Fractions Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Fractions.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
A fraction is a number of the form \frac{a}{b} where a (the numerator) counts how many equal parts you have and b (the denominator, which must not be zero) tells how many equal parts the whole is divided into.
A pizza cut into 4 slices—eating 1 slice means you ate \frac{1}{4} of the pizza.
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: Fractions represent division and parts of wholes simultaneously.
Common stuck point: Larger denominator means smaller pieces, not larger fraction.
Sense of Study hint: Draw two same-sized rectangles, split one into the denominator's number of parts, and shade the numerator's count to see the actual size.
Common Mistakes to Watch For
Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.
Worked Examples
Example 1
easySolution
- 1 Check that the denominators are the same: both fractions have denominator 5.
- 2 Since denominators match, add the numerators directly: \frac{2 + 1}{5} = \frac{3}{5}.
- 3 Simplify: \gcd(3, 5) = 1, so \frac{3}{5} is already in lowest terms.
Answer
Example 2
mediumExample 3
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.