Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-9}\right) -\left(\frac{4}{-7}\right) +\left(\frac{-7}{4}\right)\\= \frac{10}{9}+ \frac{4}{7}-\frac{7}{4}\\=\frac{280}{252}+\frac{144}{252}-\frac{441}{252}\\=\frac{280+144-441}{252}\\=\frac{-17}{252}\)
2. \(-\left(\frac{4}{5}\right) +\left(\frac{-7}{-2}\right) +\left(\frac{4}{-3}\right)\\= \frac{-4}{5}+ \frac{7}{2}-\frac{4}{3}\\=\frac{-24}{30}+\frac{105}{30}-\frac{40}{30}\\=\frac{-24+105-40}{30}\\=\frac{41}{30}\)
3. \(+\left(\frac{-2}{-7}\right) +\left(\frac{6}{9}\right) +\left(\frac{5}{6}\right)\\= \frac{2}{7}+ \frac{6}{9}+\frac{5}{6}\\=\frac{2}{7}+\frac{2}{3}+\frac{5}{6}\\=\frac{12}{42}+\frac{28}{42}+\frac{35}{42}\\=\frac{12+28+35}{42}\\=\frac{75}{42}\\=\frac{25}{14}\)
4. \(+\left(\frac{-8}{9}\right) -\left(\frac{-8}{7}\right) +\left(\frac{4}{-9}\right)\\= \frac{-8}{9}+ \frac{8}{7}-\frac{4}{9}\\=\frac{-56}{63}+\frac{72}{63}-\frac{28}{63}\\=\frac{-56+72-28}{63}\\=\frac{-12}{63}\\=\frac{-4}{21}\)
5. \(+\left(\frac{8}{9}\right) -\left(\frac{9}{-2}\right) -\left(\frac{-4}{5}\right)\\= \frac{8}{9}+ \frac{9}{2}+\frac{4}{5}\\=\frac{80}{90}+\frac{405}{90}+\frac{72}{90}\\=\frac{80+405+72}{90}\\=\frac{557}{90}\)
6. \(+\left(\frac{2}{-3}\right) -\left(\frac{9}{9}\right) -\left(\frac{3}{-12}\right)\\= \frac{-2}{3}- \frac{9}{9}+\frac{3}{12}\\=\frac{-2}{3}-\frac{1}{1}+\frac{1}{4}\\=\frac{-8}{12}-\frac{12}{12}+\frac{3}{12}\\=\frac{-8-12+3}{12}\\=\frac{-17}{12}\)
7. \(+\left(\frac{9}{5}\right) -\left(\frac{3}{3}\right) +\left(\frac{-4}{11}\right)\\= \frac{9}{5}- \frac{3}{3}-\frac{4}{11}\\=\frac{9}{5}-\frac{1}{1}-\frac{4}{11}\\=\frac{99}{55}-\frac{55}{55}-\frac{20}{55}\\=\frac{99-55-20}{55}\\=\frac{24}{55}\)
8. \(+\left(\frac{-2}{7}\right) +\left(\frac{-2}{-5}\right) +\left(\frac{5}{11}\right)\\= \frac{-2}{7}+ \frac{2}{5}+\frac{5}{11}\\=\frac{-110}{385}+\frac{154}{385}+\frac{175}{385}\\=\frac{-110+154+175}{385}\\=\frac{219}{385}\)
9. \(+\left(\frac{6}{5}\right) +\left(\frac{7}{-4}\right) -\left(\frac{10}{11}\right)\\= \frac{6}{5}- \frac{7}{4}-\frac{10}{11}\\=\frac{264}{220}-\frac{385}{220}-\frac{200}{220}\\=\frac{264-385-200}{220}\\=\frac{-321}{220}\)
10. \(+\left(\frac{-8}{-5}\right) -\left(\frac{-3}{-10}\right) +\left(\frac{-5}{-7}\right)\\= \frac{8}{5}- \frac{3}{10}+\frac{5}{7}\\=\frac{112}{70}-\frac{21}{70}+\frac{50}{70}\\=\frac{112-21+50}{70}\\=\frac{141}{70}\)
11. \(+\left(\frac{2}{9}\right) -\left(\frac{2}{2}\right) -\left(\frac{-10}{7}\right)\\= \frac{2}{9}- \frac{2}{2}+\frac{10}{7}\\=\frac{2}{9}-\frac{1}{1}+\frac{10}{7}\\=\frac{14}{63}-\frac{63}{63}+\frac{90}{63}\\=\frac{14-63+90}{63}\\=\frac{41}{63}\)
12. \(-\left(\frac{3}{-7}\right) -\left(\frac{2}{9}\right) +\left(\frac{-10}{6}\right)\\= \frac{3}{7}- \frac{2}{9}-\frac{10}{6}\\=\frac{3}{7}-\frac{2}{9}-\frac{5}{3}\\=\frac{27}{63}-\frac{14}{63}-\frac{105}{63}\\=\frac{27-14-105}{63}\\=\frac{-92}{63}\)