Quick answer
Like denominators: add numerators. Unlike: use LCD. Mixed: convert to improper fractions first. Always simplify unless the answer is already lowest terms.
Formula
- 3/8 + 1/8 = 4/8 = 1/2
- 1/4 + 2/3 = 11/12
- 1 1/2 + 2 1/4 = 3 3/4
Introduction
Examples turn rules into patterns you recognize on sight. Each type below includes setup, middle steps, and a final answer in the form a teacher would accept.
Copy the structure, not just the numbers. Say aloud what the denominator means before you add, especially when denominators differ.
Sums that include wholes belong in the adding mixed fractions notes, because conversion should happen before you line up denominators.
Types of examples on this page
Like-denominator drills train you to add tops only and then simplify. They look easy but still require a final gcd check.
Unlike-denominator problems train LCD selection and equivalent fractions. They are the bulk of middle-school fraction addition.
Mixed-number examples train improper conversion. Skipping that step is one of the fastest ways to get a plausible but wrong answer.
Word-style problems connect fractions to cups and lengths; when the steps blur together, return to how to add fractions and name each stage aloud before you copy the next example.
Reminder before you copy examples
- Wrong: 1/2 + 1/3 = 2/5
- Right: lcd 6 → 3/6 + 2/6 = 5/6
Denominators are not added in fraction addition. They are aligned, then held constant while numerators combine.
How to use these examples
- Cover the answer Work the problem fully, then reveal the solution line by line.
- Name the type Say whether it is like, unlike, or mixed before you choose a strategy.
- Check on the tool Enter the same numbers in the calculator to confirm LCD and reduction.
Four quick worked sums
Like: 3/8 + 1/8 = 4/8 = 1/2 after dividing by 2.
Unlike: 1/4 + 2/3 → lcd 12 → 3/12 + 8/12 = 11/12.
Mixed: 1 1/2 + 2 1/4 → 3/2 + 9/4 → 6/4 + 9/4 = 15/4 = 3 3/4.
Measurement: 1/3 cup + 1/4 cup → 4/12 + 3/12 = 7/12 cup total.