To find the absolute value of subtracting the rational numbers \(-22\) and \(1 \frac{1}{2}\), we first need to convert \(1 \frac{1}{2}\) into an improper fraction or a decimal.
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Convert \(1 \frac{1}{2}\) into an improper fraction: \[ 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \]
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Now express \(-22\) as a fraction: \[ -22 = -\frac{22}{1} = -\frac{44}{2} \]
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Now, subtract \(-\frac{3}{2}\) from \(-\frac{44}{2}\): \[ -22 - 1 \frac{1}{2} = -\frac{44}{2} - \frac{3}{2} = -\frac{44 + 3}{2} = -\frac{47}{2} \]
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Now we need to find the absolute value of \(-\frac{47}{2}\): \[ \left| -\frac{47}{2} \right| = \frac{47}{2} \]
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To present \(\frac{47}{2}\) in decimal form or as a mixed number: \[ \frac{47}{2} = 23.5 \quad \text{or} \quad 23 \frac{1}{2} \]
Thus, the absolute value of subtracting \(-22\) and \(1 \frac{1}{2}\) is \(\frac{47}{2}\) or \(23.5\).