Class Notes: Multiplying and Dividing Fractions

Multiplying Fractions

• Step 1: Multiply the numerators (top numbers) together.
• Step 2: Multiply the denominators (bottom numbers) together.
• Step 3: Simplify the result if possible.

Example:

• (\frac{3}{5} \times \frac{4}{9})
• Multiply across:
  • Numerators: (3 \times 4 = 12)
  • Denominators: (5 \times 9 = 45)
  • Result: (\frac{12}{45})
• Simplify the fraction:
  • Both 12 and 45 can be divided by 3
  • (\frac{12 \div 3}{45 \div 3} = \frac{4}{15})
• Final Answer: (\frac{4}{15})

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Dividing Fractions

• Use the "Keep, Change, Flip" Method:
  1. Keep the first fraction as it is
  2. Change the division sign to multiplication
  3. Flip (find the reciprocal of) the second fraction

Example:

• (\frac{5}{6} \div \frac{2}{3})
• Keep: (\frac{5}{6})
• Change: (/) becomes (\times)
• Flip: (\frac{2}{3}) becomes (\frac{3}{2})
• Now multiply:
  • Numerators: (5 \times 3 = 15)
  • Denominators: (6 \times 2 = 12)
  • Result: (\frac{15}{12})
• Simplify the fraction:
  • Both 15 and 12 can be divided by 3
  • (\frac{15 \div 3}{12 \div 3} = \frac{5}{4})
• Final Answer: (\frac{5}{4}) (an improper fraction)

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Key Points

• When multiplying fractions, multiply straight across (numerators and denominators).
• When dividing fractions, use "keep, change, flip" to convert division into multiplication.
• Always simplify the final fraction if possible.
• An improper fraction is when the numerator is larger than the denominator.

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End of Lesson