Multiplication and Division: RATIONAL ALGEBRAIC EXPRESSION

Math Lesson

MULTIPLICATION & DIVISION: RATIONAL EXPRESSIONS

Multiplying and dividing rational algebraic expressions is just like doing it with regular fractions!

To multiply, multiply the numerators together and the denominators together. To divide, multiply the first fraction by the reciprocal (flip) of the second fraction!

ab • cd = acbd   |   ab ÷ cd = ab • dc

Concept Explanation

Multiplying rational expressions works exactly like multiplying numerical fractions. You multiply the numerators to get the new numerator, and multiply the denominators to get the new denominator. Always simplify or factor if possible! For division, simply get the reciprocal of the second fraction (invert the numerator and denominator), change the division sign to multiplication, and proceed as multiplying.

Formula / Rule

1. Multiplication: ab • cd = acbd
2. Division: ab ÷ cd = ab • dc = adbc

4 Similar Worked Examples

Example 1: Multiply 2x • 3y
Multiply numerators: 2 • 3 = 6
Multiply denominators: x • y = xy
Result: 6xy

Example 2: Divide 4a ÷ 2b
Get the reciprocal of the second fraction: b2
Change to multiplication: 4a • b2
Multiply: 4b2a which simplifies to 2ba

Example 3: Multiply x3 • 6x²
Multiply numerators: x • 6 = 6x
Multiply denominators: 3 • x² = 3x²
Result: 6x3x². Cancel out 3x to simplify.
Final Answer: 2x

Example 4: Divide a5 ÷ a²10
Get reciprocal: 10a²
Change to multiplication: a5 • 10a²
Multiply: 10a5a². Cancel out 5a to simplify.
Final Answer: 2a

Guided Practice

Try It Yourself!

Answer all 3 guided questions. Hints and solutions are available if you need them!

Mastery Check

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Made for students who want to master Multiplication & Division of Rational Algebraic Expressions