is a ready reference table that shows the percentage values of fractions that come up very often in maths problems. It is helpful to memorise these as they save time during exams.

Fraction	Percent
1/1	100%
1/2	50%
1/3	33.33%
2/3	66.67%
1/4	25%
3/4	75%
1/5	20%
2/5	40%
3/5	60%
4/5	80%
1/6	16.67%
5/6	83.33%
1/8	12.5%
3/8	37.5%
5/8	62.5%
7/8	87.5%
1/10	10%
3/10	30%
7/10	70%
9/10	90%
1/20	5%
1/25	4%
1/50	2%
1/100	1%

Whenever you see a fraction like 3/4 in a problem that asks for a percentage, you can directly use this table instead of calculating.

Solved Problems on Fraction to Percent

Problem 1: Convert 2/5 to a percent.

Using the formula: (2/5) × 100 = 200/5 = 40

Answer: 2/5 = 40%

Problem 2: Convert 11/20 to a percent.

(11/20) × 100 = 1100/20 = 55

Answer: 11/20 = 55%

Problem 3: A student got 18 out of 24 questions correct in a quiz. What is the percentage of correct answers?

Write it as a fraction first: 18/24

(18/24) × 100 = 1800/24 = 75

Answer: The student got 75% correct.

Problem 4: Convert 5/8 to a percent.

(5/8) × 100 = 500/8 = 62.5

Answer: 5/8 = 62.5%

Problem 5: A school planted 3/10 of its land with trees. What percentage of the land has trees?

(3/10) × 100 = 300/10 = 30

Answer: 30% of the land has trees.

Problem 6: Convert the mixed fraction 1¾ to a percent.

First, convert 1¾ to an improper fraction: 1¾ = (4 + 3)/4 = 7/4

Now multiply by 100: (7/4) × 100 = 700/4 = 175

Answer: 1¾ = 175%

Problem 7: Out of 50 students in a class, 35 passed an exam. What percent passed?

Fraction of students who passed = 35/50

(35/50) × 100 = 3500/50 = 70

Answer: 70% of the students passed.

Problem 8: Convert 1/3 to a percent (up to two decimal places).

(1/3) × 100 = 100/3 = 33.33...

Answer: 1/3 = 33.33% (approximately)