Class Notes: Multiplying Two Fractions

Objective

Learn how to multiply two fractions and simplify the result when possible.

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Key Steps

1. Multiply the Numerators

   • Multiply the top numbers (numerators) of each fraction together.

2. Multiply the Denominators

   • Multiply the bottom numbers (denominators) of each fraction together.

3. Simplify Your Answer

   • If possible, reduce the resulting fraction by dividing both numerator and denominator by their greatest common factor.

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Examples

Example 1

• Calculation:
  ( \frac{2}{5} \times \frac{3}{7} = \frac{2 \times 3}{5 \times 7} = \frac{6}{35} )
• Final Answer: ( \frac{6}{35} )

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Example 2

• Calculation:
  ( \frac{1}{7} \times \frac{2}{9} = \frac{1 \times 2}{7 \times 9} = \frac{2}{63} )
• Final Answer: ( \frac{2}{63} )

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Example 3 (with Simplification)

• Initial Calculation:
  ( \frac{3}{8} \times \frac{4}{5} = \frac{3 \times 4}{8 \times 5} = \frac{12}{40} )
• Simplify by 2:
  ( \frac{12 \div 2}{40 \div 2} = \frac{6}{20} )
• Simplify by 2 again:
  ( \frac{6 \div 2}{20 \div 2} = \frac{3}{10} )
• Final Answer: ( \frac{3}{10} )

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Tips

• Always check if your final answer can be simplified.
• To simplify, divide both the numerator and denominator by their greatest common factor.

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Additional Practice

• For more practice problems on multiplying fractions and other math topics, check out the links in the description below.

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