Parts of Fractions

The fractions include two parts, numerator and denominator.

• Numerator: It is the upper part of the fraction, that represents the sections of the fraction
• Denominator: It is the lower or bottom part that represents the total parts in which the fraction is divided.

Example: If 3/4 is a fraction, then 3 is the numerator and 4 is the denominator.

Properties of Fractions

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

• Commutative and associative properties hold true 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

Types of Fractions

Based on the properties of numerator and denominator, fractions are sub-divided into different types. They are:

• Proper fractions
• Improper fractions
• Mixed fractions
• Like fractions
• Unlike fractions
• Equivalent fractions

Proper Fractions

The proper fractions are those where the numerator is less than the denominator. For example, 8/9 will be a proper fraction since “numerator < denominator”. 

Improper Fractions

The improper fraction is a fraction where the numerator happens to be greater than the denominator. For example, 9/8 will be an improper fraction since “numerator > denominator”.

Mixed Fractions

A mixed fraction is a combination of the integer part and a proper fraction. These are also called mixed numbers or mixed numerals. For example:

Like Fractions

Like fractions are those fractions, as the name suggests, that are alike or same.

For example, take ½ and 2/4; they are alike since if you simplify it mathematically, you will get the same fraction. 

Unlike Fractions

Unlike fractions, are those that are dissimilar.

For example, ½ and 1/3 are unlike fractions.

Equivalent Fractions

Two fractions are equivalent to each other if after simplification either of two fractions is equal to the other one. 

For example, ⅔ and 4/6 are equivalent fractions.

Since, 4/6 = (2×2)/(2×3) = 2/3

Unit Fractions

A fraction is known as a unit fraction when the numerator is equal to 1. 

• One half of whole = ½
• One-third of whole = 1/3
• One-fourth of whole = ¼
• One-fifth of whole = ⅕