Fractions - Definition, Types and Examples

Fractions are numerical expressions used to represent parts of a whole or ratios between quantities.

Example: If an apple is divided into 4 equal parts, and one part is taken out, thus the fraction representing the taken out part is 1/4 as one part is taken out of 4 equal parts.
If 3 parts are taken then the fraction representing the taken out part will be 3/4.

Some common real life examples of fractions are:

Parts of a Fraction

If we divide anything into some equal parts, then a fraction consists of two main parts and a fraction line:

• Numerator: The number at the top of the fraction represents the number of parts being considered.
• Vinculum: The line that separates the numerator and denominator is also called the fraction line.
• Denominator: The number at the bottom of the fraction, representing the total number of equal parts into which the whole is divided.

Example:

Use the following tools to understand the fraction better:

Types of Fractions

There are seven types of fractions. They are categorized based on their numerator and denominator, and they are:

Let's read them in detail:

1) Proper Fraction: Fractions in which the numerator value is less than the denominator value.

2) Improper Fractions: Fractions in which the numerator value is greater than the denominator value.

3) Mixed Fractions: Fraction that consists of a whole number with a proper fraction.

4) Like Fractions: Fractions whose denominators are the same are known as like fractions

5) Unlike Fractions: Fractions whose denominators are different are called unlike fractions.

6) Unit Fraction: A Fraction with 1 as a numerator is known as a Unit Fraction. All unit fractions are proper fractions since all unit fractions have 1 in the numerator, which is less than the denominator.

7) Equivalent Fractions: Fractions that result in the same value after simplification.

➣ Read more about Like and Unlike Fractions.

Fractions on a Number Line

Fractions on a number line are shown between two integers. The whole is divided into equal parts based on the denominator, and the numerator shows the fraction's position.

Example

➣ Check- Fraction Quiz

Fractions Operations

Some of the basic arithmetic operations that can be performed on the fractions are:

• Fraction Addition
• Fraction Subtraction
• Fraction Division
• Fraction Multiplication

Fractions- Addition and Subtraction

Fractions can be added and subtracted like simple numbers, but only after making their denominators the same.

Steps to add or subtract fractions:

1. Find the Least Common Denominator (LCD) of the fractions.
2. Convert each fraction to an equivalent fraction with the LCD as the denominator.
3. Add or subtract the numerators while keeping the denominator the same.

Example: \frac{2}{5} + \frac{1}{3} \ \text{and}, \frac{2}{5} - \frac{1}{3}

• LCD of 5 and 3 is 15.
• Convert: 2/5 = 6/15, 1/3 = 5/15
• Add: 6/15 + 5/15 = 11/15
• Subtract: 6/15 - 5/15 = 1/15

Fraction Multiplication and Division

Fraction division and multiplication are straightforward.

Steps to multiply fractions:

1. Multiply the numerators together.
2. Multiply the denominators together.
3. Simplify the resulting fraction if possible.

Example: \frac{2}{5} \times \frac{1}{3}

\frac{2}{5} \times \frac{1}{3} = \frac{2}{15}

Steps to divide fractions:

1. Flip (find the reciprocal of) the second fraction.
2. Multiply the first fraction by the reciprocal of the second fraction.
3. Simplify the resulting fraction if possible.

Example: \frac{2}{5} \div \frac{1}{3}

\dfrac{2}{5} \div \dfrac{1}{3}

= \dfrac{2}{5} \times \dfrac{3}{1}

= \frac{6}{5} \ = 1\frac{1}{5}

Fraction Worksheets

Practice the fractions with these useful worksheets on fractions.

• Equivalent Fractions Worksheet
• Simplifying Fractions Worksheet
• Comparing Fractions Worksheet

Properties of Fractions

There are some important properties of fractions similar to whole numbers, natural numbers, etc. Let's take a look at those properties:

➣ Related Articles

• Comparing Fractions
• Fun Facts about Fractions

Solved Examples of Fractions

Example 1: Write two equivalent fractions of 3/39.
Solution:

Given, fraction : 3/39

Equivalent fraction by multiplying with the same number, lets multiply by 2:
= (3 × 2)/(39 × 2)
= 6/78

Equivalent fraction by division with the same number, here, both numerator and denominator are divisible by 3, dividing by 3:
= (3 ÷ 3)/(39 ÷ 3)
= 1/13

Example 2: In a class of 90 students, 1/3rd of the students do not like cricket. How many students like cricket?
Solution:

Fraction of students that do not like cricket = 1/3
Fraction of student that like cricket = 1 - 1/3

= (3 - 1)/3
= 2/3rd students like cricket.

Number of students that like cricket = 2/3 × 90
= (2 × 30)
= 60 

Therefore, 60 students like cricket.

Example 3: What type of fraction is this - 1/2, 1/5, 1/7, 1/10, 1/3?
Soolution: 

This is a Unit fraction because all the fractions have 1 as a numerator. 

Example 4: If a recipe needs 3/4 cup of sugar and you want to make twice the quantity mentioned in the recipe, how much sugar do you need?
Solution: 

Sugar needed for recipe = 3/4 cup
Sugar needed for half the recipe = 2 × 3/4
Required sugar = 2× 3/4 = 6/4

Therefore, we need 6/4 cup of sugar.

Practice Problems on Fractions

Use your knowledge to solve these fun questions on fractions.

Question 1: What fraction of the pizza is left?

Question 2: Order the following in ascending order: 1/2, 1, 4, 1/5, 1/3, and 1/5.

Question 3: What fraction of the blocks is green compared to white?

Question 4: Which among these is the greatest? 1/6, 1/4, 1/8, 1/16, 1/32?