Cancellation Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Cancellation.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
The process of simplifying a fraction or expression by removing (dividing out) common factors that appear in both the numerator and denominator, leaving an equivalent but simpler form.
\frac{6}{8} = \frac{3}{4} because we can cancel the common factor 2 from top and bottom.
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: Cancellation simplifies by using inverse operations: \frac{a}{a} = 1, a - a = 0.
Common stuck point: Can only cancel factors, not terms: \frac{a+b}{a+c} \neq \frac{b}{c}.
Sense of Study hint: Factor both the numerator and denominator first, then cross out only the common factors -- never cancel terms that are added.
Worked Examples
Example 1
easySolution
- 1 Write as: \(\dfrac{4 \times 6}{4 \times 3}\).
- 2 The 4 appears in both top and bottom (common factor).
- 3 Cancel: \(\dfrac{\cancel{4} \times 6}{\cancel{4} \times 3} = \dfrac{6}{3}\).
- 4 Simplify: \(\dfrac{6}{3} = 2\).
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.