How to Add and Subtract Like Fractions

Here is a comprehensive explanation on how to add and subtract like fractions:

Adding and Subtracting Like Fractions

Like fractions are fractions that have the same denominator. When adding or subtracting like fractions, the process is straightforward since the denominators are already the same.

Key Points:

1. Like fractions have the same denominator. 2. When adding or subtracting like fractions, the denominator remains unchanged. 3. Only the numerators are added or subtracted.

Steps for Adding Like Fractions:

1. Verify that the fractions have the same denominator. 2. Add the numerators. 3. Keep the common denominator. 4. Simplify the resulting fraction if possible.

Example of Adding Like Fractions:

\[ \frac{3}{8} + \frac{2}{8} = \frac{3 + 2}{8} = \frac{5}{8} \]

Steps for Subtracting Like Fractions:

1. Verify that the fractions have the same denominator. 2. Subtract the numerators. 3. Keep the common denominator. 4. Simplify the resulting fraction if possible.

Example of Subtracting Like Fractions:

\[ \frac{5}{6} - \frac{1}{6} = \frac{5 - 1}{6} = \frac{4}{6} = \frac{2}{3} \]

Important Considerations:

1. Simplification: After adding or subtracting, always check if the resulting fraction can be simplified by finding common factors between the numerator and denominator.

2. Improper Fractions: The result may be an improper fraction (numerator larger than denominator). You can leave it as is or convert it to a mixed number.

3. Negative Fractions: When subtracting, if the result is negative, place the negative sign in front of the fraction.

  Example: \[ \frac{1}{4} - \frac{3}{4} = \frac{1 - 3}{4} = -\frac{2}{4} = -\frac{1}{2} \]

4. Mixed Numbers: If working with mixed numbers, convert them to improper fractions first, then add or subtract as usual.

  Example: \[ 2\frac{1}{3} + 1\frac{2}{3} = \frac{7}{3} + \frac{5}{3} = \frac{12}{3} = 4 \]

5. Zero: Adding or subtracting zero to/from a fraction leaves the fraction unchanged.

Common Mistakes to Avoid:

1. Adding or subtracting denominators: The denominator remains unchanged in operations with like fractions. 2. Forgetting to simplify: Always check if the final fraction can be reduced to its simplest form. 3. Incorrect signs: Be careful with negative fractions, especially in subtraction.

By following these steps and keeping these points in mind, you can confidently add and subtract like fractions. Remember, the key is to work with the numerators while keeping the common denominator unchanged.