Adding fractions with Same Denominators

Introduction

Adding fractions is a fundamental skill in mathematics. When you have fractions with the same denominator, the process becomes straightforward.

Concept

When adding fractions with the same denominator, you simply add the numerators and keep the denominator the same. This can be expressed mathematically as:

$$\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$$

Where:

• $a$ and $b$ are the numerators.
• $c$ is the common denominator.

Example

Let's add the fractions $\frac{2}{5}$ and $\frac{3}{5}$:

1. Identify the fractions: $\frac{2}{5}$ and $\frac{3}{5}$.
2. Add the numerators: $2 + 3 = 5$.
3. Keep the denominator the same: The common denominator is $5$.
4. Write the result: $$\frac{2}{5} + \frac{3}{5} = \frac{5}{5}$$
5. Simplify if necessary: $\frac{5}{5} = 1$.

Key Questions

• What do you do with the denominators when adding fractions with the same denominator?
• How do you simplify the result after adding?
• Can you give another example of adding fractions with the same denominator?

Conclusion

Adding fractions with the same denominator is a simple process that involves adding the numerators while keeping the denominator unchanged. Practice with different numbers to become proficient!