To add or subtract fractions with unlike denominators, you first need to rewrite them so they share a common denominator, then combine the numerators. Here's the step-by-step process:
Step 1: Find a common denominator Identify the least common multiple (LCM) of the two denominators. This is called the least common denominator (LCD). For example, for 1/4 and 1/6, the LCM of 4 and 6 is 12.
Step 2: Convert each fraction Rewrite each fraction as an equivalent fraction with the LCD as its denominator. To do this, divide the LCD by the original denominator, then multiply both the numerator and denominator by that number.
- 1/4 → multiply top and bottom by 3 → 3/12
- 1/6 → multiply top and bottom by 2 → 2/12
Step 3: Add or subtract the numerators Once denominators match, keep the denominator the same and add (or subtract) only the numerators.
- Addition: 3/12 + 2/12 = 5/12
- Subtraction: 3/12 − 2/12 = 1/12
Step 4: Simplify the result Reduce the answer to lowest terms by dividing the numerator and denominator by their greatest common factor (GCF), if possible. If the result is an improper fraction (numerator larger than denominator), convert it to a mixed number.
Quick shortcut method (if you don't want to find the LCM): Multiply the two denominators together to get a common denominator, cross-multiply the numerators accordingly, then combine. For example, for 1/4 and 1/6: use 24 as the denominator, giving 6/24 and 4/24. Add or subtract, then simplify (6/24 + 4/24 = 10/24 = 5/12). This method always works but may require more simplifying at the end.
With mixed numbers: convert them to improper fractions first, then follow the same steps, converting back at the end if needed.
Practicing with a few examples using both small and larger denominators helps build confidence with this skill.