Fractions - Definition, Types and Examples
Last Updated : 21 Jun, 2025
Fractions are numerical expressions used to represent parts of a whole or ratios between quantities. They consist of a numerator (the top number), indicating how many parts are considered, and a denominator (the bottom number), showing the total number of equal parts the whole is divided into.
For Example: If A 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.
Fractions are everywhere in daily life, helping us divide things into equal parts, represent ratios, and make comparisons. Some common examples 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:
Parts of a FractionUse 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:
7 types of fractionsLet'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:
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:
- Find the Least Common Denominator (LCD) of the fractions.
- Convert each fraction to an equivalent fraction with the LCD as the denominator.
- 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:
- Multiply the numerators together.
- Multiply the denominators together.
- 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:
- Flip (find the reciprocal of) the second fraction.
- Multiply the first fraction by the reciprocal of the second fraction.
- 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.
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:
| Property | Description | Example |
|---|
Commutative
(Addition & Multiplication) | The order of adding or multiplying fractions doesn't
change the result. | Addition: a/b + c/d = c/d + a /b
Multiplication: a/b × c/d = c/d × a /b |
Associative
(Addition & Multiplication) | The way fractions are grouped in addition or
Multiplication doesn't change the result. | Addition: (a/b + c/d )+ e/f = a/b + (c/d )+ e/f )
Multiplication: (a/b × c/d) × e/f = a/b × (c/d × e/f) |
| Identity Element | For multiplication, the identity is 1 (multiplying a
fraction by 1 gives the same fraction). For in
addition, the identity element is incorrectly
noted as 0 in the statement; it should be that
adding 0 to a fraction doesn't change its value. | Multiplication: (a/b) ×1 =a/b
Addition: a/b+0 =a/b |
| Multiplicative Inverse | The reciprocal of a fraction, when multiplied by the original fraction, gives 1. | (a/b) × (b/a) = 1 |
| Distributive | Multiplying a fraction by the sum of two fractions equals the sum of each multiplied separately. | a/b × (c/d + e/f) = a/b × c/d + a/b× e/f |
➣ Related Articles
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?
Similar Reads
Basic Arithmetic
What are Numbers?Numbers are symbols we use to count, measure, and describe things. They are everywhere in our daily lives and help us understand and organize the world.Numbers are like tools that help us:Count how many things there are (e.g., 1 apple, 3 pencils).Measure things (e.g., 5 meters, 10 kilograms).Show or
15+ min read
Arithmetic OperationsArithmetic Operations are the basic mathematical operations—Addition, Subtraction, Multiplication, and Division—used for calculations. These operations form the foundation of mathematics and are essential in daily life, such as sharing items, calculating bills, solving time and work problems, and in
9 min read
Fractions - Definition, Types and ExamplesFractions are numerical expressions used to represent parts of a whole or ratios between quantities. They consist of a numerator (the top number), indicating how many parts are considered, and a denominator (the bottom number), showing the total number of equal parts the whole is divided into. For E
7 min read
What are Decimals?Decimals are numbers that use a decimal point to separate the whole number part from the fractional part. This system helps represent values between whole numbers, making it easier to express and measure smaller quantities. Each digit after the decimal point represents a specific place value, like t
10 min read
ExponentsExponents are a way to show that a number is multiplied by itself many times. They are everywhere in math and science, helping us write big and easily.Think of exponents like a shortcut for repeated multiplication:23 means 2 x 2 x 2 = 8 52 means 5 x 5 = 25So instead of writing the same number many t
8 min read
PercentageIn mathematics, a percentage is a figure or ratio that signifies a fraction out of 100, i.e., A fraction whose denominator is 100 is called a Percent. In all the fractions where the denominator is 100, we can remove the denominator and put the % sign.For example, the fraction 23/100 can be written a
5 min read
Algebra
Variable in MathsA variable is like a placeholder or a box that can hold different values. In math, it's often represented by a letter, like x or y. The value of a variable can change depending on the situation. For example, if you have the equation y = 2x + 3, the value of y depends on the value of x. So, if you ch
5 min read
Polynomials| Degree | Types | Properties and ExamplesPolynomials are mathematical expressions made up of variables (often represented by letters like x, y, etc.), constants (like numbers), and exponents (which are non-negative integers). These expressions are combined using addition, subtraction, and multiplication operations.A polynomial can have one
9 min read
CoefficientA coefficient is a number that multiplies a variable in a mathematical expression. It tells you how much of that variable you have. For example, in the term 5x, the coefficient is 5 — it means 5 times the variable x.Coefficients can be positive, negative, or zero. Algebraic EquationA coefficient is
8 min read
Algebraic IdentitiesAlgebraic Identities are fundamental equations in algebra where the left-hand side of the equation is always equal to the right-hand side, regardless of the values of the variables involved. These identities play a crucial role in simplifying algebraic computations and are essential for solving vari
14 min read
Properties of Algebraic OperationsAlgebraic operations are mathematical processes that involve the manipulation of numbers, variables, and symbols to produce new results or expressions. The basic algebraic operations are:Addition ( + ): The process of combining two or more numbers to get a sum. For example, 3 + 5 = 8.Subtraction (−)
3 min read
Geometry
Lines and AnglesLines and Angles are the basic terms used in geometry. They provide a base for understanding all the concepts of geometry. We define a line as a 1-D figure that can be extended to infinity in opposite directions, whereas an angle is defined as the opening created by joining two or more lines. An ang
9 min read
Geometric Shapes in MathsGeometric shapes are mathematical figures that represent the forms of objects in the real world. These shapes have defined boundaries, angles, and surfaces, and are fundamental to understanding geometry. Geometric shapes can be categorized into two main types based on their dimensions:2D Shapes (Two
2 min read
Area and Perimeter of Shapes | Formula and ExamplesArea and Perimeter are the two fundamental properties related to 2-dimensional shapes. Defining the size of the shape and the length of its boundary. By learning about the areas of 2D shapes, we can easily determine the surface areas of 3D bodies and the perimeter helps us to calculate the length of
10 min read
Surface Areas and VolumesSurface Area and Volume are two fundamental properties of a three-dimensional (3D) shape that help us understand and measure the space they occupy and their outer surfaces.Knowing how to determine surface area and volumes can be incredibly practical and handy in cases where you want to calculate the
10 min read
Points, Lines and PlanesPoints, Lines, and Planes are basic terms used in Geometry that have a specific meaning and are used to define the basis of geometry. We define a point as a location in 3-D or 2-D space that is represented using coordinates. We define a line as a geometrical figure that is extended in both direction
14 min read
Coordinate Axes and Coordinate Planes in 3D spaceIn a plane, we know that we need two mutually perpendicular lines to locate the position of a point. These lines are called coordinate axes of the plane and the plane is usually called the Cartesian plane. But in real life, we do not have such a plane. In real life, we need some extra information su
6 min read
Trigonometry & Vector Algebra
Trigonometric RatiosThere are three sides of a triangle Hypotenuse, Adjacent, and Opposite. The ratios between these sides based on the angle between them is called Trigonometric Ratio. The six trigonometric ratios are: sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).As give
4 min read
Trigonometric Equations | Definition, Examples & How to SolveTrigonometric equations are mathematical expressions that involve trigonometric functions (such as sine, cosine, tangent, etc.) and are set equal to a value. The goal is to find the values of the variable (usually an angle) that satisfy the equation.For example, a simple trigonometric equation might
9 min read
Trigonometric IdentitiesTrigonometric identities play an important role in simplifying expressions and solving equations involving trigonometric functions. These identities, which include relationships between angles and sides of triangles, are widely used in fields like geometry, engineering, and physics. Some important t
10 min read
Trigonometric FunctionsTrigonometric Functions, often simply called trig functions, are mathematical functions that relate the angles of a right triangle to the ratios of the lengths of its sides.Trigonometric functions are the basic functions used in trigonometry and they are used for solving various types of problems in
6 min read
Inverse Trigonometric Functions | Definition, Formula, Types and Examples Inverse trigonometric functions are the inverse functions of basic trigonometric functions. In mathematics, inverse trigonometric functions are also known as arcus functions or anti-trigonometric functions. The inverse trigonometric functions are the inverse functions of basic trigonometric function
11 min read
Inverse Trigonometric IdentitiesInverse trigonometric functions are also known as arcus functions or anti-trigonometric functions. These functions are the inverse functions of basic trigonometric functions, i.e., sine, cosine, tangent, cosecant, secant, and cotangent. It is used to find the angles with any trigonometric ratio. Inv
9 min read
Calculus
Introduction to Differential CalculusDifferential calculus is a branch of calculus that deals with the study of rates of change of functions and the behaviour of these functions in response to infinitesimal changes in their independent variables.Some of the prerequisites for Differential Calculus include:Independent and Dependent Varia
6 min read
Limits in CalculusIn mathematics, a limit is a fundamental concept that describes the behaviour of a function or sequence as its input approaches a particular value. Limits are used in calculus to define derivatives, continuity, and integrals, and they are defined as the approaching value of the function with the inp
12 min read
Continuity of FunctionsContinuity of functions is an important unit of Calculus as it forms the base and it helps us further to prove whether a function is differentiable or not. A continuous function is a function which when drawn on a paper does not have a break. The continuity can also be proved using the concept of li
13 min read
DifferentiationDifferentiation in mathematics refers to the process of finding the derivative of a function, which involves determining the rate of change of a function with respect to its variables.In simple terms, it is a way of finding how things change. Imagine you're driving a car and looking at how your spee
2 min read
Differentiability of a Function | Class 12 MathsContinuity or continuous which means, "a function is continuous at its domain if its graph is a curve without breaks or jumps". A function is continuous at a point in its domain if its graph does not have breaks or jumps in the immediate neighborhood of the point. Continuity at a Point: A function f
11 min read
IntegrationIntegration, in simple terms, is a way to add up small pieces to find the total of something, especially when those pieces are changing or not uniform.Imagine you have a car driving along a road, and its speed changes over time. At some moments, it's going faster; at other moments, it's slower. If y
3 min read
Probability and Statistics
Basic Concepts of ProbabilityProbability is defined as the likelihood of the occurrence of any event. Probability is expressed as a number between 0 and 1, where, 0 is the probability of an impossible event and 1 is the probability of a sure event.Concepts of Probability are used in various real life scenarios : Stock Market :
6 min read
Bayes' TheoremBayes' Theorem is a mathematical formula that helps determine the conditional probability of an event based on prior knowledge and new evidence.It adjusts probabilities when new information comes in and helps make better decisions in uncertain situations.Bayes' Theorem helps us update probabilities
12 min read
Probability Distribution - Function, Formula, TableA probability distribution is a mathematical function or rule that describes how the probabilities of different outcomes are assigned to the possible values of a random variable. It provides a way of modeling the likelihood of each outcome in a random experiment.While a frequency distribution shows
15+ min read
Descriptive StatisticStatistics is the foundation of data science. Descriptive statistics are simple tools that help us understand and summarize data. They show the basic features of a dataset, like the average, highest and lowest values and how spread out the numbers are. It's the first step in making sense of informat
5 min read
What is Inferential Statistics?After learning basic statistics like how data points relate (covariance and correlation) and probability distributions, the next important step is Inferential Statistics. Unlike descriptive statistics, which just summarizes data, inferential statistics helps us make predictions and conclusions about
6 min read
Measures of Central Tendency in StatisticsCentral tendencies in statistics are numerical values that represent the middle or typical value of a dataset. Also known as averages, they provide a summary of the entire data, making it easier to understand the overall pattern or behavior. These values are useful because they capture the essence o
11 min read
Set TheorySet theory is a branch of mathematics that deals with collections of objects, called sets. A set is simply a collection of distinct elements, such as numbers, letters, or even everyday objects, that share a common property or rule.Example of SetsSome examples of sets include:A set of fruits: {apple,
3 min read
Practice