Overview
This lecture covers how to multiply fractions, including whole numbers by fractions and fraction by fraction, and how to simplify results.
Multiplying Whole Numbers by Fractions
- Convert whole numbers to fractions by placing them over 1 (e.g., 6 becomes 6/1).
- Multiply across numerators and denominators: numerator × numerator, denominator × denominator.
- Example: 6 × 1/3 → (6/1) × (1/3) = 6/3.
- Simplify improper fractions by dividing numerator by denominator (6 ÷ 3 = 2).
- Multiplying by a fraction less than one decreases the original value.
Multiplying Fractions by Fractions
- Multiply straight across: multiply numerators together and denominators together.
- Example: 3/4 × 2/3 = 6/12.
Simplifying Answers
- Check if the answer is an improper fraction and convert to a mixed number if necessary.
- Simplify fractions by dividing numerator and denominator by their greatest common factor.
- Example: 6/12 simplifies to 1/2 by dividing both by 6.
Additional Examples
- 12 × 3/5 = (12/1) × (3/5) = 36/5; 36 ÷ 5 = 7 remainder 1, so answer is 7 1/5.
- 1/7 × 2/3 = 2/21, which is already in simplest form.
Key Terms & Definitions
- Improper Fraction — Fraction where the numerator is greater than or equal to the denominator.
- Mixed Number — A number with both a whole number and a fraction part.
- Simplify — To reduce a fraction to its lowest terms by dividing by the greatest common factor.
- Numerator — The top number in a fraction.
- Denominator — The bottom number in a fraction.
Action Items / Next Steps
- Complete four multiplication practice problems in the mastery check linked in the description.