Algebra: Cancellation Of Indices Term
In this introductory lesson on algebraic cancellation, students will learn how to simplify algebraic fractions involving indices by cancelling common numerical and algebraic factors directly. The focus is on understanding when cancellation is valid and identifying common factors correctly, without relying on the formal laws of indices.
This topic lays the groundwork for more advanced cancellation techniques, where students will first need to apply factorisation before simplifying more complex algebraic expressions.
Related Lessons:
Three Key Techniques For Cancellation
When cancelling fractional indices, remember these three important techniques:
- Rewrite division as multiplication: Change every division sign into multiplication so the expression is easier to work with.
- Convert mixed fractions to improper fractions: Make sure all fractional indices are written as improper fractions before simplifying.
- Cancel common factors: Cancel common terms between the numerator and denominator.
Finally, multiply all the remaining numerator terms together, and multiply all the remaining denominator terms together to get the final answer.
Examples On Performing Cancellation
In this video, we are going to go thru 3 examples to strengthen our concepts. Students are encouraged to try their hands on the question before view the answers:
- \(\frac{(-2x)\times(5y)\times(-3z)\times(-2x)}{-3z\times(-2y)}\)
- \(\frac{x}{z}\div\frac{2x}{y}\)
- \(\frac{3ab^3}{y}\div\frac{\left(3a^2b\right)^3}{y^3}\)