Adding and Subtracting Fractions with Like Denominators

When fractions have the same bottom number, we say they have like denominators. Adding and subtracting these fractions is straightforward because the pieces you are counting are already the exact same size!

The Golden Rule

To add or subtract fractions with like denominators, you only need to remember two simple steps:

1. Add or subtract the numerators (the top numbers).
2. Keep the denominator exactly the same (the bottom number).

Adding Fractions

Let's look at an addition example: $\frac{3}{8} + \frac{2}{8} = ?$

• Step 1: Add the top numbers: $3 + 2 = 5$.
• Step 2: Keep the bottom number the same: $8$.

So, your answer is: $\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$

Subtracting Fractions

The exact same rule applies to subtraction. Let's solve: $\frac{7}{10} - \frac{3}{10} = ?$

• Step 1: Subtract the top numbers: $7 - 3 = 4$.
• Step 2: Keep the bottom number the same: $10$.

So, your answer is: $\frac{7}{10} - \frac{3}{10} = \frac{4}{10}$ (Note: If you want to challenge yourself, you can simplify this fraction to $\frac{2}{5}$!)

Working with Mixed Numbers

A mixed number has a whole number part and a fraction part. When adding or subtracting mixed numbers with like denominators, handle the whole numbers and the fractions separately.

Let's try this example: $2\frac{3}{5} + 1\frac{4}{5} = ?$

• Step 1: Add the whole numbers: $2 + 1 = 3$.
• Step 2: Add the fractions: $\frac{3}{5} + \frac{4}{5} = \frac{7}{5}$.
• Step 3: Notice that $\frac{7}{5}$ is an improper fraction (the top is bigger than the bottom). We need to change it into a mixed number: $\frac{7}{5} = 1\frac{2}{5}$.
• Step 4: Combine your whole numbers from Step 1 with your new mixed number from Step 3: $3 + 1\frac{2}{5} = 4\frac{2}{5}$.

Your final answer is: $2\frac{3}{5} + 1\frac{4}{5} = 4\frac{2}{5}$