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All courses Math Foundations · MF.RN.2 8 of 60
Add and subtract fractions and mixed numbers with appropriate common denominators.

Add or subtract with a shared denominator

Problem
Find the sum: 3/8 + 2/8. Write your answer in simplest form.
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Hint

Look at the denominators first. They are both 8, so the denominator stays the same.

When fractions already have a shared denominator, add only the numerators.

Solution walkthrough

01

Notice the shared denominator

\[3/8~+~2/8\]

Both fractions are in eighths, so the parts are already the same size. That means the denominator stays 8.

02

Add the numerators

\[(3~+~2)/8~=~5/8\]

When denominators match, you combine only the numerators. Three eighths plus two eighths is five eighths.

03

Check whether it simplifies

\[5/8\]

The numbers 5 and 8 do not have a common factor greater than 1, so 5/8 is already in simplest form.

04

State the sum

\[3/8~+~2/8~=~5/8\]

The sum is 5/8.

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Another way

  1. You can think of it as counting pieces: 3 eighth-pieces plus 2 eighth-pieces makes 5 eighth-pieces, so the result is 5/8.

!

Common mistake

A common mistake is writing 3/8 + 2/8 = 5/16 by adding both numerators and denominators. The denominator should stay 8 because both fractions are already measured in eighths.