Addition and Subtraction of Fractions

When adding or subtracting fractions, the first thing you need to check is whether they have the same denominators (bottom numbers) or different denominators. This determines how you'll solve the problem.

With fractions that have the same denominators (called like fractions), the process is simple! You only add or subtract the numerators (top numbers) while keeping the denominator exactly the same.

For example, to add $\frac{1}{5}$ and $\frac{2}{5}$, you can visualize it with a rectangle divided into 5 equal parts. When 1 part is shaded yellow $\frac{1}{5}$ and 2 parts are shaded blue $\frac{2}{5}$, you can see that a total of 3 out of 5 parts are shaded.

💡 Think of the denominator as telling you how many equal pieces make up a whole, while the numerator tells you how many of those pieces you have.

Adding Fractions with Like Denominators

Adding fractions with the same denominator is as easy as 1-2-3:

Step 1: Add the numerators together. For $\frac{1}{5} + \frac{2}{5}$, add 1 + 2 = 3.

Step 2: Keep the denominator the same. In this case, the denominator stays as 5.

Step 3: Write your answer as a single fraction. So $\frac{1}{5} + \frac{2}{5} = \frac{3}{5}$.

This same process works for subtraction too! Just subtract the numerators instead of adding them, and keep the denominator the same.

🔑 Remember: With like fractions (same denominator), just add or subtract the numerators and keep the denominator unchanged.