Adding Fractions (Unlike Denominators)
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce a common denominator
What a learner can do afterwards
- Compute 2/3 + 5/4 by converting to twelfths: 8/12 + 15/12 = 23/12
- Subtract 1 3/5 from 3 1/4 using a common denominator
- Explain the strategy of finding a common denominator and verify using a visual model
The lesson
You already know how to add fractions that have the same denominator. But 2/3 and 5/4 have different denominators, so the pieces are different sizes. You cannot add the numerators until the pieces match. First, rewrite each fraction using a common denominator.
To add 2/3 + 5/4, use 12 as the common denominator. 2/3 becomes 8/12, and 5/4 becomes 15/12. Now the pieces match: 8/12 + 15/12 = 23/12, which is the same as 1 11/12.
To subtract 1 3/5 from 3 1/4, use 20 as the common denominator, since 4 and 5 both divide into 20. 3 1/4 becomes 65/20, and 1 3/5 becomes 32/20. Subtract: 65/20 minus 32/20 is 33/20, which is the same as 1 13/20.
After you get an answer, check it with a picture. Draw two bars split into the common number of parts and shade them. If the shaded parts match your fraction answer, the common denominator worked.
Give every fraction the same size pieces first, then add or subtract the numerators.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.