Adding Fractions with Different Denominators

How to Add Fractions with different denominators:

  • Find the Least Common Denominator (LCD) of the fractions
  • Rename the fractions to have the LCD
  • Add the numerators of the fractions
  • Simplify the Fraction

Example: Find the Sum of 2/9 and 3/12

  • Determine the Greatest Common Factor of 9 and 12 which is 3
  • Either multiply the denominators and divide by the GCF (9*12=108, 108/3=36)
  • OR - Divide one of the denominators by the GCF and multiply the answer by the other denominator (9/3=3, 3*12=36)
  • Rename the fractions to use the Least Common Denominator(2/9=8/36, 3/12=9/36)
  • The result is 8/36 + 9/36
  • Add the numerators and put the sum over the LCD = 17/36
  • Simplify the fraction if possible. In this case it is not possible

Add the Fractions and Reduce to Lowest Terms

Reduce the answer to lowest terms and leave it as
a fraction or a whole number, not a mixed number.