Properties of Fractions
There are some important properties of fractions similar to whole numbers, natural numbers, etc. Let’s take a look at those properties:
| Property | Description | Example |
|---|---|---|
| Commutative Property (Addition & Multiplication) | The order of adding or multiplying fractions doesn’t change the result. | Addition: a/b + c/d = c/d + a /b Multiplication: a/b × c/d = c/d × a /b |
| Associative Property (Addition & Multiplication) | The way fractions are grouped in addition or multiplication doesn’t change the result. | Addition: (a/b + c/d )+ e/f = a/b + (c/d )+ e/f ) Multiplication: (a/b × c/d) × e/f = a/b × (c/d × e/f) |
| Identity Element | For multiplication, the identity is 1 (multiplying a fraction by 1 gives the same fraction). For addition, the identity element is incorrectly noted as 0 in the statement; it should be that adding 0 to a fraction doesn’t change its value. | Multiplication: (a/b) ×1 =a/b Addition: a/b+0 =a/b |
| Multiplicative Inverse | The reciprocal of a fraction, when multiplied by the original fraction, gives 1. | (a/b) × (b/a) = 1 |
| Distributive Property | Multiplying a fraction by the sum of two fractions equals the sum of each multiplied separately. | a/b × (c/d + e/f) = a/b × c/d + a/b × e/f |
Fractions – Definition, Properties, Types, Operations & Examples
Factions represent parts of a whole, with a numerator (the top number) indicating how many parts you have and a denominator (the bottom number) representing the total number of equal parts the whole is divided into. Simple fractions have integers in both the numerator and denominator, while complex fractions have fractions in either the numerator or denominator, or both. Proper fractions have numerators smaller than denominators.
Let’s learn about fractions in detail, including their parts, types, properties, and operations.
Table of Content
- What are Fractions?
- Fractions Definition
- Parts of Fraction
- Numerator
- Denominator
- Properties of Fractions
- Types of Fractions
- Unit Fraction
- Proper Fraction
- Improper Fraction
- Mixed Fraction
- Like and Unlike Fractions
- Like Fractions
- Unlike Fractions
- Equivalent Fractions
- Operations on Fractions
- Fraction on Number Line
- Value of Pi in Fraction
- Solved Examples on Fractions
- Fractions Practice Problems