Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-7}\right) +\left(\frac{-9}{5}\right) -\left(\frac{-9}{-3}\right)\\= \frac{10}{7}- \frac{9}{5}-\frac{9}{3}\\=\frac{10}{7}-\frac{9}{5}-\frac{3}{1}\\=\frac{50}{35}-\frac{63}{35}-\frac{105}{35}\\=\frac{50-63-105}{35}\\=\frac{-118}{35}\)
2. \(-\left(\frac{6}{7}\right) +\left(\frac{4}{5}\right) +\left(\frac{11}{-7}\right)\\= \frac{-6}{7}+ \frac{4}{5}-\frac{11}{7}\\=\frac{-30}{35}+\frac{28}{35}-\frac{55}{35}\\=\frac{-30+28-55}{35}\\=\frac{-57}{35}\)
3. \(+\left(\frac{-10}{3}\right) +\left(\frac{7}{-4}\right) +\left(\frac{-9}{5}\right)\\= \frac{-10}{3}- \frac{7}{4}-\frac{9}{5}\\=\frac{-200}{60}-\frac{105}{60}-\frac{108}{60}\\=\frac{-200-105-108}{60}\\=\frac{-413}{60}\)
4. \(-\left(\frac{-10}{-3}\right) -\left(\frac{10}{8}\right) -\left(\frac{11}{7}\right)\\= \frac{-10}{3}- \frac{10}{8}-\frac{11}{7}\\=\frac{-10}{3}-\frac{5}{4}-\frac{11}{7}\\=\frac{-280}{84}-\frac{105}{84}-\frac{132}{84}\\=\frac{-280-105-132}{84}\\=\frac{-517}{84}\)
5. \(-\left(\frac{-8}{3}\right) -\left(\frac{-10}{5}\right) -\left(\frac{-2}{-10}\right)\\= \frac{8}{3}+ \frac{10}{5}-\frac{2}{10}\\=\frac{8}{3}+\frac{2}{1}-\frac{1}{5}\\=\frac{40}{15}+\frac{30}{15}-\frac{3}{15}\\=\frac{40+30-3}{15}\\=\frac{67}{15}\)
6. \(-\left(\frac{-5}{-2}\right) -\left(\frac{9}{4}\right) -\left(\frac{11}{2}\right)\\= \frac{-5}{2}- \frac{9}{4}-\frac{11}{2}\\=\frac{-10}{4}-\frac{9}{4}-\frac{22}{4}\\=\frac{-10-9-22}{4}\\=\frac{-41}{4}\)
7. \(-\left(\frac{8}{-3}\right) -\left(\frac{-5}{-5}\right) +\left(\frac{-5}{4}\right)\\= \frac{8}{3}- \frac{5}{5}-\frac{5}{4}\\=\frac{8}{3}-\frac{1}{1}-\frac{5}{4}\\=\frac{32}{12}-\frac{12}{12}-\frac{15}{12}\\=\frac{32-12-15}{12}\\=\frac{5}{12}\)
8. \(+\left(\frac{2}{9}\right) +\left(\frac{-3}{5}\right) -\left(\frac{-9}{4}\right)\\= \frac{2}{9}- \frac{3}{5}+\frac{9}{4}\\=\frac{40}{180}-\frac{108}{180}+\frac{405}{180}\\=\frac{40-108+405}{180}\\=\frac{337}{180}\)
9. \(+\left(\frac{8}{5}\right) -\left(\frac{-3}{5}\right) +\left(\frac{4}{10}\right)\\= \frac{8}{5}+ \frac{3}{5}+\frac{4}{10}\\=\frac{8}{5}+\frac{3}{5}+\frac{2}{5}\\=\frac{8+3+2}{5}\\=\frac{13}{5}\)
10. \(-\left(\frac{-7}{-6}\right) -\left(\frac{4}{-3}\right) +\left(\frac{10}{-3}\right)\\= \frac{-7}{6}+ \frac{4}{3}-\frac{10}{3}\\=\frac{-7+4-10}{6}\\=\frac{-13}{6}\)
11. \(+\left(\frac{5}{6}\right) +\left(\frac{5}{7}\right) -\left(\frac{11}{8}\right)\\= \frac{5}{6}+ \frac{5}{7}-\frac{11}{8}\\=\frac{140}{168}+\frac{120}{168}-\frac{231}{168}\\=\frac{140+120-231}{168}\\=\frac{29}{168}\)
12. \(-\left(\frac{5}{2}\right) +\left(\frac{9}{-4}\right) +\left(\frac{5}{7}\right)\\= \frac{-5}{2}- \frac{9}{4}+\frac{5}{7}\\=\frac{-70}{28}-\frac{63}{28}+\frac{20}{28}\\=\frac{-70-63+20}{28}\\=\frac{-113}{28}\)