Fractions

Types of Fractions

Fraction:

A fraction is a quantity that expresses a part of the whole.

Example :

Suppose we divide a rectangle into 4 equal parts and colour 1 part.

indicate the shaded part and indicate non-shaded parts of the whole rectangle.

Terms of a fraction

Simplest form of the fraction

Definition: If numerator and denominator have only one common factor that is 1, then that form is the simplest form of the fraction.

Example :

Write the simplest form of

Answer:

Note: To get the simplest form divide numerator and denominator by the greatest common factor.

Divide numerator and denominator by 7.

= =

Now, 4 and 5 don’t have any common factor other than 1.

So, is the simplest form of

There are different types of fractions. Let’s learn the following types of fractions:

Unit Fractions

A fraction with numerator 1 is known as a unit fraction.

Example :

All the fractions have numerator 1. So all of these are unit fractions.

Proper Fractions

A fraction with its numerator smaller than its denominator is known as a proper fraction.

Example :

Here, 5 < 8, 3 < 8, 2 < 6

Each numerator is smaller than its denominator. Hence, all of these are proper fractions.

Improper Fractions

A fraction with numerator greater than or equal to its denominator is known as an Improper fraction.

Example :

Each circle is divided into 8 parts, in which 11 parts are coloured.

Here, 11 > 8 → Numerator is greater than the denominator.

Each hexagon is divided into 6 parts, in which 12 parts are coloured.

Here, 12 > 6 → Numerator is greater than the denominator.

Mixed Fractions

Sum of a whole number and a proper fraction is known as a mixed fraction.

Example :

2 is whole number and is proper fraction.

In the above example, each circle is divided into 8 parts and there 17 parts are coloured. So, we can write above example in the form of Improper fraction as:

Conversion of improper fractions into mixed fractions

Step 1: Divide numerator by denominator.

Step 2: Write the quotient as a whole number.

Step 3: Write remainder as numerator.

Step 4: Keep the denominator as it is.

So, the Mixed fraction can be written as: Quotient =

Example :

Write the in the form of a mixed fraction.

Answer:

Step 1: Divide numerator by denominator.

Step 2: Write the quotient as a whole number.

Step 3: Write remainder as numerator.

Step 4: Keep the denominator as it is.

= 7

Conversion of mixed fractions into improper fractions

We know that,

Dividend = Divisor × Quotient + Remainder.

Follow the steps to convert mixed fraction into improper fraction.

Step 1: Find the numerator of the improper fraction by using:

Denominator × whole number + numerator.

This will be our numerator of the improper fraction.

Step 2: Keep the denominator as it is.

Example :

Convert 7 into improper fraction.

Answer:

Step 1: Denominator × whole number + numerator.

4 × 7 + 3 = 28 + 3 = 31

So, 31 is our numerator of the improper fraction.

Step 2: Keep the denominator as it is.

7 =

We got the correct answer.

Equivalent Fractions

Fractions that have different numerators and denominators but their simplest form is the same are called equivalent fractions.

Example :

All above fractions are equivalent fractions as they represent the half part of the circle.

Simplest form of =
Simplest form of = =
Simplest form of = =
Simplest form of = =

Like Fractions

Fractions that have the same denominator are called like fractions.

Example :

All fractions have the same denominator as 6. So, all of these are like fractions.

Unlike fractions

Fractions that have different denominators are called unlike fractions

Example :

All fractions have different denominators. So, these are unlike fractions.