Question

1. \\(\frac{-1}{3} \times 2\frac{2}{3} \times 2\\)
2. \\(\frac{1}{2} \times \frac{-9}{5} \times -2\\)

Explanation:

Step1: Convert mixed number to improper fraction

The mixed number \( 2\frac{2}{3} \) can be converted 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 \( 2\frac{2}{3} \), we have \( a = 2 \), \( b = 2 \), \( c = 3 \). Then \( 2\frac{2}{3}=\frac{2\times3 + 2}{3}=\frac{6 + 2}{3}=\frac{8}{3} \). Now the expression becomes \( \frac{-1}{3}\times\frac{8}{3}\times2 \).

Step2: Multiply the fractions and the integer

First, multiply the two fractions: \( \frac{-1}{3}\times\frac{8}{3}=\frac{-1\times8}{3\times3}=\frac{-8}{9} \). Then multiply this result by 2: \( \frac{-8}{9}\times2=\frac{-8\times2}{9}=\frac{-16}{9} \).

Answer:

\( -\frac{16}{9} \)