\[ \begin{align*} \frac{5}{8} &\quad {\Huge \times} \quad \frac{-3}{7} \\ \\ 5 \times 7 &\quad \text{and} \quad (-3) \times 8 \\ \\ \color{green} 35 &\quad > \quad -24 \\ \\ \color{green} \frac{5}{8} &\quad > \quad \frac{-3}{7} \\ \end{align*} \]

Answer \( \displaystyle \color{red} \frac{5}{8} \) is greater

\[ \begin{align*} \frac{2}{3} &\quad {\Huge \times} \quad \frac{8}{9} \\ \\ 2 \times 9 &\quad \text{and} \quad 8 \times 3 \\ \\ 18 &\quad < \quad \color{green} 24 \\ \\ \frac{2}{3} &\quad < \quad \color{green} \frac{8}{9} \\ \end{align*} \]

Answer \( \displaystyle \color{red}\frac{8}{9} \) is greater

\[ \begin{align*} \frac{-4}{3} &\quad {\Huge \times} \quad \frac{-6}{7} \\ \\ (-4) \times 7 &\quad \text{and} \quad (-6) \times 3 \\ \\ -28 &\quad < \quad \color{green} -18 \\ \\ \frac{-4}{3} &\quad < \quad \color{green} \frac{-6}{7} \\ \end{align*} \]

Answer \( \displaystyle \color{red} \frac{-6}{7} \) is greater

\[ \begin{align*} \text{Convert } \frac{19}{-6} & \text{ in standard form } = \frac{-19}{6} \\ \\ \frac{-8}{3} &\quad {\Huge \times} \quad \frac{-19}{6} \\ \\ (-8) \times 6 &\quad \text{and} \quad (-19) \times 3 \\ \\ \color{green} -48 &\quad > \quad -57 \\ \\ \color{green} \frac{-8}{3} &\quad > \quad \frac{-19}{6} \\ \end{align*} \]

Answer \( \displaystyle \color{red}\frac{-8}{3} \) is greater

\[ \begin{align*} \text{Convert } \frac{-3}{-13} & \text{ in standard form} = \frac{3}{13} \\ \\ \text{Convert } \frac{-5}{-21} & \text{ in standard form} = \frac{5}{21} \\ \\ \frac{3}{13} &\quad {\Huge \times} \quad \frac{5}{21} \\ \\ 3 \times 21 &\quad \text{and} \quad 5 \times 13 \\ \\ 63 &\quad < \quad \color{green} 65 \\ \\ \frac{3}{13} &\quad < \quad \color{green} \frac{5}{21} \\ \end{align*} \]

Answer \( \displaystyle \color{red}\frac{-5}{-21} \) is greater

\[ \begin{align*} \text{Convert } \frac{5}{-8} & \text{ in standard form} = \frac{-5}{8} \\ \\ \frac{-7}{11} &\quad {\Huge \times} \quad \frac{-5}{8} \\ \\ (-7) \times 8 &\quad \text{and} \quad (-5) \times 11 \\ \\ -56 &\quad < \quad \color{green} -55 \\ \\ \frac{-7}{11} &\quad < \quad \color{green} \frac{-5}{8} \\ \end{align*} \]

Answer \( \displaystyle \color{red}\frac{5}{-8} \) is greater

\[ \begin{align*} \frac{-3}{5} & = \frac{x}{15} \\ \\ -3 \times 15 & = 5 \times x \\ \\ \frac{-3 \times \cancel{15}^3}{\cancel{5}_1} &= x \\ \\ -3 \times 3 & = x \\ \color{green} -9 & = \color{green} x \end{align*} \]

Answer \( x = -9 \)

\[ \begin{align*} \frac{9}{15} & = \frac{-x}{50} \\ \\ 9 \times 50 &= 15 \times (-x) \\ \\ \frac{\cancel9^3 \times \cancel{50}^{10}}{\cancel{15}_{\cancel5_1}} &= -x \\ \\ 30 &= -x \\ \color{green} x &= \color{green} -30 \end{align*} \]

Answer \( x = -30 \)

\[ \begin{align*} \frac{36}{x} = \frac{-4}{1} \\ \\ 36 \times 1 = -4 \times x \\ \\ \frac{\cancel{36}^9}{\cancel{-4}_{-1}} = x \\ \\ \frac{9}{-1} = x \\ \\ \color{green} -9 = \color{green}x \end{align*} \]

Answer \( x = -9 \)

\[ \begin{align*} \frac{-7}{x} &= \frac{7}{1} \\ \\ -7 \times 1 &= 7 \times x \\ \\ \frac{-7}{7} &= x \\ \\ -1 &= x \end{align*} \]

Answer \( x = -1 \)

Answer

\[ \begin{align*} \text{Convert } \frac{8}{-36} & \text{ in standard form }\\ \\ & = \frac{\cancel{(-8)}^{-2}}{\cancel{36}_9} \\ \\ & = \frac{-2}{9} \\ \\ \frac{-2}{9} &= \frac{-2}{9} \\ \\ \color{red} \frac{-2}{9} &= \color{red} \frac{8}{-36} \end{align*} \]

Answer

\[ \begin{align*} \frac{5}{9} &\quad {\Huge \times} \quad \frac{4}{6} \\ \\ 5 \times 6 &\quad \text{and} \quad 4 \times 9 \\ \\ 30 &\quad < \quad \color{green} 36 \\ \\ \frac{5}{9} &\quad < \quad \color{red} \frac{4}{6} \\ \end{align*} \]

Answer

\[ \begin{align*} \text{ Standard form} &= \frac{7}{8} \\ \\ \frac{7}{8} &\quad {\Huge \times} \quad \frac{14}{17} \\ \\ 7 \times 17 &\quad \text{and} \quad 14 \times 8 \\ \\ \color{green} 119 &\quad > \quad 112 \\ \\ \color{red} \frac{7}{8} &\quad > \quad \frac{14}{17} \\ \end{align*} \]

Answer

\[ \begin{align*} \text{Standard form} & = \frac{-5}{9} \\ \\ \frac{-4}{7} &\quad {\Huge \times} \quad \frac{-5}{9} \\ \\ (-4) \times 9 &\quad \text{and} \quad (-5) \times 7 \\ \\ -36 &\quad < \quad \color{green} -35 \\ \\ \frac{-4}{7} &\quad < \quad \color{red} \frac{5}{-9} \\ \end{align*} \]

Answer

\[ \begin{align*} \frac{-5}{8} &\quad {\Huge \times} \quad \frac{-3}{4} \\ \\ (-5) \times 4 &\quad \text{and} \quad (-3) \times 8 \\ \\ \color{green} -20 &\quad > \quad -24 \\ \\ \color{red} \frac{-5}{8} &\quad > \quad \frac{-3}{4} \\ \end{align*} \]

Answer

\[ \begin{align*} \text{Standard form } \ \frac{-54}{-63} & = \frac{6}{7} \\ \\ \frac{6}{7} \quad &= \quad \frac{6}{7} \\ \\ \color{red} \frac{6}{7} & = \color{red} \frac{-54}{-63} \end{align*} \]

Answer

\[ \begin{array}{c|ccc} 7 & 7, & 9, & 5 \\ \hline 3 & 1, & 9, & 5 \\ \hline 3 & 1, & 3, & 5 \\ \hline 5 & 1, & 1, & 5 \\ \hline & 1, & 1, & 1 \\ \end{array} \] \[ \begin{align*} \text{LCM} &= 7 \times 3 \times 3 \times 5 \\ &= 315 \\ \\ \frac{4 \times \color{green} 45 }{7 \times \color{green} 45 } & = \frac{180}{315} \\ \\ \frac{5 \times \color{green} 35 }{9 \times \color{green} 35 } & = \frac{175}{315} \\ \\ \frac{2 \times \color{green} 63 }{5 \times \color{green} 63 } & = \frac{126}{315} \\ \\ \text{Ascending order} &= \frac{126}{315}, \frac{175}{315}, \frac{180}{315} \\ \\ \implies & \color{red} \frac{2}{5}, \frac{5}{9}, \frac{4}{7} \\ \end{align*} \]

Answer

\[ \begin{align*} \text{Standard form} &= \frac{-3}{4}, \frac{5}{12}, \frac{-7}{16} \\ \\ \end{align*} \] \[ \begin{array}{c|ccc} 2 & 4, & 12, & 16 \\ \hline 2 & 2, & 6, & 8 \\ \hline 2 & 1, & 3, & 4 \\ \hline 2 & 1, & 3, & 2 \\ \hline 3 & 1, & 3, & 1 \\ \hline & 1, & 1, & 1 \\ \end{array} \] \[ \begin{align*} \text{LCM} &= 2 \times 2 \times 2 \times 2 \times 3 \\ &= 48 \\ \\ \frac{-3 \times \color{green} 12}{4 \times \color{green} 12} &= \frac{-36}{48} \\ \\ \frac{5 \times \color{green} 4}{12 \times \color{green} 4} &= \frac{20}{48} \\ \\ \frac{-7 \times \color{green} 3}{16 \times \color{green} 3} &= \frac{-21}{48} \\ \\ \text{Ascending order} &= \frac{-36}{48}, \frac{-21}{48} , \frac{20}{48} \\ \\ \implies & \color{red} \frac{-3}{4}, \frac{-7}{16} , \frac{-5}{-12} \\ \end{align*} \]

Answer

\[ \begin{align*} \text{Standard form} &= \frac{2}{5},\frac{-1}{2} , \frac{-8}{15} , \frac{3}{10} \\ \end{align*} \] \[ \begin{array}{c|cccc} 2 & 5, & 2, & 15, & 10 \\ \hline 5 & 5, & 1, & 15, & 5 \\ \hline 3 & 1, & 1, & 3, &1 \\ \hline & 1, & 1, & 1, & 1 \\ \end{array} \] \[ \begin{align*} \text{LCM } &= 2 \times 5 \times 3 \\ &= 30 \\ \\ \frac{2 \times \color{green} 6}{5 \times \color{green} 6} &= \frac{12}{30} \\ \\ \frac{-1 \times \color{green} 15}{2 \times \color{green} 15} &= \frac{-15}{30} \\ \\ \frac{-8 \times \color{green} 2}{15 \times \color{green} 2} &= \frac{-16}{30} \\ \\ \frac{3 \times \color{green} 3}{10 \times \color{green} 3} &= \frac{9}{30} \\ \\ \text{Descending Order} &= \frac{12}{30}, \frac{9}{30}, \frac{-15}{30}, \frac{-16}{30} \\ \\ \implies & \color{red} \frac{2}{5}, \frac{-3}{-10}, \frac{-1}{2}, \frac{8}{-15} \\ \end{align*} \]

Answer

\[ \begin{align*} \text{Standard form} &= \frac{-7}{10},\frac{-8}{15} , \frac{19}{30} , \frac{2}{5} \\ \end{align*} \] \[ \begin{array}{c|cccc} 2 & 10, & 15, & 30, & 5 \\ \hline 3 & 5, & 15, & 15, & 5 \\ \hline 5 & 5, & 5, & 5, & 5 \\ \hline & 1, & 1, & 1, & 1 \\ \end{array} \] \[ \begin{align*} \text{LCM } &= 2 \times 3 \times 5 \\ &= 30 \\ \\ \frac{-7 \times \color{green} 3}{10 \times \color{green} 3} &= \frac{-21}{30} \\ \\ \frac{-8 \times \color{green} 2}{15 \times \color{green} 2} &= \frac{-16}{30} \\ \\ \frac{19 \times \color{green} 1}{30 \times \color{green} 1} &= \frac{19}{30} \\ \\ \frac{2 \times \color{green} 6}{5 \times \color{green} 6} &= \frac{12}{30} \\ \\ \text{Descending Order} &= \frac{19}{30}, \frac{12}{30}, \frac{-16}{30}, \frac{-21}{30} \\ \\ \implies & \color{red} \frac{19}{30} , \frac{-2}{-5} , \frac{8}{-15} , \frac{-7}{10} \\ \end{align*} \]