Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-8}{5}\right) +\left(\frac{-3}{-4}\right) +\left(\frac{-9}{9}\right)\\= \frac{8}{5}+ \frac{3}{4}-\frac{9}{9}\\=\frac{8}{5}+\frac{3}{4}-\frac{1}{1}\\=\frac{32}{20}+\frac{15}{20}-\frac{20}{20}\\=\frac{32+15-20}{20}\\=\frac{27}{20}\)
2. \(+\left(\frac{2}{9}\right) +\left(\frac{-7}{6}\right) +\left(\frac{-10}{2}\right)\\= \frac{2}{9}- \frac{7}{6}-\frac{10}{2}\\=\frac{2}{9}-\frac{7}{6}-\frac{5}{1}\\=\frac{4}{18}-\frac{21}{18}-\frac{90}{18}\\=\frac{4-21-90}{18}\\=\frac{-107}{18}\)
3. \(+\left(\frac{-10}{3}\right) -\left(\frac{3}{-5}\right) +\left(\frac{9}{9}\right)\\= \frac{-10}{3}+ \frac{3}{5}+\frac{9}{9}\\=\frac{-10}{3}+\frac{3}{5}+\frac{1}{1}\\=\frac{-50}{15}+\frac{9}{15}+\frac{15}{15}\\=\frac{-50+9+15}{15}\\=\frac{-26}{15}\)
4. \(+\left(\frac{10}{7}\right) +\left(\frac{2}{-4}\right) -\left(\frac{-5}{-2}\right)\\= \frac{10}{7}- \frac{2}{4}-\frac{5}{2}\\=\frac{10}{7}-\frac{1}{2}-\frac{5}{2}\\=\frac{20}{14}-\frac{7}{14}-\frac{35}{14}\\=\frac{20-7-35}{14}\\=\frac{-22}{14}\\=\frac{-11}{7}\)
5. \(-\left(\frac{2}{-7}\right) -\left(\frac{10}{8}\right) +\left(\frac{-6}{10}\right)\\= \frac{2}{7}- \frac{10}{8}-\frac{6}{10}\\=\frac{2}{7}-\frac{5}{4}-\frac{3}{5}\\=\frac{40}{140}-\frac{175}{140}-\frac{84}{140}\\=\frac{40-175-84}{140}\\=\frac{-219}{140}\)
6. \(+\left(\frac{8}{3}\right) +\left(\frac{4}{3}\right) -\left(\frac{-3}{6}\right)\\= \frac{8}{3}+ \frac{4}{3}+\frac{3}{6}\\=\frac{8}{3}+\frac{4}{3}+\frac{1}{2}\\=\frac{16}{6}+\frac{8}{6}+\frac{3}{6}\\=\frac{16+8+3}{6}\\=\frac{27}{6}\\=\frac{9}{2}\)
7. \(+\left(\frac{-9}{8}\right) +\left(\frac{-7}{-3}\right) -\left(\frac{6}{-8}\right)\\= \frac{-9}{8}+ \frac{7}{3}+\frac{6}{8}\\=\frac{-9}{8}+\frac{7}{3}+\frac{3}{4}\\=\frac{-27}{24}+\frac{56}{24}+\frac{18}{24}\\=\frac{-27+56+18}{24}\\=\frac{47}{24}\)
8. \(+\left(\frac{10}{7}\right) +\left(\frac{2}{-9}\right) -\left(\frac{8}{6}\right)\\= \frac{10}{7}- \frac{2}{9}-\frac{8}{6}\\=\frac{10}{7}-\frac{2}{9}-\frac{4}{3}\\=\frac{90}{63}-\frac{14}{63}-\frac{84}{63}\\=\frac{90-14-84}{63}\\=\frac{-8}{63}\)
9. \(+\left(\frac{4}{7}\right) +\left(\frac{9}{5}\right) -\left(\frac{-4}{-9}\right)\\= \frac{4}{7}+ \frac{9}{5}-\frac{4}{9}\\=\frac{180}{315}+\frac{567}{315}-\frac{140}{315}\\=\frac{180+567-140}{315}\\=\frac{607}{315}\)
10. \(-\left(\frac{-6}{5}\right) +\left(\frac{2}{7}\right) -\left(\frac{5}{12}\right)\\= \frac{6}{5}+ \frac{2}{7}-\frac{5}{12}\\=\frac{504}{420}+\frac{120}{420}-\frac{175}{420}\\=\frac{504+120-175}{420}\\=\frac{449}{420}\)
11. \(+\left(\frac{7}{-3}\right) +\left(\frac{5}{-6}\right) +\left(\frac{-8}{3}\right)\\= \frac{-7}{3}- \frac{5}{6}-\frac{8}{3}\\=\frac{-14}{6}-\frac{5}{6}-\frac{16}{6}\\=\frac{-14-5-16}{6}\\=\frac{-35}{6}\)
12. \(-\left(\frac{8}{-5}\right) +\left(\frac{5}{3}\right) -\left(\frac{-12}{4}\right)\\= \frac{8}{5}+ \frac{5}{3}+\frac{12}{4}\\=\frac{8}{5}+\frac{5}{3}+\frac{3}{1}\\=\frac{24}{15}+\frac{25}{15}+\frac{45}{15}\\=\frac{24+25+45}{15}\\=\frac{94}{15}\)