Class Notes: Adding Fractions Using the Butterfly Method

Objective

Learn how to add two fractions using the butterfly method.

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Steps in the Butterfly Method

1. Multiply Across (Cross-Multiply for Numerators):

   • Multiply the numerator of the first fraction by the denominator of the second.
   • Multiply the numerator of the second fraction by the denominator of the first.

2. Multiply the Denominators:

   • Multiply the denominators of both fractions together.

3. Add the Results from Step 1:

   • Add the two products from the cross-multiplied numerators.

4. Write the Final Fraction:

   • The sum from step 3 becomes your new numerator.
   • The product from step 2 is your new denominator.

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Example 1

Add:
(\frac{5}{7} + \frac{2}{3})

• Cross-Multiply Numerators:
  • (5 \times 3 = 15)
  • (2 \times 7 = 14)
• Add: (15 + 14 = 29)
• Multiply Denominators:
  • (5 \times 7 = 35)
• Final Answer:
  • (\frac{29}{35})

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Example 2

Add:
(\frac{2}{9} + \frac{3}{5})

• Cross-Multiply Numerators:
  • (9 \times 3 = 27)
  • (2 \times 5 = 10)
• Add: (27 + 10 = 37)
• Multiply Denominators:
  • (9 \times 5 = 45)
• Final Answer:
  • (\frac{37}{45})

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Key Point

• The butterfly method allows you to quickly add two fractions by cross-multiplying, adding, and multiplying denominators. The result should always be checked to see if it can be simplified.

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Practice

Try the butterfly method with new fractions to reinforce your understanding!