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. In this lesson, we will learn about 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

## Conclusion

Fractions are an important part of mathematics and are used in many real-life situations, such as cooking, measuring, and calculating distances. By understanding the types of fractions and how to perform basic operations with them, we can improve our mathematical skills and problem-solving abilities.