GOZUNTA
Try it now
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
Calculate \(3/8~+~2/8\) and give the result in simplest form.
Your answer
Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
With a free account

Let your results add up.

Each saved attempt adds useful evidence about what you have practiced and what deserves another pass.

Create a free account
With paid access

Use the complete visual-support library.

Paid access opens the visual supports attached throughout the full problem bank in your subscribed course or courses.

Compare plans

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

Check the denominators

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

Both fractions are measured in eighths, so their equal-sized parts can be combined directly and the denominator remains 8.

02

Add the numerators

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

Three eighth-size parts plus two eighth-size parts make five eighth-size parts.

03

Check simplest form

\[\mathrm{GCF}(5,~8)~=~1\]

Five and eight share no positive factor greater than 1, so 5/8 is already in simplest form.

04

Check the size

\[3/8~<~5/8~<~8/8\]

The sum is greater than the larger addend 3/8 and less than one whole, which is reasonable for adding two positive proper fractions.

05

State the sum

\[5/8\]

Adding the like-denominator fractions gives 5/8 in simplest form. This matches the correct choice.

+

Another way

  1. Imagine an eight-part strip: shade three sections, then two more, for five shaded sections out of eight.

!

Common mistake

Do not add the denominators to get 5/16. The eighth-size pieces stay eighths; only the count of pieces changes.

Solution walkthrough video