To perform the subtraction \( 21 \frac{4}{8} - \frac{3}{4} \), we first convert the mixed number into an improper fraction.
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Convert \( 21 \frac{4}{8} \) into an improper fraction: \[ 21 \frac{4}{8} = \frac{(21 \times 8) + 4}{8} = \frac{168 + 4}{8} = \frac{172}{8} \]
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Now, we need a common denominator to subtract \( \frac{3}{4} \). The denominator for \( \frac{3}{4} \) can be converted to eighths: \[ \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \]
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Now we can perform the subtraction: \[ \frac{172}{8} - \frac{6}{8} = \frac{172 - 6}{8} = \frac{166}{8} \]
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Finally, we can simplify \( \frac{166}{8} \): \[ \frac{166 \div 2}{8 \div 2} = \frac{83}{4} \]
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We can convert this back into a mixed number: \[ \frac{83}{4} = 20 \frac{3}{4} \]
Therefore, the result of \( 21 \frac{4}{8} - \frac{3}{4} \) is \( 20 \frac{3}{4} \).