Lesson 29: Multiplying & Dividing Fractions

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• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

This lesson focuses on multiplying and dividing fractions and mixed numbers, with strategies to simplify results and check answers.

Learning Objectives

• Multiply fractions and simplify the result.
• Divide fractions using the reciprocal method.
• Multiply and divide mixed numbers by converting to improper fractions.
• Simplify answers and reduce fractions to lowest terms.

Topics Covered

• Review: fractions and mixed numbers
• Multiplying fractions
• Dividing fractions using reciprocals
• Converting mixed numbers to improper fractions
• Multiplying and dividing mixed numbers
• Simplifying results

Key Terms

• Reciprocal: Flipping the numerator and denominator of a fraction.
• Improper Fraction: A fraction where the numerator is larger than the denominator.
• Mixed Number: A number combining a whole number and a fraction.
• Simplify: Reducing a fraction to its lowest terms.

Lesson Examples

Example 1: Multiplying Fractions

1. Multiply 2/3 × 4/5.
2. Multiply numerators: 2 × 4 = 8.
3. Multiply denominators: 3 × 5 = 15.
4. Result: 8/15 (already simplified).

Example 2: Dividing Fractions

1. Calculate 3/4 ÷ 2/5.
2. Take reciprocal of 2/5 → 5/2.
3. Multiply: 3/4 × 5/2 = 15/8.
4. Convert to mixed number: 15/8 = 1 7/8.

Example 3: Multiplying Mixed Numbers

1. Multiply 1 2/3 × 2 1/4.
2. Convert to improper fractions: 1 2/3 = 5/3, 2 1/4 = 9/4.
3. Multiply: 5/3 × 9/4 = 45/12.
4. Simplify: 45/12 = 15/4 = 3 3/4.

Example 4: Dividing Mixed Numbers

1. Divide 3 1/2 ÷ 1 3/4.
2. Convert to improper fractions: 3 1/2 = 7/2, 1 3/4 = 7/4.
3. Take reciprocal of divisor: 7/4 → 4/7.
4. Multiply: 7/2 × 4/7 = 28/14 = 2.

Practice Problems

1. 2/5 × 3/4 = ?
2. 5/6 ÷ 1/3 = ?
3. 1 1/2 × 2 2/3 = ?
4. 3 3/4 ÷ 1 1/2 = ?
5. 7/8 × 4/7 = ?

Tips & Common Mistakes

• Always convert mixed numbers to improper fractions before multiplying or dividing.
• Remember to flip the divisor when dividing fractions.
• Simplify your final answer whenever possible.

Summary

Multiplying and dividing fractions involves straightforward multiplication of numerators and denominators, and division uses the reciprocal method. Converting mixed numbers and simplifying results ensures accurate answers.

Challenge Problems

1. Multiply 3 1/3 × 1 1/2 and simplify.
2. Divide 5 1/4 ÷ 2 2/5 and simplify your answer.
3. Create a real-world problem involving multiplication or division of fractions and solve it.