** Introduction**:

Fractions are a fundamental concept in mathematics that represent a part of a whole. They are used to describe and compare quantities that are not whole numbers. In this lesson, we will explore the basic concepts of fractions and learn hncepts:**

ow to manipulate and work with them.

**Key Concepts:**

1. **Definition of Fractions:**

- A fraction consists of two parts: the numerator and the denominator.

- The numerator represents the part of the whole, while the denominator represents the total number of equal parts the whole is divided into.

Example: In the fraction \( \frac{3}{5} \), 3 is the numerator, and 5 is the denominator.

2. **Types of Fractions:**

- **Proper Fractions:** The numerator is smaller than the denominator (e.g., \( \frac{2}{3} \)).

- **Improper Fractions:** The numerator is equal to or greater than the denominator (e.g., \( \frac{5}{4} \)).

- **Mixed Numbers:** A whole number combined with a proper fraction (e.g., \( 1 \frac{1}{2} \)).

3.** Equivalent Fractions:**

- Equivalent fractions represent the same part of a whole.

- They are obtained by multiplying or dividing both the numerator and denominator by the same non-zero number.

Example: \( \frac{2}{3} \) is equivalent to \( \frac{4}{6} \) because both represent two-thirds of a whole.

4. **Comparing Fractions:**

- To compare fractions, find a common denominator.

- If the denominators are the same, compare the numerators.

Example: Comparing \( \frac{2}{5} \) and \( \frac{3}{5} \), since the denominators are the same, \( \frac{3}{5} \) is greater.

5. **Adding and Subtracting Fractions:**

- To add or subtract fractions, find a common denominator.

- Add or subtract the numerators while keeping the denominator the same.

Example: \( \frac{1}{4} + \frac{2}{4} = \frac{3}{4} \)

6**. Multiplying and Dividing Fractions**:

- To multiply fractions, multiply the numerators together and the denominators together.

- To divide fractions, multiply by the reciprocal of the divisor.

Example: \( \frac{2}{3} \times \frac{4}{5} = \frac{8}{15} \)

**Important Notes**:

- **Zero in the Denominator**: Division by zero is undefined, so fractions with a denominator of zero are not valid.

- **Simplifying Fractions**: Always simplify fractions to their lowest terms by dividing both the numerator and denominator by their greatest common factor.

- **Real-world Applications**: Fractions are commonly used in everyday situations, such as cooking, measurements, and financial calculations.