I disagree with Shannon's statement. The subtraction of mixed numbers must be performed with attention to both the whole numbers and the fractional parts, and this requires a proper procedure, especially when the fractions have unlike denominators.
To subtract mixed numbers with unlike denominators, follow these steps:
- Convert mixed numbers to improper fractions: This makes them easier to work with.
- Find a common denominator: This is necessary for subtracting fractions with unlike denominators.
- Rewrite the fractions using the common denominator: Convert each fraction to have this common denominator.
- Subtract the fractions: This involves subtracting the numerators while keeping the common denominator.
- Subtract the whole numbers: Finally, combine the results from the fractions and whole numbers.
Example
Let's subtract \( 7 \frac{5}{8} - 5 \frac{1}{3} \) step by step.
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Convert to improper fractions:
- \( 7 \frac{5}{8} = \frac{(7 \times 8) + 5}{8} = \frac{56 + 5}{8} = \frac{61}{8} \)
- \( 5 \frac{1}{3} = \frac{(5 \times 3) + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \)
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Find a common denominator: The least common multiple of 8 and 3 is 24.
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Rewrite fractions using common denominator:
- \( \frac{61}{8} = \frac{61 \times 3}{8 \times 3} = \frac{183}{24} \)
- \( \frac{16}{3} = \frac{16 \times 8}{3 \times 8} = \frac{128}{24} \)
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Subtract the fractions:
- \( \frac{183}{24} - \frac{128}{24} = \frac{183 - 128}{24} = \frac{55}{24} \)
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Combine with whole numbers: The whole number from \( 7 \) and \( 5 \) gives \( 7 - 5 = 2 \).
So the final result is: \[ 7 \frac{5}{8} - 5 \frac{1}{3} = 2 \frac{55}{24} \]
This is the correct process for subtracting mixed numbers with unlike denominators.