What is Fraction: Types, Examples, Parts, Uses of Fractions

Updated: 16 Sep 2024

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Fractions are used all the time in our daily lives. Fractions help us understand how to divide and share things.
If we share a tasty pizza with friends or divide the bill of this pizza with friends, the fraction is there to help us.

Pizza Fraction:
Two friends want to eat a pizza. One friend wants to eat 5 slices, and the other wants to eat 3 slices. How to divide the pizza among them? Solution: Cut the pizza into 8 equal slices. *Friend 1* eats 5 slices out of 8. So, the fraction of pizza he eats is $\frac{5}{8}$ . *Friend 2* eats 3 slices out of 8. So, the fraction of pizza he eats is $\frac{3}{8}$ .

Pizza Fraction:

Two friends want to eat a pizza. One friend wants to eat 5 slices, and the other wants to eat 3 slices. How to divide the pizza among them?

Solution:

Cut the pizza into 8 equal slices.
Friend 1 eats 5 slices out of 8. So, the fraction of pizza he eats is $\frac{5}{8}$ .
Friend 2 eats 3 slices out of 8. So, the fraction of pizza he eats is $\frac{3}{8}$ .

What is a fraction?

In math, a fraction is an expression that shows splitting of a whole into equal parts. It consists of the numerator and denominator, separated by a fraction bar.
Fractions can represent various quantities, such as parts of an object, a group, or a number. Depending on the relationship between the numerator and denominator, they can be proper, improper, or mixed.

History of Fractions

The term “fraction” comes from the Latin word “fractio,” meaning “a breaking.” This shows the idea of splitting a whole into parts. This is what fraction represent.

Define Fraction

When one unit or whole quantity is divided into equal parts, all those parts are called fractions.
A fraction is a numerical value showing a portion of a whole or splitting a quantity into equal parts.
Fractions are defined as portions or sections of any quantity into equal parts.

Fraction must always divide the whole into equally sized parts.

The term “whole quantity” can refer to a region, numbers, values, objects, or a group of objects.

Meaning of Fraction:

When something is divided into equal parts, the number of parts taken makes a fraction. Fractions express parts of a whole, ratios, or comparisons between numbers. For example, in the fraction $\frac{3}{4}$ , $3$ is the numerator, and $4$ is the denominator, meaning three out of four equal parts are being considered.

Explanation of Fraction:

A fraction is a way to divide a whole into equal parts. It consists of a numerator and a denominator, where the numerator tells how many parts are being considered, and the denominator shows the total number of equal parts in the whole. Fractions can represent various quantities, such as parts of an object, a group, or a number. Depending on the relationship between the numerator and denominator, they can be proper, improper, or mixed.

Parts of a Fraction

A fraction is a mathematical expression representing dividing one quantity by another. It consists of two parts: the numerator and denominator, which are separated by a fraction bar.

Fraction Bar

The fraction bar is the horizontal line that separates the numerator (the top part) from the denominator (the bottom part) in a fraction. It indicates division, showing that the numerator is divided by the denominator.

Numerator:

The upper part of the fraction indicates the portion/section of a fraction.

Denominator

The lower part of the fraction indicates the whole part of a fraction.

Types of Fractions

Proper Fraction

In a proper fraction, the denominator is smaller than the denominator.
General Form
$\frac{a}{b}$ where $a < b$
Example of Proper Fractions:
$\frac{3}{4}$
$\frac{3}{5}$

Improper Fraction

In an improper fraction, the numerator is greater than or equal to the denominator.
General Form
$\frac{a}{b}$ where $a \geq b$ .
Example of Improper Fractions:

In $\frac{5}{3}$ , the numerator is greater than the denominator.
In $\frac{7}{7}$ , the numerator and denominator are same.

Mixed Fraction

In a mixed fraction, a whole number is combined with a proper fraction.
Example of Mixed Fractions:
$7 \frac{1}{2}$
$2 \frac{1}{3}$

Unit Fraction

In Unit Fraction, the numerator is always 1.
Example:
$\frac{1}{6}$

Like Fractions

In like fractions, all the fractions have the same denominator.
Examples of Like Fractions:
$\frac{2}{9}$ , $\frac{7}{9}$ and $\frac{5}{9}$ are like fractions because 9 is the denominator of all three fractions.

Unlike Fractions

In unlike fractions, all the fractions have different denominators.
Example of Unlike Fractions:
$\frac{3}{4}$ and $\frac{2}{7}$ are unlike fractions because they have different denominators.

Equivalent Fractions

In equivalent fractions, different fractions represent the same value.
For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions because they both represent the same portion of a whole.
Example of Equivalent Fractions:
$\frac{1}{2}$ and $\frac{2}{4}$
$\frac{15}{10}=\frac{9}{6}=\frac{3}{2}$

Different Ways to Represent Fractions

There are various ways to represent fractions. Here are the five common ways to represent fractions:

1. Common Fraction (Vulgar Fraction)

A common fraction is a fraction that has a horizontal line between the numerator and the denominator.
Example:
$\frac{3}{4}$

2. Mixed Fraction (Mixed Number)

A mixed fraction is a fraction that combines a whole number with a proper fraction.
Example:
$2 \frac{1}{3}$

3. Decimal Fraction

A fraction expressed in decimal form.
Example:
$\frac{3}{4} =0.75$

4. Percentage

A fraction expressed as a percent signifies “per 100.”
Example:
$75 \% = \frac{75}{100}=\frac{3}{4}$

5. Ratio

A fraction in the form of a comparison between two similar quantities.
Example:
3:4 (equivalent to $\frac{3}{4}$ )

Operation on Fractions

Addition of Fractions

Make sure the denominators are the same. If they aren’t, make them the same or identical.
Add the numerators and take the common denominator.
Write the sum of the numerators over the common denominator.
Simplify the fraction (if possible).

Examples:

Addition of Like Fractions
Add $\frac{7}{8} + \frac{3}{8}$ Solution: $\frac{7}{8} + \frac{3}{8}$ $=\frac{7+3}{8}$ $=\frac{10}{8}$ $=\frac{5}{4}$

Addition of Unlike Fractions:
Add $\frac{7}{8} + \frac{5}{12}$ Solution: $\frac{7}{8} + \frac{5}{12}$ First make the denominators same by taking LCM. $\begin{array}{l\|rr} 2 & 8, & 12 \\ \hline 2 & 4, & 6 \\ \hline 2 & 2, & 3 \\ \hline 3 & 1, & 3 \\ \hline & 1, & 1 \end{array}$ $2 \times 2 \times 2 \times 3=24$ Make all the denominators same i.e. 24. $\frac{7}{8} \times \frac{3}{3} + \frac{5}{12} \times \frac{2}{2}$ $=\frac{21}{24} + \frac{10}{24}$ $=\frac{21+10}{24}$ $=\frac{31}{24}$

Addition of Unlike Fractions:

Add $\frac{7}{8} + \frac{5}{12}$
Solution:
$\frac{7}{8} + \frac{5}{12}$
First make the denominators same by taking LCM.

\begin{array}{l|rr} 2 & 8, & 12 \\ \hline 2 & 4, & 6 \\ \hline 2 & 2, & 3 \\ \hline 3 & 1, & 3 \\ \hline & 1, & 1 \end{array}

$2 \times 2 \times 2 \times 3=24$
Make all the denominators same i.e. 24.
$\frac{7}{8} \times \frac{3}{3} + \frac{5}{12} \times \frac{2}{2}$
$=\frac{21}{24} + \frac{10}{24}$
$=\frac{21+10}{24}$
$=\frac{31}{24}$

Subtraction of Fractions

Make sure the denominators are the same. If they aren’t, make them the same or identical.
Subtract the numerators and take the denominator common.
Write the difference of the numerators over the common denominator.
Simplify the fraction (if possible).

Example

Subtraction of Like Fractions
Simplify: $\frac{7}{8} - \frac{3}{8}$ Solution: $\frac{7}{8} - \frac{3}{8}$ $=\frac{7-3}{8}$ $=\frac{4}{8}$ $=\frac{1}{2}$

Subtraction of Like Fractions

Simplify: $\frac{7}{8} - \frac{3}{8}$

Solution:
$\frac{7}{8} - \frac{3}{8}$
$=\frac{7-3}{8}$
$=\frac{4}{8}$
$=\frac{1}{2}$

Subtraction of Unlike Fractions
Simplify: $\frac{7}{8} - \frac{5}{12}$ Solution: $\frac{7}{8} - \frac{5}{12}$ First make the denominators same by taking LCM. $\begin{array}{l\|rr} 2 & 8, & 12 \\ \hline 2 & 4, & 6 \\ \hline 2 & 2, & 3 \\ \hline 3 & 1, & 3 \\ \hline & 1, & 1 \end{array}$ $2 \times 2 \times 2 \times 3=24$ Make all the denominators same i.e. 24. $\frac{7}{8} \times \frac{3}{3} - \frac{5}{12} \times \frac{2}{2}$ $=\frac{21}{24} - \frac{10}{24}$ $=\frac{21-10}{24}$ $=\frac{11}{24}$

Subtraction of Unlike Fractions

Simplify: $\frac{7}{8} - \frac{5}{12}$
Solution:
$\frac{7}{8} - \frac{5}{12}$
First make the denominators same by taking LCM.

\begin{array}{l|rr} 2 & 8, & 12 \\ \hline 2 & 4, & 6 \\ \hline 2 & 2, & 3 \\ \hline 3 & 1, & 3 \\ \hline & 1, & 1 \end{array}

$2 \times 2 \times 2 \times 3=24$
Make all the denominators same i.e. 24.
$\frac{7}{8} \times \frac{3}{3} - \frac{5}{12} \times \frac{2}{2}$
$=\frac{21}{24} - \frac{10}{24}$
$=\frac{21-10}{24}$
$=\frac{11}{24}$

Multiplication of Fractions

Simplify the fraction to its lowest form, if necessary.
Multiply all the numerators of the fractions.
Multiply all the denominators of the fractions.
Reduce the fraction to its lowest form if possible.

Examples

Multiplication of Fractions
$\frac{3}{4} \times \frac{5}{6}$ $=\frac{15}{24}$ $\frac{3}{35} \times \frac{25}{7}$ $=\frac{3}{7} \times \frac{5}{7}$ $=\frac{15}{49}$ $\frac{36}{4} \times \frac{7}{28}$ $=\frac{9}{1} \times \frac{1}{4}$ $=\frac{9}{4}$ $4 \times \frac{2}{3}$ $=\frac{8}{3}$ $8 \times \frac{5}{36}$ $=2 \times \frac{5}{9}$ $=\frac{10}{9}$

Division of Fractions

Steps to Divide Fractions:

Find the Reciprocal: Reverse the second fraction by switching its numerator and denominator.
Change Division to Multiplication: Replace the division sign with multiplication, then multiply the first fraction by the reciprocal of the second.
Multiply the Numerators and Denominators: Multiply the numerators together and the denominators together as per Multiplication Rules.

General Form
$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$
Example:

Division of Fractions
Example: $\frac{3}{35} \div \frac{5}{7}$ $=\frac{3}{35} \times \frac{7}{5}$ $=\frac{3}{5} \times \frac{1}{5}$ $=\frac{3}{25}$

Example of Fractions in Real Life

Here are some practical applications of fractions in everyday life:

Cooking and Baking
Construction and Carpentry
Time Management
Finance and Money
Education and Grading
Sports and Statistics
Shopping and Discounts
Maps and Scale Models
Dividing Property or Resources
Music and Rhythm