Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{7}\right) +\left(\frac{-9}{2}\right) -\left(\frac{-12}{-8}\right)\\= \frac{10}{7}- \frac{9}{2}-\frac{12}{8}\\=\frac{10}{7}-\frac{9}{2}-\frac{3}{2}\\=\frac{20}{14}-\frac{63}{14}-\frac{21}{14}\\=\frac{20-63-21}{14}\\=\frac{-64}{14}\\=\frac{-32}{7}\)
2. \(-\left(\frac{-8}{5}\right) -\left(\frac{5}{4}\right) +\left(\frac{-10}{7}\right)\\= \frac{8}{5}- \frac{5}{4}-\frac{10}{7}\\=\frac{224}{140}-\frac{175}{140}-\frac{200}{140}\\=\frac{224-175-200}{140}\\=\frac{-151}{140}\)
3. \(+\left(\frac{-10}{-7}\right) +\left(\frac{9}{-3}\right) +\left(\frac{9}{8}\right)\\= \frac{10}{7}- \frac{9}{3}+\frac{9}{8}\\=\frac{10}{7}-\frac{3}{1}+\frac{9}{8}\\=\frac{80}{56}-\frac{168}{56}+\frac{63}{56}\\=\frac{80-168+63}{56}\\=\frac{-25}{56}\)
4. \(-\left(\frac{-4}{3}\right) -\left(\frac{-10}{-5}\right) -\left(\frac{9}{-10}\right)\\= \frac{4}{3}- \frac{10}{5}+\frac{9}{10}\\=\frac{4}{3}-\frac{2}{1}+\frac{9}{10}\\=\frac{40}{30}-\frac{60}{30}+\frac{27}{30}\\=\frac{40-60+27}{30}\\=\frac{7}{30}\)
5. \(-\left(\frac{3}{-8}\right) -\left(\frac{-9}{-9}\right) +\left(\frac{-3}{-9}\right)\\= \frac{3}{8}- \frac{9}{9}+\frac{3}{9}\\=\frac{3}{8}-\frac{1}{1}+\frac{1}{3}\\=\frac{9}{24}-\frac{24}{24}+\frac{8}{24}\\=\frac{9-24+8}{24}\\=\frac{-7}{24}\)
6. \(-\left(\frac{3}{8}\right) -\left(\frac{-10}{4}\right) -\left(\frac{-10}{-2}\right)\\= \frac{-3}{8}+ \frac{10}{4}-\frac{10}{2}\\=\frac{-3}{8}+\frac{5}{2}-\frac{5}{1}\\=\frac{-3+5-5}{8}\\=\frac{-3}{8}\)
7. \(-\left(\frac{-5}{6}\right) -\left(\frac{-4}{10}\right) +\left(\frac{-5}{-3}\right)\\= \frac{5}{6}+ \frac{4}{10}+\frac{5}{3}\\=\frac{5}{6}+\frac{2}{5}+\frac{5}{3}\\=\frac{25}{30}+\frac{12}{30}+\frac{50}{30}\\=\frac{25+12+50}{30}\\=\frac{87}{30}\\=\frac{29}{10}\)
8. \(+\left(\frac{-4}{3}\right) +\left(\frac{5}{8}\right) +\left(\frac{11}{-6}\right)\\= \frac{-4}{3}+ \frac{5}{8}-\frac{11}{6}\\=\frac{-32}{24}+\frac{15}{24}-\frac{44}{24}\\=\frac{-32+15-44}{24}\\=\frac{-61}{24}\)
9. \(-\left(\frac{-7}{-8}\right) -\left(\frac{8}{9}\right) +\left(\frac{3}{-11}\right)\\= \frac{-7}{8}- \frac{8}{9}-\frac{3}{11}\\=\frac{-693}{792}-\frac{704}{792}-\frac{216}{792}\\=\frac{-693-704-216}{792}\\=\frac{-1613}{792}\)
10. \(-\left(\frac{4}{3}\right) -\left(\frac{9}{-10}\right) -\left(\frac{5}{-7}\right)\\= \frac{-4}{3}+ \frac{9}{10}+\frac{5}{7}\\=\frac{-280}{210}+\frac{189}{210}+\frac{150}{210}\\=\frac{-280+189+150}{210}\\=\frac{59}{210}\)
11. \(-\left(\frac{6}{5}\right) +\left(\frac{10}{-3}\right) -\left(\frac{-12}{6}\right)\\= \frac{-6}{5}- \frac{10}{3}+\frac{12}{6}\\=\frac{-6}{5}-\frac{10}{3}+\frac{2}{1}\\=\frac{-18}{15}-\frac{50}{15}+\frac{30}{15}\\=\frac{-18-50+30}{15}\\=\frac{-38}{15}\)
12. \(+\left(\frac{9}{-7}\right) -\left(\frac{3}{-7}\right) -\left(\frac{7}{-10}\right)\\= \frac{-9}{7}+ \frac{3}{7}+\frac{7}{10}\\=\frac{-90}{70}+\frac{30}{70}+\frac{49}{70}\\=\frac{-90+30+49}{70}\\=\frac{-11}{70}\)