To perform the subtraction \( 21 \text{ ft } 9 \frac{1}{2} - 22 \text{ ft } 2 \frac{3}{4} \), let's first convert the measurements to a common format with feet and inches.
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Convert both lengths to inches:
- \( 21 \text{ ft } 9 \frac{1}{2} \): \[ 21 \times 12 + 9.5 = 252 + 9.5 = 261.5 \text{ inches} \]
- \( 22 \text{ ft } 2 \frac{3}{4} \): \[ 22 \times 12 + 2.75 = 264 + 2.75 = 266.75 \text{ inches} \]
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Now perform the subtraction: \[ 261.5 - 266.75 = -5.25 \text{ inches} \]
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Convert -5.25 inches back to feet and inches:
- Since -5.25 is negative, it indicates we have 5.25 inches below zero: \[ -5.25 \text{ inches} = -5 \text{ inches } - 0.25 \text{ inches} \]
Thus, \( 21 \text{ ft } 9 \frac{1}{2} - 22 \text{ ft } 2 \frac{3}{4} = -5 \text{ inches } - 0.25 \text{ inches} \), or simply -5.25 inches.
Alternatively, you could report it as "5.25 inches short" as appropriate based on your context.