(i) \(\frac{-1}{3}\) is greater than -1 and less than 0.
Therefore, it lies between -1 and 0
(ii) \(\frac{-3}{4}\) is greater than -1 and less than 0.
Therefore, it lies between -1 and 0
(iii) \(-1\frac{2}{3}=-\frac{(3\times1)+2}{3}=-\frac{3+2}{3}=\frac{-5}{3}\)
\(\frac{-5}{3}\)is greater than -2 and less than -1.
Therefore, it lies between -2 and -1
(iv) \(-3\frac{1}{7}=-\frac{(7\times3)+1}{3}=-\frac{21+1}{3}=\frac{-22}{3}\)
\(\frac{-22}{7}\) is greater than -8 and less than -7.
Therefore, it lies between -8 and -7
(v) \(-4\frac{3}{5}=-\frac{(5\times4)+3}{3}=-\frac{20+3}{5}=\frac{-23}{5}\)
\(\frac{-23}{5}\) is greater than -5 and less than -4.
Therefore, it lies between -5 and -4
(vi) \(-2\frac{5}{6}=-\frac{(6\times2)+5}{6}=-\frac{12+5}{5}=\frac{-17}{6}\)
\(\frac{-23}{5}\) is greater than -3 and less than -2.
Therefore, it lies between -3 and -2
(vii) The number line representation of -3 is
(viii) \(-2\frac{7}{8}=-\frac{(8\times2)+7}{8}=-\frac{16+7}{8}=\frac{-23}{8}\)
\(\frac{-23}{8}\)is greater than -3 and less than -2.
Therefore, it lies between -3 and -2