Class Notes: Subtracting Mixed Numbers with Unlike Denominators

Objective

Learn how to subtract mixed numbers when the fractions have different (unlike) denominators.

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Step-by-Step Process

1. Write Mixed Numbers as Whole Number Plus Fraction

• Example 1: ( 7 \frac{4}{5} ) can be written as ( 7 + \frac{4}{5} )
• Example 2: ( 2 \frac{1}{3} ) (when subtracting) becomes ( -2 - \frac{1}{3} )
  Note: Apply the negative sign to both the whole number and the fraction.

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2. Subtract Whole Numbers

• ( 7 - 2 = 5 )
• Leftover: Subtract the fractions separately: ( \frac{4}{5} - \frac{1}{3} )

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3. Get Common Denominators for Fractions

• Find the least common denominator (LCD).
• Multiply each fraction so their denominators are the same:
  • ( \frac{4}{5} \times \frac{3}{3} = \frac{12}{15} )
  • ( \frac{1}{3} \times \frac{5}{5} = \frac{5}{15} )

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4. Subtract the Fractions

• ( \frac{12}{15} - \frac{5}{15} = \frac{7}{15} )

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5. Add the Result to the Subtracted Whole Numbers

• Result: ( 5 + \frac{7}{15} = 5 \frac{7}{15} )

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Second Example

1. ( 6 \frac{2}{3} - 4 \frac{1}{5} )
   • Break up as: ( (6 - 4) + \left(\frac{2}{3} - \frac{1}{5}\right) )
   • ( 6 - 4 = 2 )
2. Find common denominator for ( \frac{2}{3} - \frac{1}{5} ) (LCD = 15):
   • ( \frac{2}{3} \times \frac{5}{5} = \frac{10}{15} )
   • ( \frac{1}{5} \times \frac{3}{3} = \frac{3}{15} )
   • ( \frac{10}{15} - \frac{3}{15} = \frac{7}{15} )
3. Combine with whole number: ( 2 + \frac{7}{15} = 2 \frac{7}{15} )

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Summary

• Always break mixed numbers into whole numbers and fractions.
• Subtract the whole numbers and the fractions separately.
• Always find a common denominator before subtracting fractions.
• Combine the results to get the simplified mixed number answer.

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Final Key Point

This method applies to any mixed numbers with unlike denominators:

1. Separate into whole and fractional parts.
2. Find the LCD and rewrite fractions.
3. Subtract parts, then combine for your answer.