Adding fractions (different denominators)
Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator
What a learner can do afterwards
- Calculate 1/3 + 1/6 by converting to sixths: 2/6 + 1/6 = 3/6 = 1/2
- Calculate 3/4 − 1/8 by converting to eighths
- Add 2/5 + 3/10 and simplify the answer
The lesson
You already know how to build equivalent fractions and how to add fractions that share the same denominator. Now you'll combine those two skills. When two fractions have different denominators, rewrite them first so they share one denominator. Only then can you add or subtract the numerators.
Add 1/3 + 1/6. First, change 1/3 into sixths: 1/3 = 2/6. Now both fractions have the same denominator, so add the numerators: 2/6 + 1/6 = 3/6. Simplify: 3/6 = 1/2.
Now try 3/4 − 1/8. Change 3/4 into eighths: 3/4 = 6/8. Subtract the numerators: 6/8 − 1/8 = 5/8. That fraction is already in simplest form.
Check whether one denominator is a multiple of the other, like 3 and 6, or 4 and 8. If it is, the bigger denominator is already your common denominator, so you only need to convert the smaller fraction.
Match the denominators 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.