1/2 + 1/3 isn't 2/5. To add fractions, both must speak the same language — that language is the common denominator.
A common denominator is a number that's a multiple of all the denominators you're working with. Once everyone shares one, you can add and subtract directly.
Adding and subtracting fractions, comparing fractions, simplifying mixed expressions — common denominators are the bridge.
Quick way: multiply
Multiply the denominators together. 1/2 + 1/3 → common denominator 2 × 3 = 6. Always works, but might not be the smallest.
Better way: LCM
Use the Lowest Common Multiple of the denominators. 1/4 + 1/6: LCM(4, 6) = 12, not 24. Smaller numbers, easier arithmetic.
Smallest common denominator for 1/4 and 5/6?
Compute 2/3 + 1/4.
Common denominator 12. 2/3 = 8/12, 1/4 = 3/12. Sum = 11/12.
Don't add denominators. 1/2 + 1/3 ≠ 2/5. Rewrite both with the same denominator first.
LCM via prime factors: take the highest power of each prime that appears in either denominator.
- Common denominator = a multiple of all denominators.
- LCM gives the smallest one — easier arithmetic.
- Required for adding and subtracting fractions.