Fraction Definition, Types, and Real Life Examples

What is a Fraction in Mathematics?

A fraction in maths represents a part or portion of a whole. It has two components - a numerator and a denominator. The top number, or the numerator , signifies the number of equal parts taken, while the bottom number, or the denominator , indicates the total number of equal parts that make up the whole.

To illustrate, consider the fraction 3/8.

Here, 3 is the numerator and 8 is the denominator.

Practical Applications

Fractions are prevalent in everyday life, such as:

• If a chocolate bar is divided into three equal parts, each part represents 1/3 of the whole bar.
• If a day is divided into 24 equal parts (hours), each hour represents 1/24 of the day.

Categories of Fractions

Fractions can be classified into four primary types:

• Unit Fraction – A fraction with a numerator of 1. For example, 1/3, 1/5.
• Proper Fraction – When the numerator is less than the denominator. Example: 3/4, 7/10.
• Improper Fraction – When the numerator exceeds the denominator. Example: 9/4, 11/7.
• Mixed Fraction – A whole number combined with a proper fraction. Example 2 1/2, 4 3/5.

Other Types

• Like Fractions – Fractions with the same denominator.

Example: 5/7, 9/7, 11/7.

In this case, all fractions have a denominator of 7, thus they are like fractions.

• Unlike Fractions – Fractions with different denominators.

Example: 3/4, 5/6, 7/8.

Here, the denominators are distinct in all the fractions, hence they are unlike fractions.

• Equivalent Fractions – Fractions that simplify to the same value.

Example: 2/4 and 1/2 are equivalent fractions, since 2/4 = (1×2)/(2×2) = 1/2.

Fraction Examples

Question:

Identify the type of fractions below:

(a) 4 1/2

(b) 3/5, 7/5, 9/5

Solution:

(a) 4 1/2 – This is a mixed fraction, as it includes a whole number and a proper fraction.

(b) 3/5, 7/5, 9/5 – These are like fractions, as all fractions share the same denominator, i.e., 5.