Worked Example 1: Adding 5/12 + 7/18
- Find the LCM of the denominators (12 and 18):12 = 2² × 3¹ | 18 = 2¹ × 3² → LCM(12, 18) = 2² × 3² = 36
- Scale each fraction up to denominator 36:
- For 5/12: 36 ÷ 12 = 3, so multiply top and bottom by 3 → (5 × 3) / (12 × 3) = 15/36
- For 7/18: 36 ÷ 18 = 2, so multiply top and bottom by 2 → (7 × 2) / (18 × 2) = 14/36
- Add the numerators and keep the common denominator:15/36 + 14/36 = 29/36
Because 29 is prime, 29/36 is already in simplest form. Try this pair in our LCD Calculator.
Worked Example 2: Subtracting Three Fractions (7/8 − 1/6 + 5/12)
When you have three fractions at once, finding the LCM of all three denominators saves you from having to combine them two at a time:
- Step 1: Find LCM(6, 8, 12) = 24.
- Step 2: Convert each fraction to twenty-fourths: 7/8 = 21/24, 1/6 = 4/24, and 5/12 = 10/24.
- Step 3: Combine the numerators in order: (21 − 4 + 10) / 24 = 27/24, which simplifies by dividing top and bottom by 3 to give 9/8 (or 1 1/8).