Adding Fractions with Unlike Denominators Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Adding Fractions with Unlike Denominators.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
Adding fractions with different denominators by first rewriting them with a common denominator (usually the LCD), then adding numerators.
You can't add thirds and fourths directly—it's like adding apples and oranges. Convert both to twelfths first, then add.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Find equivalent fractions with a common denominator so the pieces are the same size, then add normally.
Common stuck point: Finding the least common denominator (LCD) efficiently, especially with larger numbers.
Sense of Study hint: List the first several multiples of each denominator until you spot one they share -- that's your LCD.
Worked Examples
Example 1
easySolution
- 1 Find the LCD of 3 and 4: \text{LCD} = 12.
- 2 Rewrite each fraction: \frac{1}{3} = \frac{4}{12} and \frac{1}{4} = \frac{3}{12}.
- 3 Add: \frac{4}{12} + \frac{3}{12} = \frac{7}{12}.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
mediumExample 2
hardRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.