Class Notes: Dividing Fractions Using the Cancellation Method

Objective

To learn how to divide fractions using the Cancellation Method with the "Keep Change Flip" strategy.

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Key Concepts

1. Keep Change Flip (KCF)

• Keep: Keep the first fraction the same.
• Change: Change the division sign to multiplication.
• Flip: Flip (find the reciprocal of) the second fraction.

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The Cancellation Method Steps

1. Apply KCF: Convert the division of fractions into multiplication by the reciprocal.
2. Factor Numbers: Break down large numbers in the numerators and denominators into their prime factors.
3. Cancel Common Factors: Cross out common factors that appear in both the numerator and the denominator.
4. Simplify: Multiply the remaining numbers to get the simplified answer.

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Example Problems & Solutions

Example 1

Problem: 16/15 ÷ 8/5

Steps:

• Apply KCF: 16/15 × 5/8
• Factor: 16 = 8×2, 15 = 5×3
• Rewrite: (8×2)/(5×3) × 5/8
• Cancel: 8 with 8, 5 with 5
• Left: 2/3

Answer: 2/3

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Example 2

Problem: 27/14 ÷ 21/18

Steps:

• Apply KCF: 27/14 × 18/21
• Factor: 27 = 9×3, 14 = 7×2, 18 = 9×2, 21 = 7×3
• Cancel: 9 with 9, 7 with 7, 3 with 3, 2 with 2 (as applicable)
• Left: 3/2

Answer: 3/2 (improper fraction)

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Practice Problems

1. 5/9 ÷ 25/36

   • KCF: 5/9 × 36/25
   • Factor: 36 = 9×4, 25 = 5×5
   • Cancel: 9 with 9, 5 with 5
   • Left: 4/5

   Answer: 4/5

2. 15/16 ÷ 35/48

   • KCF: 15/16 × 48/35
   • Factor: 15 = 5×3, 16 = 8×2, 48 = 8×6, 35 = 7×5, 6 = 3×2
   • Cancel: 5 with 5, 8 with 8, 3 with 3, 2 with 2
   • Left: 9/7 (multiply remaining numerators and denominators)

   Answer: 9/7 (improper fraction)

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Summary

• Use "Keep Change Flip" to rewrite division of fractions as multiplication.
• Break down numbers into factors and cancel common ones to simplify.
• Multiply what's left to get your answer.

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Additional Resources

• For more videos on math, visit: video.net (also covers Chemistry and Physics).

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End of Notes