To rewrite the expression \( 27 \frac{1}{2} \cdot 27 \frac{1}{4} \), we first convert the mixed numbers into improper fractions.
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Convert \( 27 \frac{1}{2} \): \[ 27 \frac{1}{2} = 27 + \frac{1}{2} = \frac{54}{2} + \frac{1}{2} = \frac{55}{2} \]
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Convert \( 27 \frac{1}{4} \): \[ 27 \frac{1}{4} = 27 + \frac{1}{4} = \frac{108}{4} + \frac{1}{4} = \frac{109}{4} \]
Now, we can multiply the two improper fractions: \[ \frac{55}{2} \cdot \frac{109}{4} = \frac{55 \cdot 109}{2 \cdot 4} = \frac{5995}{8} \]
So, the expression \( 27 \frac{1}{2} \cdot 27 \frac{1}{4} \) can be rewritten as: \[ \frac{5995}{8} \]
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