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 \( \frac{3\times6 + 1}{6}=\frac{18 + 1}{6}=\frac{19}{6} \).

Next, convert \( 1\frac{3}{4} \) to an improper fraction. Using the same formula, we get \( \frac{1\times4 + 3}{4}=\frac{4 + 3}{4}=\frac{7}{4} \).

Step2: Find a common denominator

The denominators are 6 and 4. The least common multiple of 6 and 4 is 12. So we rewrite the 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 subtract the two fractions: \( \frac{38}{12}-\frac{21}{12}=\frac{38 - 21}{12}=\frac{17}{12} \).

Step4: Convert back to a mixed number (optional)

Convert \( \frac{17}{12} \) 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:

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