To Reduce an Algebraic Fraction
This Grade 6 algebra skill from Yoshiwara Elementary Algebra teaches students to reduce (simplify) algebraic fractions by canceling common factors in the numerator and denominator. Students apply factoring skills to identify and cancel shared factors, producing equivalent fractions in lowest terms.
Key Concepts
Property 1. Factor numerator and denominator completely. 2. Divide numerator and denominator by any common factors. We can cancel common factors (expressions that are multiplied together), but not common terms (expressions that are added or subtracted).
Examples Problem: Reduce the fraction $\frac{x^2 + 3x + 2}{x^2 4}$.
Step 1: Factor everything. The numerator factors into $(x+1)(x+2)$. The denominator is a difference of squares, factoring into $(x 2)(x+2)$.
Common Questions
How do you reduce an algebraic fraction?
Factor the numerator and denominator completely, then cancel any common factors that appear in both. The remaining expression is the simplified algebraic fraction.
What does it mean for an algebraic fraction to be in lowest terms?
An algebraic fraction is in lowest terms when the numerator and denominator share no common factors other than 1.
Can you cancel terms instead of factors in an algebraic fraction?
No. You can only cancel factors (multiplied parts), not terms (added or subtracted parts). For example, (x+2)/(x+3) cannot be simplified by canceling x.
What is an example of reducing an algebraic fraction?
(6x^2) / (9x) = (2x) / 3 after canceling the common factor 3x from numerator and denominator.
Where is reducing algebraic fractions taught?
Reducing algebraic fractions is covered in the Yoshiwara Elementary Algebra textbook for Grade 6.