Question

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Explanation:

Step1: Convert mixed number to improper fraction

The mixed number \(1\frac{7}{8}\) can be converted to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(1\frac{7}{8}\), we have \(a = 1\), \(b = 7\), \(c = 8\). Then \(\frac{1\times8 + 7}{8}=\frac{8 + 7}{8}=\frac{15}{8}\).

Step2: Divide the total paint by paint per bookcase

To find the number of bookcases, we divide the total amount of paint \(\frac{15}{8}\) gallons by the amount of paint per bookcase \(\frac{3}{16}\) gallon. When dividing fractions, we multiply by the reciprocal. So \(\frac{15}{8}\div\frac{3}{16}=\frac{15}{8}\times\frac{16}{3}\).

Step3: Simplify the multiplication

Simplify the fractions before multiplying. The 16 and 8 can be simplified: \(16\div8 = 2\), \(8\div8 = 1\). The 15 and 3 can be simplified: \(15\div3 = 5\), \(3\div3 = 1\). So now we have \(\frac{5}{1}\times\frac{2}{1}=10\).

Answer:

10