Math with Mr. J: Multiplying Fractions Using Cancellation

Introduction

• Topic: Multiplying fractions using cancellation
• Purpose: Simplify fractions before multiplying for easier computation
• Benefits: Smaller, easier numbers to work with; makes problems simpler

Process of Cancellation

• Focus: Look for common factors between numerators and denominators (top and bottom), not horizontally or side to side
• Method: Simplify using common factors of all numbers in the problem

Examples

Example 1: 14/15 * 5/16*

1. Identify common factors:
   • 15 and 5 have common factor: 5
   • 14 and 16 have common factor: 2
2. Divide by common factors:
   • 15 ÷ 5 = 3, 5 ÷ 5 = 1
   • 14 ÷ 2 = 7, 16 ÷ 2 = 8
3. New simplified problem: 7/3 * 1/8
4. Multiply across: 7/24
5. Check simplification: 7/24 is in simplest form*

Example 2: 7/18 * 6/7*

1. Identify common factors:
   • Sevens have common factor: 7
   • 18 and 6 have common factor: 6
2. Divide by common factors:
   • 7 ÷ 7 = 1
   • 18 ÷ 6 = 3, 6 ÷ 6 = 1
3. New simplified problem: 1/3 * 1/1
4. Multiply across: 1/3
5. Result: Already in simplest form*

Example 3: 2/3 * 27*

1. Convert whole number to fraction: 27/1
2. Identify common factors:
   • 3 and 27 have common factor: 3
3. Divide by common factors:
   • 3 ÷ 3 = 1, 27 ÷ 3 = 9
4. Multiply across: 18/1 = 18

Example 4: 2 2/9 * 4/5*

1. Convert mixed number to improper fraction:
   • Calculate: 9 * 2 + 2 = 20/9
2. Identify common factors:
   • 20 and 5 have common factor: 5
3. Divide by common factors:
   • 20 ÷ 5 = 4, 5 ÷ 5 = 1
4. Multiply across: 16/9
5. Convert to mixed number:
   • 16 ÷ 9 = 1 remainder 7
   • Result: 1 7/9*

Key Points

• Cancellation can only be used for fraction multiplication and division
• For division, cancellation applies after converting to multiplication
• Does not apply for addition and subtraction of fractions

Conclusion

• Outcome: Simplification of fraction problems using cancellation
• Note: Practicing these techniques can improve efficiency in solving fraction multiplication problems.
• Thank You: End of lecture, until next time!