Fraction Definition

In Mathematics, a fraction is used to represent the part of the whole thing. Fractions help to distribute and judge the number easily and make the calculation faster. Instead of using decimal values, the representation of fractions looks simpler. In this article, let us discuss the fraction definition, types of fraction, its properties and examples in detail.

Fraction Definition in Maths

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.

For example, 5/10 is a fraction.

Here, 5 is a numerator

10 is a denominator

Types of Fractions

There are four different types of fractions. They are:

  • Unit Fraction – In a fraction, the numerator with 1 is called a unit fraction. For example, ½, ¼
  • Proper Fraction – If a numerator value is less than the denominator value, it is called a proper fraction. Example: 7/9, 8/10
  • Improper Fraction – If a numerator value is greater than the denominator value, then it is called an improper fraction. Example: 6/5, 11/10
  • Mixed Fraction – If a fraction consists of a whole number with a proper fraction, it is called a mixed fraction. Example 5 ¾, 10 ½

Apart from these four important types of fractions, the other two types of fractions which are used in mathematical problems are like and unlike fractions.

  • Like Fractions – The fractions with the same denominator is called a like fraction.

Example: 4/2, 7/2, 9/2

Here, the denominators of all the fractions are 2. Hence, it is called a like fraction.

  • Unlike Fractions – The fractions with different denominators are called an unlike fraction.

Example: 5/2, 4/6, 9/4

Here, the denominator values are different in all the fractions. Hence, it is called unlike fractions.

Fraction Properties

Similar to real numbers and whole numbers, a fractional number also holds some of the important properties. They are:

  • Commutative and associative properties hold for fractional addition and multiplication
  • The identity element of fractional addition is 0, and fractional multiplication is 1
  • The multiplicative inverse of a/b is b/a, where a and b should be non zero elements
  • Fractional numbers obey the distributive property of multiplication over addition

Fraction Example

Question:

Determine the type of fractions given below:

  1. 5 ⅓ (b) 4/6, 8/6, 9/6

Solution:

(a) 5 ⅓ – The given fraction is a mixed fraction. Because it is a combination of both whole number and a proper fraction

(b) 4/6, 8/6, 9/6 – The given fractions are like fractions. Because the denominators of all the numbers are the same, i.e., 6

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