تمارين رياضيات مع الحلول التفصيلية

$$\frac{-\frac{5}{2}}{-\frac{3}{7} \div -\frac{4}{7}} = \frac{-\frac{5}{2}}{-\frac{3}{7} \times -\frac{7}{4}} = \frac{-\frac{5}{2}}{-\frac{3 \times 7}{7 \times 4}} = \frac{-\frac{5}{2}}{-\frac{3}{4}}$$

$$= \frac{-\frac{5}{2} \times -\frac{4}{3}} = -\frac{5}{2} \times -\frac{4}{3} = \frac{5 \times 4}{2 \times 3} = \frac{20}{6} = \frac{10}{3}$$

الجواب هو $$\frac{10}{3}$$

$$\frac{-\frac{7}{5}}{-\frac{3}{4}} = -\frac{7}{5} \times -\frac{4}{3} = \frac{7 \times 4}{5 \times 3} = \frac{28}{15}$$

الجواب هو $$\frac{28}{15}$$

$$\frac{\frac{3}{4}}{\frac{7}{5}} = \frac{3}{4} \times \frac{5}{7} = \frac{3 \times 5}{4 \times 7} = \frac{15}{28}$$

الجواب هو $$\frac{15}{28}$$

$$\frac{-\frac{5}{2}}{-\frac{2}{5}} = -\frac{5}{2} \times -\frac{5}{2} = \frac{5 \times 5}{2 \times 2} = \frac{25}{4} = 6\frac{1}{4}$$

الجواب هو $$6\frac{1}{4}$$

$$\frac{\frac{3}{2}}{-\frac{3}{2}} = \frac{3}{2} \times (-\frac{2}{3}) = \frac{3 \times (-2)}{2 \times 3} = \frac{-6}{6} = -1$$

الجواب هو $$-1$$

$$\frac{\frac{1}{29}}{-\frac{31}{1}} = \frac{1}{29} \times (-\frac{1}{31}) = \frac{1 \times (-1)}{29 \times 31} = -\frac{1}{899}$$

الجواب هو $$-\frac{1}{899}$$

$$\frac{\frac{1}{5}}{-\frac{1}{10}} = \frac{1}{5} \times (-\frac{10}{1}) = \frac{1 \times (-10)}{5 \times 1} = -\frac{10}{5} = -2$$

الجواب هو $$-2$$

$$\frac{-\frac{3}{1}}{-\frac{1}{2}} = -\frac{3}{1} \times -\frac{2}{1} = \frac{3 \times 2}{1 \times 1} = 6$$

الجواب هو $$6$$

$$\frac{\frac{3}{2}}{-8} = \frac{3}{2} \times \frac{-1}{8} = \frac{3 \times (-1)}{2 \times 8} = -\frac{3}{16}$$

الجواب هو $$-\frac{3}{16}$$

$$\frac{\frac{1}{-50}}{\frac{3}{75}} = \frac{1}{-50} \times \frac{75}{3} = \frac{1 \times 75}{-50 \times 3} = \frac{75}{-150} = -\frac{1}{2}$$

الجواب هو $$-\frac{1}{2}$$

$$\frac{-100}{\frac{9}{-200} \div \frac{-27}{1}} = \frac{-100}{\frac{9}{-200} \times \frac{1}{-27}} = \frac{-100}{\frac{9 \times 1}{-200 \times -27}} = \frac{-100}{\frac{9}{5400}}$$

$$= -100 \times \frac{5400}{9} = \frac{-100 \times 5400}{9} = \frac{-540000}{9} = -60000$$

الجواب هو $$-60000$$

$$\frac{\frac{14}{15}}{\frac{-25}{-7}} = \frac{14}{15} \times \frac{-7}{-25} = \frac{14 \times (-7)}{15 \times (-25)} = \frac{-98}{-375} = \frac{98}{375}$$

نبسط الكسر: $$\frac{98}{375} = \frac{98 \div 1}{375 \div 1} = \frac{98}{375}$$

الجواب هو $$\frac{98}{375}$$

$$\frac{-14}{\frac{5}{-4.9}} = -14 \times \frac{-4.9}{5} = \frac{-14 \times (-4.9)}{5} = \frac{68.6}{5} = 13.72$$

الجواب هو $$13.72$$

$$\frac{-3.6}{5.4} = \frac{-36}{54} = \frac{-36 \div 18}{54 \div 18} = \frac{-2}{3}$$

الجواب هو $$-\frac{2}{3}$$

$$\frac{-2.2}{\frac{33}{4}} = -2.2 \times \frac{4}{33} = \frac{-2.2 \times 4}{33} = \frac{-8.8}{33} = -\frac{8.8}{33}$$

نحول $$-2.2$$ إلى كسر: $$-2.2 = -\frac{22}{10} = -\frac{11}{5}$$

$$\frac{-\frac{11}{5}}{\frac{33}{4}} = -\frac{11}{5} \times \frac{4}{33} = \frac{-11 \times 4}{5 \times 33} = \frac{-44}{165} = -\frac{4}{15}$$

الجواب هو $$-\frac{4}{15}$$

$$A = \frac{2+\frac{5}{4}}{2-\frac{5}{6}} = \frac{\frac{8}{4}+\frac{5}{4}}{\frac{12}{6}-\frac{5}{6}} = \frac{\frac{13}{4}}{\frac{7}{6}}$$

$$= \frac{13}{4} \times \frac{6}{7} = \frac{13 \times 6}{4 \times 7} = \frac{78}{28} = \frac{39}{14}$$

الجواب هو $$\frac{39}{14}$$

$$B = 1+\frac{-3+\frac{7}{2}}{-\frac{3}{2}} = 1+\frac{-\frac{6}{2}+\frac{7}{2}}{-\frac{3}{2}} = 1+\frac{\frac{1}{2}}{-\frac{3}{2}}$$

$$= 1+\frac{1}{2} \times \frac{-2}{3} = 1+\frac{-1}{3} = \frac{3}{3}+\frac{-1}{3} = \frac{2}{3}$$

الجواب هو $$\frac{2}{3}$$

$$C = \frac{\frac{-5}{6} \times \frac{1}{5}}{\frac{-7}{6}+\frac{1}{3}} = \frac{\frac{-5 \times 1}{6 \times 5}}{\frac{-7}{6}+\frac{2}{6}} = \frac{\frac{-1}{6}}{\frac{-5}{6}} = \frac{-1}{6} \times \frac{6}{-5} = \frac{-1 \times 6}{6 \times (-5)} = \frac{-6}{-30} = \frac{1}{5}$$

الجواب هو $$\frac{1}{5}$$

$$D = \frac{-3}{\left|\frac{3}{4}-\frac{4}{3}\right|} = \frac{-3}{\left|\frac{9}{12}-\frac{16}{12}\right|} = \frac{-3}{\left|\frac{-7}{12}\right|} = \frac{-3}{\frac{7}{12}}$$

$$= -3 \times \frac{12}{7} = \frac{-36}{7} = -\frac{36}{7}$$

الجواب هو $$-\frac{36}{7}$$

$$E = \frac{2 \times \left(\frac{1}{2}+\frac{1}{3}\right)}{\frac{2}{3}-\frac{5}{2}} = \frac{2 \times \left(\frac{3}{6}+\frac{2}{6}\right)}{\frac{4}{6}-\frac{15}{6}} = \frac{2 \times \frac{5}{6}}{\frac{-11}{6}} = \frac{2 \times \frac{5}{6}}{-\frac{11}{6}}$$

$$= \frac{10}{6} \times \frac{-6}{11} = \frac{10 \times (-6)}{6 \times 11} = \frac{-60}{66} = -\frac{10}{11}$$

الجواب هو $$-\frac{10}{11}$$

$$F = \frac{\frac{6}{-5}+1}{\frac{3}{-5}} = \frac{\frac{6}{-5}+\frac{-5}{-5}}{\frac{3}{-5}} = \frac{\frac{6-5}{-5}}{\frac{3}{-5}} = \frac{\frac{1}{-5}}{\frac{3}{-5}}$$

$$= \frac{1}{-5} \times \frac{-5}{3} = \frac{1 \times (-5)}{-5 \times 3} = \frac{-5}{-15} = \frac{1}{3}$$

الجواب هو $$\frac{1}{3}$$

$$B = \frac{\frac{3}{5}-\frac{3}{2}}{\frac{3}{5}+\frac{3}{2}} = \frac{\frac{6}{10}-\frac{15}{10}}{\frac{6}{10}+\frac{15}{10}} = \frac{\frac{-9}{10}}{\frac{21}{10}} = \frac{-9}{10} \times \frac{10}{21} = \frac{-9}{21} = \frac{-3}{7}$$

الجواب هو $$-\frac{3}{7}$$

$$A = \frac{\frac{100}{-49}}{\frac{-25}{14}} = \frac{100}{-49} \times \frac{14}{-25} = \frac{100 \times 14}{-49 \times (-25)} = \frac{1400}{1225} = \frac{1400 \div 175}{1225 \div 175} = \frac{8}{7}$$

الجواب هو $$\frac{8}{7}$$

$$A = \frac{1-\frac{4}{3}}{\frac{-5}{3}+\frac{5}{3} \times 2} = \frac{\frac{3}{3}-\frac{4}{3}}{\frac{-5}{3}+\frac{10}{3}} = \frac{\frac{-1}{3}}{\frac{5}{3}} = \frac{-1}{3} \times \frac{3}{5} = \frac{-1 \times 3}{3 \times 5} = \frac{-3}{15} = -\frac{1}{5}$$

الجواب هو $$-\frac{1}{5}$$

$$B = \frac{\frac{2}{3}-\frac{2}{5}}{\frac{5}{3}} = \frac{\frac{10}{15}-\frac{6}{15}}{\frac{5}{3}} = \frac{\frac{4}{15}}{\frac{5}{3}} = \frac{4}{15} \times \frac{3}{5} = \frac{4 \times 3}{15 \times 5} = \frac{12}{75} = \frac{4}{25}$$

الجواب هو $$\frac{4}{25}$$

$$C = \frac{-5}{11} \times \frac{1}{-\frac{1}{11}} = \frac{-5}{11} \times \frac{11}{-1} = \frac{-5 \times 11}{11 \times (-1)} = \frac{-55}{-11} = 5$$

الجواب هو $$5$$

$$D = 1- \frac{-1}{1+\frac{1}{2}} = 1- \frac{-1}{\frac{2}{2}+\frac{1}{2}} = 1- \frac{-1}{\frac{3}{2}} = 1- \frac{-1 \times 2}{3} = 1- \frac{-2}{3} = 1+ \frac{2}{3} = \frac{3}{3}+\frac{2}{3} = \frac{5}{3}$$

الجواب هو $$\frac{5}{3}$$

$$E = \frac{\frac{5}{2}-\frac{3}{5}+1}{\frac{2}{5} \times \frac{3}{-1}} = \frac{\frac{25}{10}-\frac{6}{10}+\frac{10}{10}}{\frac{2}{5} \times \frac{3}{-1}} = \frac{\frac{25-6+10}{10}}{\frac{2 \times 3}{5 \times (-1)}} = \frac{\frac{29}{10}}{\frac{-6}{5}} = \frac{29}{10} \times \frac{-5}{6} = \frac{29 \times (-5)}{10 \times 6} = \frac{-145}{60} = -\frac{29}{12}$$

الجواب هو $$-\frac{29}{12}$$

$$F = \frac{-1-\frac{1}{6}}{1-\frac{1}{6}} = \frac{\frac{-6}{6}-\frac{1}{6}}{\frac{6}{6}-\frac{1}{6}} = \frac{\frac{-7}{6}}{\frac{5}{6}} = \frac{-7}{6} \times \frac{6}{5} = \frac{-7 \times 6}{6 \times 5} = \frac{-42}{30} = -\frac{7}{5}$$

الجواب هو $$-\frac{7}{5}$$

نبدأ بحساب الجزء الداخلي: $$1+\frac{1}{2} = \frac{2}{2}+\frac{1}{2} = \frac{3}{2}$$

ثم: $$1+\frac{1}{\frac{3}{2}} = 1+\frac{2}{3} = \frac{3}{3}+\frac{2}{3} = \frac{5}{3}$$

وأخيراً: $$A = \frac{1}{\frac{5}{3}} = \frac{1 \times 3}{5} = \frac{3}{5}$$

الجواب هو $$\frac{3}{5}$$

$$B = \frac{1+\frac{4}{3}}{1-\frac{4}{3}} = \frac{\frac{3}{3}+\frac{4}{3}}{\frac{3}{3}-\frac{4}{3}} = \frac{\frac{7}{3}}{-\frac{1}{3}} = \frac{7}{3} \times \frac{-3}{1} = -7$$

الجواب هو $$-7$$

$$C = \frac{-1+\frac{7}{8}}{-1+\frac{8}{9}} = \frac{\frac{-8}{8}+\frac{7}{8}}{\frac{-9}{9}+\frac{8}{9}} = \frac{\frac{-1}{8}}{\frac{-1}{9}} = \frac{-1}{8} \times \frac{9}{-1} = \frac{-1 \times 9}{8 \times (-1)} = \frac{-9}{-8} = \frac{9}{8}$$

الجواب هو $$\frac{9}{8}$$

$$D = \left(\frac{1}{2}-\frac{1}{3}\right) \times \frac{\frac{2}{3}}{\frac{3}{5}} = \left(\frac{3}{6}-\frac{2}{6}\right) \times \frac{\frac{2}{3}}{\frac{3}{5}} = \frac{1}{6} \times \frac{\frac{2}{3}}{\frac{3}{5}}$$

$$= \frac{1}{6} \times \frac{2}{3} \times \frac{5}{3} = \frac{1 \times 2 \times 5}{6 \times 3 \times 3} = \frac{10}{54} = \frac{5}{27}$$

الجواب هو $$\frac{5}{27}$$

$$E = \frac{\frac{-5}{3}}{\frac{-9}{14}} = \frac{-5}{3} \times \frac{14}{-9} = \frac{-5 \times 14}{3 \times (-9)} = \frac{-70}{-27} = \frac{70}{27}$$

الجواب هو $$\frac{70}{27}$$

$$F = \frac{-1-\frac{1}{7}--1+\frac{1}{7}}{1-\frac{1}{7}-1+\frac{1}{7}} = \frac{-1-\frac{1}{7}+1-\frac{1}{7}}{1-\frac{1}{7}-1+\frac{1}{7}} = \frac{-\frac{2}{7}}{0} = \text{غير معرف}$$

في المقام: $$1-\frac{1}{7}-1+\frac{1}{7} = 0$$، لذلك العملية غير معرفة لأن القسمة على صفر غير ممكنة.

الجواب هو: غير معرف (لا يوجد حل)