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Fractions in Maths

Last Updated : 29 Jan, 2026

Fractions are numerical expressions used to represent parts of a whole or ratios between quantities.

Example: If an apple is divided into 4 equal parts, and one part is taken out, thus the fraction representing the taken out part is 1/4 as one part is taken out of 4 equal parts.
If 3 parts are taken then the fraction representing the taken out part will be 3/4.

Parts of a Fraction

If we divide anything into some equal parts, then a fraction consists of two main parts and a fraction line:

👁 fraction
  • Numerator: The number at the top of the fraction represents the number of parts being considered.
  • Vinculum: The line that separates the numerator and denominator is also called the fraction line.
  • Denominator: The number at the bottom of the fraction, representing the total number of equal parts into which the whole is divided.

Types of Fractions

They are categorized based on their numerator and denominator, and they are:

1) Proper Fraction: Fractions in which the numerator value is less than the denominator value.

2) Improper Fractions: Fractions in which the numerator value is greater than the denominator value.

3) Mixed Fractions: A fraction that consists of a whole number with a proper fraction.

Fraction Properties

Fractions follow important mathematical properties similar to whole numbers and integers. These properties help us perform operations like addition and multiplication correctly.

1. Commutative Property (Addition and Multiplication)

The order of fractions does not change the result.

  • Addition:
  • Multiplication:

2. Associative Property (Addition and Multiplication)

The grouping of fractions does not change the result.

  • Addition:
  • Multiplication:

3. Identity Property

The identity element is a number that keeps the fraction unchanged.

  • Additive identity:
  • Multiplicative identity:

4. Multiplicative Inverse

The reciprocal of a fraction, when multiplied by the original fraction, gives 1.

5. Distributive Property

Multiplying a fraction by a sum is the same as multiplying each fraction separately and then adding the results.

Fractions Operations

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