To Multiply Algebraic Fractions
This Grade 6 algebra skill from Yoshiwara Elementary Algebra teaches students to multiply algebraic fractions. Students factor the numerators and denominators, cancel common factors across numerator and denominator, and then multiply remaining factors to produce a simplified result.
Key Concepts
Property 1. Factor each numerator and denominator completely. 2. If any factor appears in both a numerator and a denominator, divide out that factor. 3. Multiply the remaining factors.
Examples Problem: Multiply $\frac{x^2 9}{5x} \cdot \frac{10}{x+3}$.
Step 1: Factor all parts. The first numerator is $x^2 9 = (x 3)(x+3)$. The fraction is $\frac{(x 3)(x+3)}{5x} \cdot \frac{10}{x+3}$.
Common Questions
How do you multiply algebraic fractions?
Multiply the numerators together and the denominators together, then simplify by canceling any common factors. Or cancel common factors before multiplying to keep numbers small.
Why should you factor before multiplying algebraic fractions?
Factoring first allows you to cancel common factors across the fraction before multiplying, which simplifies the work and produces a reduced answer directly.
What is an example of multiplying algebraic fractions?
(3x/4) x (8/x^2) = 24x / (4x^2) = 6/x after canceling common factors 4 and x.
Can you cancel across two separate fractions being multiplied?
Yes. When multiplying fractions, any factor in any numerator can be canceled with any matching factor in any denominator.
Where is multiplying algebraic fractions taught?
Multiplying algebraic fractions is covered in the Yoshiwara Elementary Algebra textbook for Grade 6.