Definition:

In mathematics, whole numbers are the set of numbers {0, 1, 2, 3, 4, 5…….}. A fraction is defined as a part of a whole number that has been divided into an * equal* number of parts.

A fraction is written as **𝑎 / 𝑏** where a and b are whole numbers. a is known as the numerator and b is known as the denominator. Note that the denominator cannot be equal to zero.

In the above figure (a), the rectangle is divided into 4 equal parts. One of these parts is shaded. Hence, the shaded portion is represented by the fraction 1/4

Similarly, in figure (b) the shaded portion is represented by the fraction 3/8

In figure (c) the shaded portion is represented by the fraction 2/4 which is the same as 1/2

Types of fractions

★ Proper fractions

If the numerator of a fraction is less than its denominator then the fraction is known as a proper fraction.

For example: 3/8 , 1/7 , 5/12 are all proper fractions as the numerator is less than the denominator in each of these fractions.

★ Improper fractions

If the numerator of a fraction is greater than or equal to its denominator then the fraction is known as an improper fraction.

For example: 8/3 , 12/7 , 15/2 are all improper fractions as the numerator is greater than the denominator in each of these fractions. Each of these fractions has a value more than 1.

★ Mixed fractions

A mixed fraction is the combination of a whole number and a proper fraction. Improper fractions can be converted to mixed fractions and vice versa

For example: are all mixed fractions as they include a whole number and a proper fraction.

You can convert an improper fraction to a mixed fraction by dividing the numerator by the denominator.

Mixed fraction can now be obtained as :

Similarly, you can convert a mixed fraction into an improper fraction by using the formula

★ Like fractions

When two or more fractions have the same denominator, they are referred to as like fractions.

For example: 3/8 , 5/8 , 1/8 all have the same denominator 8 and are thus like fractions.

★ Unlike fractions

When two or more fractions have different denominators, they are referred to as unlike fractions.

★ For example: 3/8 , 1/7 , 5/12 all have different denominators and are thus unlike fractions.

**Fractions basic worksheets:**

Q1: Write the fractions representing the shaded parts in the following figure:

A1:

Q2. Shade the figures according to the given fractions.

A2.

Q3. Classify the following fractions as proper, improper and mixed fractions:

A3. Proper fractions: 5/7, 1/124 , 9/19

Improper fractions: 17/5 , 15/4

Mixed fractions:

Q4. Convert the improper fraction 8/3 into a mixed fraction.

A4. When we divide 8 by 3, the Quotient is 2 and remainder is 2.

Q5. Convert the mixed fraction into an improper fraction.

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