جواب تمرین صفحه 17 درس 1 ریاضی هشتم (عددهای صحیح و گویا)

\(\begin{array}{l}( - \frac{6}{{17}}) + ( - \frac{{ - 8}}{{17}}) = ( - \frac{6}{{17}}) + ( + \frac{8}{{17}}) = \\\\\frac{{ - 6 + 8}}{{17}} = \frac{2}{{17}}\end{array}\)

\(\begin{array}{l}( - \frac{{12}}{{35}}) - ( + \frac{{11}}{{42}}) = ( - \frac{{12 \times 6}}{{35 \times 6}}) - (\frac{{11 \times 5}}{{42 \times 5}}) = \\\\( - \frac{{72}}{{210}}) - (\frac{{55}}{{210}}) = \frac{{ - 72 - 55}}{{210}} = - \frac{{127}}{{210}}\end{array}\)

\(\begin{array}{l}( - \frac{2}{{63}}) - ( - \frac{5}{{72}}) = ( - \frac{2}{{63}}) + (\frac{5}{{72}}) = \\\\( - \frac{{2 \times 8}}{{63 \times 8}}) + (\frac{{5 \times 7}}{{72 \times 7}}) = ( - \frac{{16}}{{504}}) + (\frac{{35}}{{504}}) = \\\\\frac{{ - 16 + 35}}{{504}} = \frac{{19}}{{504}}\end{array}\)

\(\begin{array}{l}( - \frac{7}{{12}}) + ( - 3) = ( - \frac{7}{{12}}) - (\frac{3}{1}) = \\\\( - \frac{7}{{12}}) - (\frac{{3 \times 12}}{{1 \times 12}}) = \frac{{ - 7 - 36}}{{12}} = - \frac{{43}}{{12}}\end{array}\)

\(\begin{array}{l}( + \frac{2}{{11}}) \times ( - \frac{6}{9}) = ( + \frac{2}{{11}}) \times ( - \frac{2}{3}) = \\\\\frac{{2 \times ( - 2)}}{{11 \times 3}} = - \frac{4}{{33}}\end{array}\)

\(\begin{array}{l}( - \frac{1}{{10}}) \times ( + \frac{8}{{12}}) = ( - \frac{1}{{10}}) \times ( + \frac{2}{3}) = \\\\\frac{{ - 1 \times 2}}{{10 \times 3}} = - \frac{2}{{30}} = - \frac{1}{{15}}\end{array}\)

\( - 8 \div ( + 5) = - \frac{8}{5}\)

\(( - 12) \div ( - 28) = \frac{{ - 12}}{{ - 28}} = \frac{{12}}{{28}} = \frac{3}{7}\)

\(\begin{array}{l}( - \frac{7}{9}) \div ( - \frac{{28}}{{27}}) = ( - \frac{7}{9}) \times ( - \frac{{27}}{{28}}) = \\\\\frac{7}{9} \times \frac{{27}}{{28}} = \frac{{7 \times 27}}{{9 \times 28}} = \frac{{1 \times 3}}{{1 \times 4}} = \frac{3}{4}\end{array}\)

\( - 2/4 \div 1/2 = \frac{{ - 2/4}}{{1/2}} = \frac{{ - 24}}{{12}} = - 2\)

\(\begin{array}{l} - ( - \frac{5}{8}) = \frac{5}{8}\\\\ - (\frac{{14}}{{ - 19}}) = \frac{{14}}{{19}}\\\\ - (\frac{{ - 5}}{{ - 13}}) = - \frac{5}{{13}}\\\\ - \frac{3}{5} = - \frac{3}{5}\end{array}\)

\(\begin{array}{l}(\frac{3}{5} - ( + \frac{2}{5})) \times \frac{5}{{12}} = (\frac{{3 - 2}}{5}) \times \frac{5}{{12}} = \\\\\frac{1}{5} \times \frac{5}{{12}} = \frac{5}{{60}} = \frac{1}{{12}}\end{array}\)

\(\begin{array}{l}( - \frac{3}{5}) \div ( - \frac{2}{5} + \frac{5}{6}) = \\\\( - \frac{3}{5}) \div (\frac{{ - 12 + 25}}{{30}}) = \\\\( - \frac{3}{5}) \div (\frac{{13}}{{30}}) = - \frac{3}{5} \times \frac{{30}}{{13}} = \\\\ - \frac{{90}}{{65}} = - \frac{{18}}{{13}}\end{array}\)

\(\begin{array}{l}(\frac{2}{5} - \frac{3}{5} - \frac{7}{5} + \frac{4}{5}) \times ( - \frac{5}{3}) = \\\\(\frac{{2 - 3 - 7 + 4}}{5}) \times ( - \frac{5}{3}) = \\\\(\frac{{ - 4}}{5}) \times ( - \frac{5}{3}) = \frac{{20}}{{15}} = \frac{4}{3}\end{array}\)

\(\begin{array}{l}( - \frac{3}{8} + \frac{1}{6} - \frac{8}{9}) \div \frac{{ - 7}}{{24}} = \\\\(\frac{{ - 27 + 12 - 64}}{{72}}) \div \frac{{ - 7}}{{24}} = \\\\(\frac{{ - 79}}{{72}}) \div \frac{{ - 7}}{{24}} = \frac{{ - 79}}{{72}} \times \frac{{24}}{{ - 7}} = \\\\\frac{{79 \times 24}}{{72 \times 7}} = \frac{{79 \times 1}}{{3 \times 7}} = \frac{{79}}{{21}}\end{array}\)

\(\begin{array}{l}( - 2 + 3 - 7) + ( - \frac{1}{3} + \frac{2}{5} - \frac{1}{{15}}) = \\\\( - 6) + (\frac{{ - 5 + 6 - 1}}{{15}}) = \\\\ - 6 + \frac{0}{{15}} = - 6 + 0 = - 6\end{array}\)

\( - 1\frac{1}{2} \times ( - 3\frac{1}{3}) = ( - \frac{3}{2}) \times ( - \frac{{10}}{3}) = \frac{{30}}{6} = 5\)

\(\begin{array}{l} - 4\frac{1}{2} \div 1\frac{1}{4} = ( - \frac{9}{2}) \div (\frac{5}{4}) = \\\\ - \frac{9}{2} \times \frac{4}{5} = - \frac{{36}}{{10}} = - \frac{{18}}{5}\end{array}\)

\(\begin{array}{l} - 1\frac{2}{3} - 1\frac{1}{4} \times \frac{{ - 8}}{5} = - \frac{5}{3} - (\frac{5}{4} \times \frac{{ - 8}}{5}) = \\\\ - \frac{5}{3} - (\frac{{ - 40}}{{20}}) = - \frac{5}{3} - ( - 2) = \\\\ - \frac{5}{3} + 2 = \frac{{ - 5 + 6}}{3} = \frac{1}{3}\end{array}\)