Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{-5}\right) -\left(\frac{2}{-8}\right) +\left(\frac{2}{6}\right)\\= \frac{6}{5}+ \frac{2}{8}+\frac{2}{6}\\=\frac{6}{5}+\frac{1}{4}+\frac{1}{3}\\=\frac{72}{60}+\frac{15}{60}+\frac{20}{60}\\=\frac{72+15+20}{60}\\=\frac{107}{60}\)
2. \(-\left(\frac{3}{4}\right) -\left(\frac{-8}{-7}\right) +\left(\frac{7}{3}\right)\\= \frac{-3}{4}- \frac{8}{7}+\frac{7}{3}\\=\frac{-63}{84}-\frac{96}{84}+\frac{196}{84}\\=\frac{-63-96+196}{84}\\=\frac{37}{84}\)
3. \(-\left(\frac{2}{-3}\right) -\left(\frac{-7}{-6}\right) +\left(\frac{5}{-6}\right)\\= \frac{2}{3}- \frac{7}{6}-\frac{5}{6}\\=\frac{4}{6}-\frac{7}{6}-\frac{5}{6}\\=\frac{4-7-5}{6}\\=\frac{-8}{6}\\=\frac{-4}{3}\)
4. \(-\left(\frac{8}{7}\right) +\left(\frac{-5}{-10}\right) +\left(\frac{-8}{8}\right)\\= \frac{-8}{7}+ \frac{5}{10}-\frac{8}{8}\\=\frac{-8}{7}+\frac{1}{2}-\frac{1}{1}\\=\frac{-16}{14}+\frac{7}{14}-\frac{14}{14}\\=\frac{-16+7-14}{14}\\=\frac{-23}{14}\)
5. \(+\left(\frac{7}{-3}\right) +\left(\frac{-4}{10}\right) -\left(\frac{8}{7}\right)\\= \frac{-7}{3}- \frac{4}{10}-\frac{8}{7}\\=\frac{-7}{3}-\frac{2}{5}-\frac{8}{7}\\=\frac{-245}{105}-\frac{42}{105}-\frac{120}{105}\\=\frac{-245-42-120}{105}\\=\frac{-407}{105}\)
6. \(+\left(\frac{-3}{-2}\right) +\left(\frac{9}{-3}\right) +\left(\frac{-6}{9}\right)\\= \frac{3}{2}- \frac{9}{3}-\frac{6}{9}\\=\frac{3}{2}-\frac{3}{1}-\frac{2}{3}\\=\frac{9}{6}-\frac{18}{6}-\frac{4}{6}\\=\frac{9-18-4}{6}\\=\frac{-13}{6}\)
7. \(-\left(\frac{-10}{-7}\right) +\left(\frac{4}{-9}\right) +\left(\frac{-8}{-10}\right)\\= \frac{-10}{7}- \frac{4}{9}+\frac{8}{10}\\=\frac{-10}{7}-\frac{4}{9}+\frac{4}{5}\\=\frac{-450}{315}-\frac{140}{315}+\frac{252}{315}\\=\frac{-450-140+252}{315}\\=\frac{-338}{315}\)
8. \(-\left(\frac{9}{5}\right) -\left(\frac{-10}{6}\right) +\left(\frac{2}{-7}\right)\\= \frac{-9}{5}+ \frac{10}{6}-\frac{2}{7}\\=\frac{-9}{5}+\frac{5}{3}-\frac{2}{7}\\=\frac{-189}{105}+\frac{175}{105}-\frac{30}{105}\\=\frac{-189+175-30}{105}\\=\frac{-44}{105}\)
9. \(+\left(\frac{-8}{-5}\right) +\left(\frac{6}{-8}\right) +\left(\frac{5}{8}\right)\\= \frac{8}{5}- \frac{6}{8}+\frac{5}{8}\\=\frac{8}{5}-\frac{3}{4}+\frac{5}{8}\\=\frac{64}{40}-\frac{30}{40}+\frac{25}{40}\\=\frac{64-30+25}{40}\\=\frac{59}{40}\)
10. \(-\left(\frac{-9}{2}\right) +\left(\frac{-7}{-8}\right) -\left(\frac{6}{-6}\right)\\= \frac{9}{2}+ \frac{7}{8}+\frac{6}{6}\\=\frac{9}{2}+\frac{7}{8}+\frac{1}{1}\\=\frac{36}{8}+\frac{7}{8}+\frac{8}{8}\\=\frac{36+7+8}{8}\\=\frac{51}{8}\)
11. \(+\left(\frac{-8}{9}\right) +\left(\frac{4}{-3}\right) +\left(\frac{7}{8}\right)\\= \frac{-8}{9}- \frac{4}{3}+\frac{7}{8}\\=\frac{-64}{72}-\frac{96}{72}+\frac{63}{72}\\=\frac{-64-96+63}{72}\\=\frac{-97}{72}\)
12. \(+\left(\frac{9}{7}\right) +\left(\frac{9}{4}\right) -\left(\frac{-11}{-10}\right)\\= \frac{9}{7}+ \frac{9}{4}-\frac{11}{10}\\=\frac{180}{140}+\frac{315}{140}-\frac{154}{140}\\=\frac{180+315-154}{140}\\=\frac{341}{140}\)