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

Return to Top

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.


Copyright (C) 2009 J. Banfill. All Rights Reserved.