Question

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

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(3\frac{1}{6}\) 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 \(3\frac{1}{6}\), we have \(a = 3\), \(b = 1\), \(c = 6\). Then \(\frac{3\times6 + 1}{6}=\frac{18 + 1}{6}=\frac{19}{6}\).

Next, convert \(1\frac{3}{4}\) to an improper fraction. Here, \(a = 1\), \(b = 3\), \(c = 4\). So \(\frac{1\times4 + 3}{4}=\frac{4 + 3}{4}=\frac{7}{4}\).

Step2: Find a common denominator

The denominators are 6 and 4. The least common multiple of 6 and 4 is 12. So we need to rewrite both fractions with a denominator of 12.

For \(\frac{19}{6}\), multiply the numerator and denominator by 2: \(\frac{19\times2}{6\times2}=\frac{38}{12}\).

For \(\frac{7}{4}\), multiply the numerator and denominator by 3: \(\frac{7\times3}{4\times3}=\frac{21}{12}\).

Step3: Subtract the fractions

Now that both fractions have the same denominator, we can subtract them: \(\frac{38}{12}-\frac{21}{12}=\frac{38 - 21}{12}=\frac{17}{12}\).

Step4: Convert back to a mixed number (optional)

Convert \(\frac{17}{12}\) back to a mixed number. Divide 17 by 12: \(17\div12 = 1\) with a remainder of 5. So \(\frac{17}{12}=1\frac{5}{12}\).

Answer:

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