جواب تمرین صفحه 22 درس 2 ریاضی نهم (عددهای حقیقی)

\(\begin{array}{l}( - 2\frac{5}{6} + 3\frac{1}{2}) \div ( - 1 - \frac{1}{9}):\\\\\left\{ \begin{array}{l} - 2\frac{5}{6} + 3\frac{1}{2} = - \frac{{17}}{6} + \frac{7}{2} = \\\\ - \frac{{17}}{6} + \frac{{21}}{6} = \frac{{ - 17 + 21}}{6} = \frac{4}{6} = \frac{2}{3}\end{array} \right.\\\\\left\{ { - 1 - \frac{1}{9} = - \frac{9}{9} - \frac{1}{9} = - \frac{{10}}{9}} \right.\\\\ \Rightarrow ( - 2\frac{5}{6} + 3\frac{1}{2}) \div ( - 1 - \frac{1}{9}) = \\\\\frac{2}{3} \div ( - \frac{{10}}{9}) = \frac{2}{3} \times ( - \frac{9}{{10}}) = - \frac{3}{5} = - 0/6\end{array}\)

\(\begin{array}{l}\frac{{1 - \frac{1}{2} + \frac{3}{4}}}{{\frac{5}{{10}} - \frac{3}{4} - \frac{1}{2}}} \div 5\frac{1}{3}:\\\\\left\{ {1 - \frac{1}{2} + \frac{3}{4} = \frac{4}{4} - \frac{2}{4} + \frac{3}{4} = \frac{5}{4}} \right.\\\\\left\{ {\frac{5}{{10}} - \frac{3}{4} - \frac{1}{2} = \frac{1}{2} - \frac{3}{4} - \frac{1}{2} = - \frac{3}{4}} \right.\\\\\left\{ {\frac{{1 - \frac{1}{2} + \frac{3}{4}}}{{\frac{5}{{10}} - \frac{3}{4} - \frac{1}{2}}} = \frac{{\frac{5}{4}}}{{ - \frac{3}{4}}} = - \frac{{5 \times 4}}{{4 \times 3}} = - \frac{5}{3}} \right.\\\\ \Rightarrow \frac{{1 - \frac{1}{2} + \frac{3}{4}}}{{\frac{5}{{10}} - \frac{3}{4} - \frac{1}{2}}} \div 5\frac{1}{3} = - \frac{5}{3} \div 5\frac{1}{3} = \\\\ - \frac{5}{3} \div \frac{{16}}{3} = - \frac{5}{3} \times \frac{3}{{16}} = - \frac{5}{{16}} = - 0/3125\end{array}\)

\(\begin{array}{l} - \frac{1}{2} + \frac{{ - 5}}{6} \div \frac{7}{3} \times \frac{7}{5} + \frac{2}{3}:\\\\\left\{ {\frac{{ - 5}}{6} \div \frac{7}{3} = \frac{{ - 5}}{6} \times \frac{3}{7} = - \frac{5}{{14}}} \right.\\\\\left\{ {\frac{{ - 5}}{6} \div \frac{7}{3} \times \frac{7}{5} = - \frac{5}{{14}} \times \frac{7}{5} = - \frac{1}{2}} \right.\\\\ \Rightarrow - \frac{1}{2} + \frac{{ - 5}}{6} \div \frac{7}{3} \times \frac{7}{5} + \frac{2}{3} = \\\\ - \frac{1}{2} - \frac{1}{2} + \frac{2}{3} = - 1 + \frac{2}{3} = \\\\ - \frac{3}{3} + \frac{2}{3} = - \frac{1}{3}\end{array}\)

\(\begin{array}{l}\frac{1}{{ - 1 - \frac{1}{{ - 1 - \frac{1}{3}}}}}:\\\\\left\{ { - 1 - \frac{1}{3} = - \frac{3}{3} - \frac{1}{3} = - \frac{4}{3}} \right.\\\\\left\{ \begin{array}{l} - 1 - \frac{1}{{ - 1 - \frac{1}{3}}} = - 1 - \frac{1}{{ - \frac{4}{3}}} = \\\\ - 1 + \frac{3}{4} = - \frac{4}{4} + \frac{3}{4} = - \frac{1}{4}\end{array} \right.\\\\ \Rightarrow \frac{1}{{ - 1 - \frac{1}{{ - 1 - \frac{1}{3}}}}} = \frac{1}{{ - \frac{1}{4}}} = - 4\end{array}\)

الف

\(\begin{array}{l}\frac{7}{8}\;,\; - \frac{2}{3}\;,\;\frac{3}{4}\;,\;2\;,\; - 3\frac{5}{6}\\\\ \Rightarrow \left[ {8\,,\,6\,,\,4\,,\,3\,,\,1} \right] = 24\\\\\left\{ \begin{array}{l}\frac{7}{8} = \frac{{21}}{{24}}\\\\ - \frac{2}{3} = - \frac{{16}}{{24}}\\\\\frac{3}{4} = \frac{{18}}{{24}}\\\\2 = \frac{{48}}{{24}}\\\\ - 3\frac{5}{6} = - \frac{{23}}{6} = - \frac{{92}}{{24}}\end{array} \right.\\\\ \Rightarrow - \frac{{92}}{{24}} < - \frac{{16}}{{24}} < \frac{{18}}{{24}} < \frac{{21}}{{24}} < \frac{{48}}{{24}}\\\\ \Rightarrow - 3\frac{5}{6} < - \frac{2}{3} < \frac{3}{4} < \frac{7}{8} < 2\\\\ \Rightarrow - 3\frac{5}{6}\,,\, - \frac{2}{3}\,,\,\frac{3}{4}\,,\,\frac{7}{8}\,,\,2\end{array}\)

ب

\(\begin{array}{l}\frac{{16}}{7}\;,\; - \frac{3}{4}\;,\;2/75\;,\; - \frac{5}{6}\;,\;4\frac{3}{5}\;,\;\frac{{56}}{{13}}\\\\\left\{ \begin{array}{l}\frac{{16}}{7} = 2\frac{2}{7} \simeq 2/28\\\\ - \frac{3}{4} = - 0/75\\\\ - \frac{5}{6} \simeq - 0/83\\\\4\frac{3}{5} = 4/6\\\\\frac{{56}}{{13}} = 4\frac{4}{{13}} \simeq 4/3\end{array} \right.\\\\ \Rightarrow - 0/83 < - 0/75 < 2/75 < 2/28 < 4/3 < 4/6\\\\ \Rightarrow - \frac{5}{6} < - \frac{3}{4} < 2/75 < \frac{{16}}{7} < \frac{{56}}{{13}} < 4\frac{3}{5}\\\\ \Rightarrow - \frac{5}{6}\,,\, - \frac{3}{4}\,,\,2/75\,,\,\frac{{16}}{7}\,,\,\frac{{56}}{{13}}\,,\,4\frac{3}{5}\end{array}\)

الف

\(\begin{array}{l}\frac{{10}}{{11}} = \frac{{10 \times 13}}{{11 \times 13}} = \frac{{130}}{{143}} = \frac{{130 \times 10}}{{143 \times 10}} = \frac{{1300}}{{1430}}\\\\\frac{{12}}{{13}} = \frac{{12 \times 11}}{{13 \times 11}} = \frac{{132}}{{143}}\frac{{132 \times 10}}{{143 \times 10}} = \frac{{1320}}{{1430}}\\\\\frac{{10}}{{11}} = \frac{{1300}}{{1430}} < \frac{{1301}}{{1430}}\,,\,\frac{{1302}}{{1430}}\,,\,\frac{{1303}}{{1430}} < \frac{{1320}}{{1430}} = \frac{{12}}{{13}}\\\\ \Rightarrow \frac{{1301}}{{1430}}\,,\,\frac{{1302}}{{1430}}\,,\,\frac{{1303}}{{1430}}\end{array}\)

ب

\(\begin{array}{l} - \frac{1}{3} = - \frac{{1 \times 10}}{{3 \times 10}} = - \frac{{10}}{{30}}\\\\0 = \frac{{0 \times 10}}{{1 \times 10}} = \frac{0}{{10}} = 0\\\\ - \frac{1}{3} = - \frac{{10}}{{30}} < - \frac{9}{{30}}\,,\, - \frac{8}{{30}}\,,\, - \frac{7}{{30}} < 0\\\\ \Rightarrow - \frac{9}{{30}} = - \frac{3}{{10}}\,,\, - \frac{8}{{30}} = - \frac{4}{{15}}\,,\, - \frac{7}{{30}}\\\\ \Rightarrow - \frac{3}{{10}}\,,\, - \frac{4}{{15}}\,,\, - \frac{7}{{30}}\end{array}\)