Question

1. $12\frac{1}{3} - 5\frac{4}{6}$

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(12\frac{1}{3}\) to an improper fraction. \(12\frac{1}{3}=\frac{12\times3 + 1}{3}=\frac{37}{3}\). Then, convert \(5\frac{4}{6}\) to an improper fraction. \(5\frac{4}{6}=\frac{5\times6+4}{6}=\frac{34}{6}\). But we can also convert \(\frac{37}{3}\) to a fraction with denominator 6 to have a common denominator. \(\frac{37}{3}=\frac{37\times2}{3\times2}=\frac{74}{6}\).

Step2: Subtract the fractions

Now subtract \(\frac{34}{6}\) from \(\frac{74}{6}\). \(\frac{74}{6}-\frac{34}{6}=\frac{74 - 34}{6}=\frac{40}{6}\).

Step3: Simplify the result

Simplify \(\frac{40}{6}\) by dividing numerator and denominator by 2, we get \(\frac{20}{3}\). Then convert it back to a mixed number: \(\frac{20}{3}=6\frac{2}{3}\).

Answer:

\(6\frac{2}{3}\)