Question

1. $4\frac{3}{6} - 2\frac{5}{6} = \underline{\quad\quad}$

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(4\frac{3}{6}\) and \(2\frac{5}{6}\) to improper fractions. For a mixed number \(a\frac{b}{c}\), the improper fraction is \(\frac{a\times c + b}{c}\).

For \(4\frac{3}{6}\):
\(4\times6 + 3 = 24 + 3 = 27\), so \(4\frac{3}{6}=\frac{27}{6}\)

For \(2\frac{5}{6}\):
\(2\times6 + 5 = 12 + 5 = 17\), so \(2\frac{5}{6}=\frac{17}{6}\)

Step2: Subtract the improper fractions

Now subtract the two improper fractions: \(\frac{27}{6}-\frac{17}{6}=\frac{27 - 17}{6}=\frac{10}{6}\)

Step3: Simplify the result

Simplify \(\frac{10}{6}\) by dividing numerator and denominator by their greatest common divisor, which is 2.
\(\frac{10\div2}{6\div2}=\frac{5}{3}\)
We can also convert \(\frac{5}{3}\) back to a mixed number: \(1\frac{2}{3}\) (since \(5\div3 = 1\) with a remainder of 2)

Answer:

\(1\frac{2}{3}\) (or \(\frac{5}{3}\))