Questions: 1 1/6 - 2 3/4 =

Solution Steps

To solve the given problem, we need to convert the mixed numbers to improper fractions, perform the subtraction, and then convert the result back to a mixed number if necessary.

First, we convert the mixed numbers to improper fractions: \[ 1 \frac{1}{6} = \frac{1 \times 6 + 1}{6} = \frac{7}{6} \] \[ 2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{11}{4} \]

Next, we subtract the improper fractions: \[ \frac{7}{6} - \frac{11}{4} \] To subtract these fractions, we need a common denominator. The least common multiple of 6 and 4 is 12: \[ \frac{7}{6} = \frac{7 \times 2}{6 \times 2} = \frac{14}{12} \] \[ \frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12} \] Now, subtract the fractions: \[ \frac{14}{12} - \frac{33}{12} = \frac{14 - 33}{12} = \frac{-19}{12} \]

Finally, we convert the improper fraction \(\frac{-19}{12}\) to a mixed number: \[ \frac{-19}{12} = -2 \frac{5}{12} \] This is because: \[ -19 \div 12 = -2 \text{ remainder } 5 \] So, \(\frac{-19}{12} = -2 \frac{5}{12}\).

Final Answer