Overview
This lecture explains how to multiply whole numbers and fractions, including rewriting whole numbers as fractions, multiplying, and converting improper fractions to mixed numbers.
Steps for Multiplying Whole Numbers by Fractions
- Rewrite the whole number as a fraction by placing it over 1 (e.g., 3 = 3/1).
- Multiply the numerators together for the new numerator.
- Multiply the denominators together for the new denominator.
- The result is often an improper fraction.
- Convert improper fractions to mixed numbers by dividing the numerator by the denominator.
- The quotient becomes the whole number; the remainder is the new numerator over the original denominator.
- Always check if the fractional part of your answer can be simplified.
Example Problems
- Example 1: 3 × 1/2 = (3/1) × (1/2) = 3/2 = 1 and 1/2.
- Example 2: 8 × 4/5 = (8/1) × (4/5) = 32/5 = 6 and 2/5.
- Example 3: 5/7 × 5 = (5/7) × (5/1) = 25/7 = 3 and 4/7.
- Example 4: 3/4 × 12 = (3/4) × (12/1) = 36/4 = 9.
Important Notes
- Multiplying by a fraction less than one gives an answer less than the original whole number.
- Answers should always be given in simplest form or as a mixed number if improper.
Key Terms & Definitions
- Whole number — a non-fractional, non-decimal number (e.g., 3, 8).
- Fraction — a number representing part of a whole, with a numerator and denominator (e.g., 1/2).
- Improper fraction — numerator is greater than or equal to the denominator (e.g., 7/4).
- Mixed number — a whole number plus a proper fraction (e.g., 1 1/2).
- Simplify — to reduce a fraction to its smallest possible numerator and denominator.
Action Items / Next Steps
- Practice multiplying whole numbers by fractions and converting to mixed numbers.
- Remember to always simplify your answers.
- Review your notes if you need a refresher on converting improper fractions to mixed numbers.