Algebraic Fractions
6-2Multiplying Fractions
Overview
(a/b)(c/d) = ac/bd. Factor first, then cancel common factors before multiplying.
Key ideas
- Factor every numerator and denominator.
- Cancel across the equality sign.
- Watch domain restrictions.
Worked examples
Example 1
Problem. (2/3)(9/4)
Solution. = 18/12 = 3/2
Example 2
Problem. (x/(x+1)) · ((x+1)/x^2)
Solution. = 1/x
Practice
Try each one. Click Show answer when ready.
- 1.
(3/5)(10/9)
- 2.
((x+2)/x)·(x/(x+2))
- 3.
(6a/b)(b^2/3)
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Multiply and simplify: [(x² − 4)/(x + 3)] · [(x + 3)/(x − 2)].
- 2.
Multiply and simplify: (3a²b/5c) · (10c²/9ab²).