Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

1. \(-\left(\frac{9}{2}\right) +\left(\frac{-7}{-3}\right) +\left(\frac{2}{10}\right)\)
2. \(+\left(\frac{-2}{-5}\right) +\left(\frac{-6}{8}\right) -\left(\frac{-3}{-6}\right)\)
3. \(-\left(\frac{-7}{3}\right) +\left(\frac{4}{-8}\right) -\left(\frac{-6}{-6}\right)\)
4. \(+\left(\frac{-7}{-4}\right) +\left(\frac{-9}{-2}\right) +\left(\frac{-7}{7}\right)\)
5. \(+\left(\frac{2}{3}\right) -\left(\frac{-6}{-5}\right) -\left(\frac{3}{-2}\right)\)
6. \(-\left(\frac{-7}{9}\right) +\left(\frac{9}{8}\right) +\left(\frac{12}{-2}\right)\)
7. \(-\left(\frac{3}{4}\right) -\left(\frac{10}{-4}\right) +\left(\frac{-6}{-12}\right)\)
8. \(-\left(\frac{5}{-9}\right) +\left(\frac{-7}{8}\right) -\left(\frac{-12}{10}\right)\)
9. \(+\left(\frac{-9}{-4}\right) -\left(\frac{2}{-9}\right) -\left(\frac{-4}{-8}\right)\)
10. \(+\left(\frac{-2}{-7}\right) -\left(\frac{-2}{2}\right) +\left(\frac{2}{9}\right)\)
11. \(-\left(\frac{-5}{-3}\right) -\left(\frac{5}{10}\right) +\left(\frac{9}{3}\right)\)
12. \(-\left(\frac{-5}{7}\right) -\left(\frac{-9}{5}\right) -\left(\frac{-11}{9}\right)\)

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{2}\right) +\left(\frac{-7}{-3}\right) +\left(\frac{2}{10}\right)\\= \frac{-9}{2}+ \frac{7}{3}+\frac{2}{10}\\=\frac{-9}{2}+\frac{7}{3}+\frac{1}{5}\\=\frac{-135}{30}+\frac{70}{30}+\frac{6}{30}\\=\frac{-135+70+6}{30}\\=\frac{-59}{30}\)
2. \(+\left(\frac{-2}{-5}\right) +\left(\frac{-6}{8}\right) -\left(\frac{-3}{-6}\right)\\= \frac{2}{5}- \frac{6}{8}-\frac{3}{6}\\=\frac{2}{5}-\frac{3}{4}-\frac{1}{2}\\=\frac{8}{20}-\frac{15}{20}-\frac{10}{20}\\=\frac{8-15-10}{20}\\=\frac{-17}{20}\)
3. \(-\left(\frac{-7}{3}\right) +\left(\frac{4}{-8}\right) -\left(\frac{-6}{-6}\right)\\= \frac{7}{3}- \frac{4}{8}-\frac{6}{6}\\=\frac{7}{3}-\frac{1}{2}-\frac{1}{1}\\=\frac{14}{6}-\frac{3}{6}-\frac{6}{6}\\=\frac{14-3-6}{6}\\=\frac{5}{6}\)
4. \(+\left(\frac{-7}{-4}\right) +\left(\frac{-9}{-2}\right) +\left(\frac{-7}{7}\right)\\= \frac{7}{4}+ \frac{9}{2}-\frac{7}{7}\\=\frac{7}{4}+\frac{9}{2}-\frac{1}{1}\\=\frac{7+9-1}{4}\\=\frac{15}{4}\)
5. \(+\left(\frac{2}{3}\right) -\left(\frac{-6}{-5}\right) -\left(\frac{3}{-2}\right)\\= \frac{2}{3}- \frac{6}{5}+\frac{3}{2}\\=\frac{20}{30}-\frac{36}{30}+\frac{45}{30}\\=\frac{20-36+45}{30}\\=\frac{29}{30}\)
6. \(-\left(\frac{-7}{9}\right) +\left(\frac{9}{8}\right) +\left(\frac{12}{-2}\right)\\= \frac{7}{9}+ \frac{9}{8}-\frac{12}{2}\\=\frac{7}{9}+\frac{9}{8}-\frac{6}{1}\\=\frac{56}{72}+\frac{81}{72}-\frac{432}{72}\\=\frac{56+81-432}{72}\\=\frac{-295}{72}\)
7. \(-\left(\frac{3}{4}\right) -\left(\frac{10}{-4}\right) +\left(\frac{-6}{-12}\right)\\= \frac{-3}{4}+ \frac{10}{4}+\frac{6}{12}\\=\frac{-3}{4}+\frac{5}{2}+\frac{1}{2}\\=\frac{-3+5+1}{4}\\=\frac{3}{4}\)
8. \(-\left(\frac{5}{-9}\right) +\left(\frac{-7}{8}\right) -\left(\frac{-12}{10}\right)\\= \frac{5}{9}- \frac{7}{8}+\frac{12}{10}\\=\frac{5}{9}-\frac{7}{8}+\frac{6}{5}\\=\frac{200}{360}-\frac{315}{360}+\frac{432}{360}\\=\frac{200-315+432}{360}\\=\frac{317}{360}\)
9. \(+\left(\frac{-9}{-4}\right) -\left(\frac{2}{-9}\right) -\left(\frac{-4}{-8}\right)\\= \frac{9}{4}+ \frac{2}{9}-\frac{4}{8}\\=\frac{9}{4}+\frac{2}{9}-\frac{1}{2}\\=\frac{81}{36}+\frac{8}{36}-\frac{18}{36}\\=\frac{81+8-18}{36}\\=\frac{71}{36}\)
10. \(+\left(\frac{-2}{-7}\right) -\left(\frac{-2}{2}\right) +\left(\frac{2}{9}\right)\\= \frac{2}{7}+ \frac{2}{2}+\frac{2}{9}\\=\frac{2}{7}+\frac{1}{1}+\frac{2}{9}\\=\frac{18}{63}+\frac{63}{63}+\frac{14}{63}\\=\frac{18+63+14}{63}\\=\frac{95}{63}\)
11. \(-\left(\frac{-5}{-3}\right) -\left(\frac{5}{10}\right) +\left(\frac{9}{3}\right)\\= \frac{-5}{3}- \frac{5}{10}+\frac{9}{3}\\=\frac{-5}{3}-\frac{1}{2}+\frac{3}{1}\\=\frac{-10}{6}-\frac{3}{6}+\frac{18}{6}\\=\frac{-10-3+18}{6}\\=\frac{5}{6}\)
12. \(-\left(\frac{-5}{7}\right) -\left(\frac{-9}{5}\right) -\left(\frac{-11}{9}\right)\\= \frac{5}{7}+ \frac{9}{5}+\frac{11}{9}\\=\frac{225}{315}+\frac{567}{315}+\frac{385}{315}\\=\frac{225+567+385}{315}\\=\frac{1177}{315}\)