To rewrite the expression \( 27 \frac{1}{2} \times 27 \frac{1}{4} \), we first convert the mixed numbers to improper fractions:
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Convert \( 27 \frac{1}{2} \): \[ 27 \frac{1}{2} = \frac{27 \times 2 + 1}{2} = \frac{54 + 1}{2} = \frac{55}{2} \]
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Convert \( 27 \frac{1}{4} \): \[ 27 \frac{1}{4} = \frac{27 \times 4 + 1}{4} = \frac{108 + 1}{4} = \frac{109}{4} \]
Now, we can multiply the two fractions: \[ \frac{55}{2} \times \frac{109}{4} = \frac{55 \times 109}{2 \times 4} = \frac{5995}{8} \]
The result, \( \frac{5995}{8} \), is a rational number because it can be expressed as a fraction of two integers.
In summary, \( 27 \frac{1}{2} \times 27 \frac{1}{4} \) can be rewritten as \( \frac{5995}{8} \), which is a rational number.