Adding Fractions with Like 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 Like 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 that share the same denominator by adding the numerators and keeping the denominator.
If you have \frac{2}{5} of a pie and get \frac{1}{5} more, you now have \frac{3}{5}—same size pieces, just count them up.
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: When denominators match, the pieces are the same size, so just add the number of pieces (numerators).
Common stuck point: Students add the denominators too, writing \frac{2}{5} + \frac{1}{5} = \frac{3}{10}.
Sense of Study hint: Think of the denominator as a label, like 'fifths.' You're adding 2 fifths + 1 fifth = 3 fifths -- the label stays the same.
Worked Examples
Example 1
easySolution
- 1 The denominators are both 8, so the pieces are the same size.
- 2 Add the numerators: 3 + 4 = 7. Keep the denominator: \frac{7}{8}.
- 3 Check: \gcd(7, 8) = 1, so the fraction is already in simplest form.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
mediumRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.