Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-8}{-7}\right) -\left(\frac{-4}{-7}\right) -\left(\frac{8}{-7}\right)\\= \frac{-8}{7}- \frac{4}{7}+\frac{8}{7}\\=\frac{-8-4+8}{7}\\=\frac{-4}{7}\)
2. \(+\left(\frac{-6}{5}\right) -\left(\frac{-8}{-7}\right) -\left(\frac{11}{-12}\right)\\= \frac{-6}{5}- \frac{8}{7}+\frac{11}{12}\\=\frac{-504}{420}-\frac{480}{420}+\frac{385}{420}\\=\frac{-504-480+385}{420}\\=\frac{-599}{420}\)
3. \(-\left(\frac{2}{7}\right) +\left(\frac{4}{9}\right) -\left(\frac{-3}{3}\right)\\= \frac{-2}{7}+ \frac{4}{9}+\frac{3}{3}\\=\frac{-2}{7}+\frac{4}{9}+\frac{1}{1}\\=\frac{-18}{63}+\frac{28}{63}+\frac{63}{63}\\=\frac{-18+28+63}{63}\\=\frac{73}{63}\)
4. \(-\left(\frac{-9}{2}\right) -\left(\frac{-10}{-7}\right) +\left(\frac{9}{6}\right)\\= \frac{9}{2}- \frac{10}{7}+\frac{9}{6}\\=\frac{9}{2}-\frac{10}{7}+\frac{3}{2}\\=\frac{63}{14}-\frac{20}{14}+\frac{21}{14}\\=\frac{63-20+21}{14}\\=\frac{64}{14}\\=\frac{32}{7}\)
5. \(+\left(\frac{7}{2}\right) +\left(\frac{-9}{-10}\right) +\left(\frac{11}{-6}\right)\\= \frac{7}{2}+ \frac{9}{10}-\frac{11}{6}\\=\frac{105}{30}+\frac{27}{30}-\frac{55}{30}\\=\frac{105+27-55}{30}\\=\frac{77}{30}\)
6. \(+\left(\frac{3}{5}\right) +\left(\frac{-8}{-5}\right) +\left(\frac{-7}{5}\right)\\= \frac{3}{5}+ \frac{8}{5}-\frac{7}{5}\\=\frac{3+8-7}{5}\\=\frac{4}{5}\)
7. \(+\left(\frac{5}{2}\right) +\left(\frac{4}{6}\right) -\left(\frac{12}{8}\right)\\= \frac{5}{2}+ \frac{4}{6}-\frac{12}{8}\\=\frac{5}{2}+\frac{2}{3}-\frac{3}{2}\\=\frac{15}{6}+\frac{4}{6}-\frac{9}{6}\\=\frac{15+4-9}{6}\\=\frac{10}{6}\\=\frac{5}{3}\)
8. \(+\left(\frac{5}{4}\right) +\left(\frac{6}{-8}\right) -\left(\frac{6}{5}\right)\\= \frac{5}{4}- \frac{6}{8}-\frac{6}{5}\\=\frac{5}{4}-\frac{3}{4}-\frac{6}{5}\\=\frac{25}{20}-\frac{15}{20}-\frac{24}{20}\\=\frac{25-15-24}{20}\\=\frac{-14}{20}\\=\frac{-7}{10}\)
9. \(-\left(\frac{3}{-7}\right) +\left(\frac{3}{8}\right) +\left(\frac{11}{4}\right)\\= \frac{3}{7}+ \frac{3}{8}+\frac{11}{4}\\=\frac{24}{56}+\frac{21}{56}+\frac{154}{56}\\=\frac{24+21+154}{56}\\=\frac{199}{56}\)
10. \(-\left(\frac{4}{-5}\right) -\left(\frac{3}{-8}\right) +\left(\frac{6}{7}\right)\\= \frac{4}{5}+ \frac{3}{8}+\frac{6}{7}\\=\frac{224}{280}+\frac{105}{280}+\frac{240}{280}\\=\frac{224+105+240}{280}\\=\frac{569}{280}\)
11. \(+\left(\frac{7}{8}\right) +\left(\frac{6}{4}\right) +\left(\frac{10}{-9}\right)\\= \frac{7}{8}+ \frac{6}{4}-\frac{10}{9}\\=\frac{7}{8}+\frac{3}{2}-\frac{10}{9}\\=\frac{63}{72}+\frac{108}{72}-\frac{80}{72}\\=\frac{63+108-80}{72}\\=\frac{91}{72}\)
12. \(+\left(\frac{4}{9}\right) -\left(\frac{-7}{10}\right) -\left(\frac{-2}{8}\right)\\= \frac{4}{9}+ \frac{7}{10}+\frac{2}{8}\\=\frac{4}{9}+\frac{7}{10}+\frac{1}{4}\\=\frac{80}{180}+\frac{126}{180}+\frac{45}{180}\\=\frac{80+126+45}{180}\\=\frac{251}{180}\)