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Calculating Composite Intervals
Method 1: Subtraction
- 9/7 = interval for 9 subtract interval for 7 = 9/8 - 7/4 = 204¢ - 969¢ = -765¢ mod 1200 = 435¢
Method 2: Using Reciprocals
- 9/7 = 9/8 × 8/7
- 9/8 = 204¢ and 8/7 = 231¢
- Therefore: 204¢ + 231¢ = 435¢
General Strategy:
- You can either subtract the denominator's cent value from the numerator's cent value, OR add the numerator to the denominator's reciprocal value
- It varies on which one will be easier per problem
What is Complexity?
- Complexity = numerator × denominator
- Example: the interval 3/2 has complexity 3 × 2 = 6
- Higher complexity generally means more difficult intervals to identify
Level Progression
- Part A (e.g., "3a"): Focused range of complexity
- Part B (e.g., "3b"): Cumulative from 0 to that complexity
Recommended mastery criteria before advancing:
- Average error < 0.3¢
- Average answer time < 5 seconds