Overview ✏️
This lecture explains how to convert improper fractions to mixed numbers without long division, by breaking the numerator into a sum of multiples of the denominator.
Converting Improper Fractions to Mixed Numbers ➗
- To convert, write the numerator as the sum of the largest multiple of the denominator (less than or equal to the numerator) and the remainder.
- Example: 11/4
- 11 = 8 + 3 (8 is the largest multiple of 4 under 11)
- 11/4 = 8/4 + 3/4
- 8/4 = 2, so 11/4 = 2 and 3/4
- Example: 17/5
- 17 = 15 + 2 (15 is the largest multiple of 5 under 17)
- 17/5 = 15/5 + 2/5
- 15/5 = 3, so 17/5 = 3 and 2/5
Using Multiples to Find the Breakdown 🔢
- Find the greatest multiple of the denominator less than or equal to the numerator.
- Example: 53/6
- Largest multiple of 6 under 53 is 48
- 53 - 48 = 5, so 53 = 48 + 5
- 53/6 = 48/6 + 5/6
- 48/6 = 8, so 53/6 = 8 and 5/6
- Example: 45/7
- Largest multiple of 7 under 45 is 42
- 45 - 42 = 3, so 45 = 42 + 3
- 45/7 = 42/7 + 3/7
- 42/7 = 6, so 45/7 = 6 and 3/7
Checking Your Work ✅
- To check, convert the mixed number back to an improper fraction:
- Multiply the whole number by the denominator, add the numerator, and keep the denominator the same.
- Example: 6 and 3/7 → 6×7 + 3 = 45, so 45/7
Key Terms & Definitions 📚
- Improper fraction: Numerator is equal to or larger than the denominator.
- Mixed number: A whole number combined with a proper fraction.
Action Items / Next Steps 📝
- Practice breaking down more improper fractions into mixed numbers using this method.
- Try listing multiples of denominators for other examples.