Question

6 ( 3\frac{1}{6} - 1\frac{3}{4} )

Explanation:

Step1: Simplify the mixed numbers

First, simplify \(3\frac{1}{6}\) and \(1\frac{3}{4}\). \(3\frac{1}{6}\) remains as is, and \(1\frac{3}{4}\) remains as is. But we need to find a common denominator for the fractions. The denominators are 6 and 4, so the least common denominator (LCD) is 12.

Step2: Convert the fractions to have the LCD

Convert \(\frac{1}{6}\) to twelfths: \(\frac{1}{6}=\frac{1\times2}{6\times2}=\frac{2}{12}\), so \(3\frac{1}{6}=3\frac{2}{12}\).
Convert \(\frac{3}{4}\) to twelfths: \(\frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12}\), so \(1\frac{3}{4}=1\frac{9}{12}\).

Step3: Subtract the whole numbers and the fractions

Now subtract: \(3\frac{2}{12}-1\frac{9}{12}\). Since \(\frac{2}{12}<\frac{9}{12}\), we need to borrow 1 from the whole number 3. So \(3\frac{2}{12}=2 + 1+\frac{2}{12}=2\frac{12 + 2}{12}=2\frac{14}{12}\).
Now subtract: \(2\frac{14}{12}-1\frac{9}{12}=(2 - 1)+(\frac{14}{12}-\frac{9}{12})=1\frac{5}{12}\).

Answer:

\(1\frac{5}{12}\)