Adding and subtracting fractions with unlike denominators involves a few steps. Here’s a clear guide to help you through the process:
Step-by-Step Guide
1. Find a Common Denominator:
- The first step is to find a common denominator for the fractions. The least common denominator (LCD) is often the easiest choice, as it’s the smallest multiple of both denominators.
- To find the LCD, list the multiples of each denominator and identify the smallest multiple they share.
2. Convert Each Fraction:
- Once you have the LCD, you will convert each fraction to an equivalent fraction with this common denominator.
- To do this, divide the LCD by the original denominator of each fraction and multiply both the numerator and denominator of the fraction by this result.
Example:
- For the fractions \( \frac{1}{3} \) and \( \frac{1}{4} \):
- The LCD of 3 and 4 is 12.
- For \( \frac{1}{3} \):
- LCD ÷ original denominator = 12 ÷ 3 = 4.
- Multiply the numerator and denominator: \( \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \).
- For \( \frac{1}{4} \):
- LCD ÷ original denominator = 12 ÷ 4 = 3.
- Multiply the numerator and denominator: \( \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \).
3. Add or Subtract the Fractions:
- Now you can add or subtract the fractions since they have a common denominator.
- Add or subtract the numerators, and keep the common denominator.
Example:
- Now, with \( \frac{4}{12} \) and \( \frac{3}{12} \):
- To add: \( \frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12} \).
- To subtract: \( \frac{4}{12} - \frac{3}{12} = \frac{4 - 3}{12} = \frac{1}{12} \).
4. Simplify the Result (if necessary):
- If the resulting fraction can be simplified, you should do that. You can simplify by dividing the numerator and the denominator by their greatest common divisor (GCD).
Summary
- Find the LCD.
- Convert each fraction to an equivalent fraction using the LCD.
- Add or subtract the numerators, and keep the common denominator.
- Simplify if possible.
Example Problems
Example 1: Addition
- \( \frac{2}{5} + \frac{1}{3} \)
- LCD = 15
- \( \frac{2}{5} = \frac{6}{15} \), \( \frac{1}{3} = \frac{5}{15} \)
- \( \frac{6}{15} + \frac{5}{15} = \frac{11}{15} \)
Example 2: Subtraction
- \( \frac{3}{8} - \frac{1}{6} \)
- LCD = 24
- \( \frac{3}{8} = \frac{9}{24} \), \( \frac{1}{6} = \frac{4}{24} \)
- \( \frac{9}{24} - \frac{4}{24} = \frac{5}{24} \)
Following these steps will help you accurately add and subtract fractions with unlike denominators!