Last updated on July 4th, 2025
A fraction is a mathematical value representing a part of a whole, such as a pizza slice from a full pizza. In this topic, we will be learning about fractions, their types, and properties.
Fractions represent a part of a whole. They are usually expressed in this form: ab, where ‘a’ and ‘b’ are called the numerator and denominator, respectively. Out of the whole, numerator represents a part of the whole while, denominator denotes the whole number. Together, they tell us how much of something we have.
A fraction represents how to divide a whole into equal parts. For example, if a circle is divided into 12 equal parts and one piece of the circle is represented as 1/12, it is read as one-twelfth.
Fractions are categorized based on the relationship between the numerator and denominator. Let's take a look at the types of fractions:
Proper Fractions: In proper fractions, the numerator is less than the denominator. For instance, 2/8, 6/15, 7/9, …
Improper Fractions: The numerator is greater than or equal to the denominator
For instance, 8/2, 5/3, 15/6, …
Unit Fractions: In a fraction, where the numerator is always 1, it is called a unit fraction. Unit fractions have a numerator of 1 and are always proper fractions (e.g., 1/5, 1/9, 1/12).
Mixed Fractions: A mixed fraction consists of a whole number and a proper fraction. For example, 614, here, 6 is the whole number and ¼ is the proper fraction.
Equivalent Fractions: Equivalent fractions are two or more fractions with different numbers but the same value. For example, 1/2 = 2/4 = 3/6. Here, 1/2, 2/4, and 3/6 share the same value because they all represent half of a whole. Equivalent fractions are resulted by multiplying or dividing the numerator and denominator by the same number (e.g., 1/2 × 2/2 = 2/4).
Like Fractions: The fractions with the same denominators are called fractions. For example, 5/17, 6/17, 9/17,…
Unlike Fractions: Fractions with different denominators. E.g., 5/12, 6/18, 9/11, …
The visual representation of numbers using a horizontal straight line is the number line. A fraction on a number line helps students to understand how the number is divided into parts between the two whole numbers. The denominator represents the number of parts the number line will be divided into.
Fractions share properties with other numbers. Here, we are going to discuss some of the properties of fractions.
Fractions play an important role in our everyday lives. In fact, we use them often even without realizing it. Fractions are used daily in tasks like cooking, measuring, and calculating discounts.
Take a look at the below-mentioned scenarios where fractions are used:
When learning fractions and doing calculations, students often make errors when working with fractions. This section covers common mistakes and how to avoid them when working on fractions.
A farmer planted three-fifths of his land with wheat and two-sevenths with corn. What fraction of his land is planted with crops?
The fraction of his land planted with crops is 31/35
3/5 of the farmer’s land is used to grow wheat, while 2/7 of his land is dedicated to corn.
The fraction of his land planted with wheat and corn is 3/5 + 2/7
Since the fractions have different denominators, we should convert them before adding. To convert the fractions, let us first find the least common denominator (LCD).
The LCD of 5 and 7 is 35.
Now, let us convert 3/5 such that it has 35 as the denominator:
3/5 = (3 × 7) / (5 × 7) = 21/35
Converting 2/7, we get, 2/7 = (2 × 5) / (7 × 5) = 10/35
Thus, 3/5 + 2/7 = 21/35 + 10/35 = 31/35.
A recipe requires three-fourths of a cup of sugar. If you want to make five-sixths of the recipe, how much sugar do you need?
The amount of sugar needed is ⅝ cups.
The amount of sugar needed = 3/4
So, to make 5/6 of the recipe, the sugar required = (¾) × (⅚)
= 15/24 = 5/8
A rope is four-ninths of a meter long. It is cut into pieces, each measuring two-thirds of a meter. How many pieces can be made?
The number of pieces that can be made is 2/3
To determine how many pieces you can make, divide the total length of the rope by the length of one piece = (4/9) ÷ (2/3)
= (4/9) × (3/2)
= 12/18 = 2/3
Lisa bought 2 whole pizzas and three-fifths of another pizza. Express the total as an improper fraction.
So, it can be expressed as 13/5
The pizza Lisa bought = 235
It can be converted to improper fraction as 2 × 5 + 3 = 13
That is 13/5
A group of students collected seventeen-fourths of a kilogram of rice. Express this as a mixed fraction.
The amount of rice collected by the students is 414 kgs
The amount of rice collected by the students = 17/4
To express 17/4 as a mixed fraction, we divide 17 by 4, with the remainder of 1
So, it can be expressed as 414.
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.