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جد ناتج ما يأتي:

$\frac{2}{7}+\frac{5}{8}$

$\begin{array}{rl}\frac{2}{7}+\frac{5}{8}& =\frac{2\times 8}{7\times 8}+\frac{5\times 7}{8\times 7}\\ & =\frac{16}{56}+\frac{35}{56}=\frac{51}{56}\end{array}$

$\frac{4}{6}+\frac{2}{3}$

$\frac{4}{6}+\frac{2}{3}=\frac{4}{6}+\frac{4}{6}=\frac{4+4}{6}=\frac{8}{6}$

$\frac{5}{6}+\frac{4}{9}$

$\begin{array}{r}\frac{5}{6}+\frac{4}{9}=\frac{5\times 3}{6\times 3}+\frac{4\times 2}{9\times 2}\\ =\frac{15}{18}+\frac{8}{18}=\frac{23}{18}\end{array}$

$\frac{7}{12}+\frac{3}{8}$

$\begin{array}{rl}\frac{7}{12}+\frac{3}{8}& =\frac{7\times 2}{12\times 2}+\frac{3\times 3}{8\times 3}\\ & =\frac{14}{24}+\frac{9}{24}=\frac{23}{24}\end{array}$

$-4.6+(-3.7)$

$\begin{array}{rl}& -4.6+(-3.7)=\frac{-46}{10}+\left(\frac{-37}{10}\right)\\ & =-\left(\frac{46+37}{10}\right)=\frac{-83}{10}=-8.3\end{array}$

$-4.6+(-7.9)$

$\begin{array}{rl}& -4.6+(-7.9)=\frac{-46}{10}+\left(\frac{-79}{10}\right)\\ & =-\left(\frac{46+79}{-125}\right)=-12.5\end{array}$

$8.5+(-9.6)$

$\begin{array}{rl}& 8.5+(-9.6)=\frac{85}{10}+\left(\frac{-96}{10}\right)\\ & =-\left(\frac{96-85}{10}\right)=\frac{-11}{10}=-1.1\end{array}$

$\frac{3}{4}-\frac{6}{5}$

$\begin{array}{rl}& \frac{3}{4}-\frac{6}{5}=\frac{3}{4}+\left(\frac{-6}{5}\right)\\ =& \frac{3\times 5}{4\times 5}+\left(\frac{-6\times 4}{6\times 4}\right)=\frac{15}{20}+\left(\frac{-24}{20}\right)\\ =& -\left(\frac{24-15}{20}\right)=\frac{-9}{20}\end{array}$

$\frac{7}{9}-\frac{8}{5}$

$\begin{array}{rl}& \frac{7}{9}-\frac{8}{5}=\frac{7}{9}+\left(\frac{-8}{5}\right)\\ & =\frac{7\times 5}{9\times 5}+\left(\frac{-8\times 9}{5\times 9}\right)=\frac{35}{45}+\left(\frac{-72}{45}\right)\\ & =-\left(\frac{72-35}{45}\right)=\frac{-37}{45}\end{array}$

$\frac{11}{10}-\frac{12}{15}$

$\begin{array}{rl}& \frac{11}{10}-\frac{12}{15}=\frac{11}{10}+\left(\frac{-12}{15}\right)\\ & =\frac{11\times 3}{10\times 3}+\left(\frac{-12\times 2}{15\times 2}\right)=\frac{33}{30}+\left(\frac{-24}{30}\right)\\ & =\left(\frac{33-24}{30}\right)=\frac{9}{30}\end{array}$

$2.10\times (-2)$

$\begin{array}{rl}21\times (-2)& =\frac{210}{100}\times \left(\frac{-2}{1}\right)\\ & =\frac{-420}{100}=-4.20\end{array}$

$4\times 11.2$

$\begin{array}{rl}4\times 11.2& =\frac{4}{1}\times \frac{112}{10}\\ & =\frac{448}{10}=44.8\end{array}$

$-5\times (-3.1)$

$\begin{array}{rl}-5\times (-3.1)& =\frac{-5}{1}\times \frac{-31}{10}\\ & =\frac{+155}{10}=15.5\end{array}$

$\frac{8}{9}÷\frac{2}{3}$

$\frac{8}{9}÷\frac{2}{3}=\frac{8}{9}\times \frac{3}{2}=\frac{24}{18}$

$\frac{6}{7}÷16\frac{3}{5}$

$\begin{array}{rl}\frac{6}{7}÷16\frac{3}{5}& =\frac{6}{7}÷\frac{83}{5}\\ & =\frac{6}{7}\times \frac{5}{83}=\frac{30}{581}\end{array}$

$\frac{-4}{11}÷\frac{-6}{8}$

$\frac{-4}{11}÷\frac{-6}{8}=\frac{-4}{11}\times \frac{-8}{6}=\frac{+32}{66}$