Questions and Answers
How do you multiply algebraic fractions?
Multiply the numerators then multiply the denominators. Express the fractions in their simplest form by cancelling where necessary.
Solve and simplify 3a/8 × 2b/a.
3b/4a
How do you divide algebraic fractions?
Flip the second fraction and then multiply.
Solve and simplify 5m/6n ÷ 4m² / 3n.
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Study Notes
Multiplying Algebraic Fractions
- To multiply algebraic fractions, multiply the numerators together.
- Multiply the denominators together.
- Simplify the resulting fraction by cancelling any common factors.
Example of Multiplication
- For the expression 3a/8 × 2b/a:
- Multiply: (3a × 2b) / (8 × a) = 6ab / 8a.
- Simplify: 6ab / 8a = 3b / 4a after cancelling common factors.
Dividing Algebraic Fractions
- To divide algebraic fractions, take the reciprocal of the second fraction (flip it).
- Multiply the first fraction by this flipped second fraction.
Example of Division
- For the expression 5m/6n ÷ 4m² / 3n:
- Rewrite: 5m/6n × 3n/4m² after flipping the second fraction.
- Multiply: (5m × 3n) / (6n × 4m²) = 15mn / 24m²n.
- Simplify: The final expression becomes 5/8m after cancelling common factors.
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Description
This quiz focuses on the rules for multiplying and dividing algebraic fractions. You will learn how to multiply numerators and denominators, as well as how to simplify the resulting expressions. Additionally, it covers how to divide algebraic fractions by taking the reciprocal of the second fraction and multiplying.
