تدرب وحل التمرينات

جد ناتج ما يأتي:

$\frac{12}{14}+\frac{1}{7}$

$\begin{array}{rl}& \frac{12}{14}+\frac{1}{4}=\frac{12\times 2}{14\times 2}+\frac{1\times 7}{4\times 7}\\ & =\frac{24}{28}+\frac{7}{28}=\frac{24+7}{28}=\frac{31}{28}\end{array}$

$\frac{3}{5}+\frac{2}{8}$

$\begin{array}{rl}\frac{3}{5}+\frac{2}{8}& =\frac{3\times 8}{5\times 8}+\frac{2\times 5}{8\times 5}\\ & =\frac{24}{40}+\frac{10}{40}=\frac{34}{40}\end{array}$

$\frac{4}{9}+\frac{5}{12}$

$\begin{array}{rl}\frac{4}{9}+\frac{5}{12}& =\frac{4\times 4}{9\times 4}+\frac{5\times 3}{12\times 3}\\ & =\frac{16}{36}+\frac{15}{36}=\frac{31}{36}\end{array}$

$-5.2+(-1.7)$

$\begin{array}{rl}& -5.2+(-1.7)=\frac{-52}{10}+\left(\frac{-17}{10}\right)\\ & =-\left(\frac{52+17}{10}\right)=\frac{-69}{10}=-6.9\end{array}$

$6.4+(-8.7)$

$\begin{array}{rl}6.4& +(-8.7)=\frac{64}{10}+\left(\frac{-87}{10}\right)\\ =& -\left(\frac{87-64}{10}\right)=\frac{-23}{10}=-2.3\end{array}$

$1.8+(-3.9)$

$\begin{array}{rl}1.8& +(-3.9)=\frac{18}{10}+\left(\frac{-39}{10}\right)\\ =& -\left(\frac{39-18}{10}\right)=\frac{-21}{10}=-2.1\end{array}$

$\frac{6}{3}-\frac{40}{5}$

$$\begin{gathered} \frac{6}{3}-\frac{40}{5}=\frac{6}{3}+\left(\frac{-40}{5}\right) \\ \begin{array}{rl}& =\frac{6\times 5}{3\times 5}+\left(\frac{-40\times 3}{5\times 3}\right)=\frac{30}{15}+\left(\frac{-120}{15}\right)\\ & =-\left(\frac{120-30}{15}\right)=\frac{-90}{15}\end{array} \end{gathered}$$

$\frac{5}{4}-\frac{8}{7}$

$\begin{array}{rl}& \frac{5}{4}-\frac{8}{7}=\frac{5}{4}+\left(\frac{-8}{7}\right)\\ & =\frac{5\times 7}{4\times 7}+\left(\frac{-8\times 4}{7\times 4}\right)=\frac{35}{28}+\left(\frac{-32}{28}\right)\\ & =+\left(\frac{35-32}{28}\right)=\frac{3}{28}\end{array}$

$\frac{6}{11}-\frac{4}{5}$

$\begin{array}{rl}& \frac{6}{11}-\frac{4}{5}=\frac{6}{11}+\left(\frac{-4}{5}\right)\\ =& \frac{6\times 5}{11\times 5}+\left(\frac{-4\times 11}{5\times 11}\right)\\ =& \frac{30}{55}+\left(\frac{-44}{55}\right)\\ =& -\left(\frac{44-30}{55}\right)=\frac{-14}{55}\end{array}$

$14.1\times (-4)$

$\begin{array}{rl}& 14.1\times (-4)=\frac{141}{10}\times \frac{-4}{1}\\ & =\frac{-564}{10}=-56.4\end{array}$

$-3\times (-10.3)$

$\begin{array}{c}-3\times (-10.3)=\frac{-3}{1}\times \frac{-103}{10}\\ =\frac{+309}{10}=30.9\end{array}$

$\frac{15}{14}÷\frac{2}{3}$

$\frac{15}{14}÷\frac{2}{3}=\frac{15}{14}\times \frac{3}{2}=\frac{45}{28}$

$-\frac{9}{10}÷\frac{6}{5}$

$\frac{-9}{10}÷\frac{6}{5}=\frac{-9}{10}\times \frac{5}{6}=\frac{-45}{60}$

$\frac{8}{3}-\frac{7}{6}$

$\frac{8}{3}÷\frac{7}{6}=\frac{8}{3}\times \frac{6}{7}=\frac{48}{21}$

$1\frac{2}{3}\times \frac{-3}{10}$

$1\frac{2}{3}\times \frac{-3}{10}=\frac{5}{3}\times \frac{-3}{10}=\frac{-15}{30}$

$2\frac{1}{5}÷\frac{11}{5}$

$2\frac{1}{5}÷\frac{11}{5}=\frac{11}{5}\times \frac{5}{11}=\frac{55}{55}=1$

$13.2÷2$

$\begin{array}{rl}13.2÷2& =\frac{132}{10}÷\frac{2}{1}\\ & =\frac{132}{10}\times \frac{1}{2}=\frac{132}{20}\end{array}$

$-3\frac{1}{2}÷\frac{-2}{7}$

$-3\frac{1}{2}÷\frac{-2}{7}=\frac{-7}{2}\times \frac{-7}{2}=\frac{49}{4}$