Fractions are an essential part of mathematics and can be found everywhere in our daily lives. They represent a part of a whole or a portion of a quantity, and understanding them is crucial in solving mathematical problems. The different types of fractions and how to perform basic operations with them.

## Types of Fractions

**Proper Fractions:**

A proper fraction is a fraction where the numerator is smaller than the denominator. For example, 2/5, 3/4, and 7/8 are all proper fractions.

**Improper Fractions:**

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, 5/3, 7/4, and 11/5 are all improper fractions.

**Mixed Numbers:**

A mixed number is a combination of a whole number and a proper fraction. For example, 2 1/3, 3 2/5, and 4 3/4 are all mixed numbers.

**Equivalent Fractions:**

Equivalent fractions are fractions that represent the same quantity but are written in different forms. For example, 1/2 and 2/4 are equivalent fractions because they represent the same amount.

## Basic Operations with Fractions

### Addition and Subtraction:

To add or subtract fractions, we need to have a common denominator. We can find the common denominator by multiplying the denominators of the two fractions. Once we have a common denominator, we can add or subtract the numerators and write the result over the common denominator.

For example: 1/4 + 2/5 = (5/5) x (1/4) + (4/4) x (2/5) = 5/20 + 8/20 = 13/20 3/5 – 1/6 = (6/6) x (3/5) – (5/5) x (1/6) = 18/30 – 5/30 = 13/30

### Multiplication:

To multiply fractions, we multiply the numerators together and the denominators together. We can simplify the fraction by canceling out common factors in the numerator and denominator.

For example: 2/3 x 3/4 = 6/12 = 1/2 5/6 x 4/5 = 20/30 = 2/3

### Division:

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by switching the numerator and the denominator.

For example: 2/3 ÷ 4/5 = 2/3 x 5/4 = 10/12 = 5/6 3/4 ÷ 1/2 = 3/4 x 2/1 = 6/4 = 3/2

Fractions are an important part of mathematics and are used in many real-life situations, such as cooking, measuring, and calculating distances.

The types of fractions and how to perform basic operations with them, we can improve our mathematical skills and problem-solving abilities.