Question

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Explanation:

Step1: Convert mixed number to improper fraction

The number of Mercury years is \( 6\frac{3}{4} \). To convert this mixed number to an improper fraction, we use the formula \( a\frac{b}{c}=\frac{a\times c + b}{c} \). So, \( 6\frac{3}{4}=\frac{6\times4 + 3}{4}=\frac{24 + 3}{4}=\frac{27}{4} \).

Step2: Multiply by Earth days per Mercury year

We know that 1 Mercury year is 88 Earth days. To find the number of Earth days equivalent to \( \frac{27}{4} \) Mercury years, we multiply \( \frac{27}{4} \) by 88. So, \( \frac{27}{4}\times88 \). We can simplify this by dividing 88 by 4 first: \( 88\div4 = 22 \). Then, \( 27\times22 = 594 \).

Answer:

594