Class Notes: Subtracting Two Fractions

Objective

Learn how to subtract two fractions by finding a common denominator.

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Steps to Subtract Fractions

1. Find a Common Denominator

   • Multiply the denominators of both fractions.
   • Example: For (\frac{7}{8}) and (\frac{3}{5}), common denominator = (8 \times 5 = 40).
   • Note: This method gives a common denominator (not necessarily the least common denominator).

2. Adjust Fractions

   • Multiply the first fraction by the denominator of the second (as both numerator and denominator).
   • Multiply the second fraction by the denominator of the first (as both numerator and denominator).
   • This keeps the value the same but gives common denominators.

3. Perform the Multiplication

   • First fraction: (\frac{7}{8} \times \frac{5}{5} = \frac{35}{40})
   • Second fraction: (\frac{3}{5} \times \frac{8}{8} = \frac{24}{40})

4. Subtract the Numerators

   • Since denominators are the same, subtract the numerators: (35 - 24 = 11).
   • Write the result over the common denominator: (\frac{11}{40}).

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Example 1

Subtract (\frac{7}{8}) by (\frac{3}{5}):

• Common denominator: (8 \times 5 = 40)
• Adjusted fractions:
  • (\frac{7}{8} \rightarrow \frac{35}{40})
  • (\frac{3}{5} \rightarrow \frac{24}{40})
• Subtract numerators: (35 - 24 = 11)
• Result: (\frac{11}{40})

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Example 2

Subtract (\frac{4}{9}) by (\frac{1}{7}):

• Common denominator: (9 \times 7 = 63)
• Adjusted fractions:
  • (\frac{4}{9} \rightarrow \frac{28}{63}) ((4 \times 7))
  • (\frac{1}{7} \rightarrow \frac{9}{63}) ((1 \times 9))
• Subtract numerators: (28 - 9 = 19)
• Result: (\frac{19}{63})

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Key Points

• Always convert to a common denominator before subtracting.
• Multiply each fraction by a form of 1 to adjust denominators.
• After adjusting, subtract the numerators only.
• Express your answer as a single fraction over the common denominator.

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Practice

Try subtracting other fractions using these steps!