Class Note: Multiplying Improper Fractions

Objective

• Understand how to multiply improper fractions.
• Learn how to simplify before multiplying.

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Key Points

1. What is an Improper Fraction?

• An improper fraction has a numerator equal to or greater than the denominator.

2. Steps to Multiply Improper Fractions

1. Multiply Across
   • Multiply the numerators together.
   • Multiply the denominators together.
2. Simplify If Possible
   • Reduce the fraction to its lowest terms if possible.

3. Examples

Example 1

• ( \frac{6}{5} \times \frac{8}{5} )
  • Multiply numerators: ( 6 \times 8 = 48 )
  • Multiply denominators: ( 5 \times 5 = 25 )
  • Answer: ( \frac{48}{25} ) (already simplified)

Example 2

• ( \frac{4}{3} \times \frac{7}{5} )
  • Multiply numerators: ( 4 \times 7 = 28 )
  • Multiply denominators: ( 3 \times 5 = 15 )
  • Answer: ( \frac{28}{15} )

Example 3

• ( \frac{9}{5} \times \frac{2}{3} )
  • Notice: ( 9 ) is divisible by ( 3 )
  • Write as ( \frac{3 \times 3}{5} \times \frac{2}{3 \times 1} )
  • Cancel a 3 from the top and bottom.
  • Multiply: ( 3 \times 2 = 6 ) (numerator), ( 5 \times 1 = 5 ) (denominator)
  • Answer: ( \frac{6}{5} )

Example 4

• ( \frac{8}{5} \times \frac{15}{4} )
  • Write: ( \frac{4 \times 2}{5} \times \frac{5 \times 3}{4} )
  • Cancel one 4 and one 5.
  • Left with: ( 2 \times 3 = 6 ) (numerator), ( 1 \times 1 = 1 ) (denominator)
  • Answer: ( \frac{6}{1} = 6 )

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Summary

• Multiply numerators and denominators directly.
• Simplify before multiplying if possible (cancel common factors).
• Write your answer as an improper fraction or whole number if applicable.