Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{8}\right) +\left(\frac{5}{2}\right) -\left(\frac{-7}{7}\right)\\= \frac{-7}{8}+ \frac{5}{2}+\frac{7}{7}\\=\frac{-7}{8}+\frac{5}{2}+\frac{1}{1}\\=\frac{-7+5+1}{8}\\=\frac{-1}{8}\)
2. \(-\left(\frac{9}{4}\right) -\left(\frac{-5}{6}\right) -\left(\frac{-4}{-10}\right)\\= \frac{-9}{4}+ \frac{5}{6}-\frac{4}{10}\\=\frac{-9}{4}+\frac{5}{6}-\frac{2}{5}\\=\frac{-135}{60}+\frac{50}{60}-\frac{24}{60}\\=\frac{-135+50-24}{60}\\=\frac{-109}{60}\)
3. \(+\left(\frac{-2}{7}\right) -\left(\frac{4}{-5}\right) +\left(\frac{5}{-9}\right)\\= \frac{-2}{7}+ \frac{4}{5}-\frac{5}{9}\\=\frac{-90}{315}+\frac{252}{315}-\frac{175}{315}\\=\frac{-90+252-175}{315}\\=\frac{-13}{315}\)
4. \(+\left(\frac{8}{-3}\right) +\left(\frac{7}{-6}\right) -\left(\frac{2}{10}\right)\\= \frac{-8}{3}- \frac{7}{6}-\frac{2}{10}\\=\frac{-8}{3}-\frac{7}{6}-\frac{1}{5}\\=\frac{-80}{30}-\frac{35}{30}-\frac{6}{30}\\=\frac{-80-35-6}{30}\\=\frac{-121}{30}\)
5. \(+\left(\frac{3}{8}\right) +\left(\frac{-9}{-10}\right) +\left(\frac{2}{11}\right)\\= \frac{3}{8}+ \frac{9}{10}+\frac{2}{11}\\=\frac{165}{440}+\frac{396}{440}+\frac{80}{440}\\=\frac{165+396+80}{440}\\=\frac{641}{440}\)
6. \(+\left(\frac{-8}{-5}\right) +\left(\frac{10}{-4}\right) -\left(\frac{-9}{5}\right)\\= \frac{8}{5}- \frac{10}{4}+\frac{9}{5}\\=\frac{8}{5}-\frac{5}{2}+\frac{9}{5}\\=\frac{16}{10}-\frac{25}{10}+\frac{18}{10}\\=\frac{16-25+18}{10}\\=\frac{9}{10}\)
7. \(-\left(\frac{-7}{2}\right) -\left(\frac{6}{-3}\right) -\left(\frac{-10}{7}\right)\\= \frac{7}{2}+ \frac{6}{3}+\frac{10}{7}\\=\frac{7}{2}+\frac{2}{1}+\frac{10}{7}\\=\frac{49}{14}+\frac{28}{14}+\frac{20}{14}\\=\frac{49+28+20}{14}\\=\frac{97}{14}\)
8. \(-\left(\frac{-2}{-3}\right) +\left(\frac{5}{9}\right) -\left(\frac{10}{-11}\right)\\= \frac{-2}{3}+ \frac{5}{9}+\frac{10}{11}\\=\frac{-66}{99}+\frac{55}{99}+\frac{90}{99}\\=\frac{-66+55+90}{99}\\=\frac{79}{99}\)
9. \(-\left(\frac{-4}{9}\right) -\left(\frac{2}{5}\right) -\left(\frac{2}{-5}\right)\\= \frac{4}{9}- \frac{2}{5}+\frac{2}{5}\\=\frac{20}{45}-\frac{18}{45}+\frac{18}{45}\\=\frac{20-18+18}{45}\\=\frac{20}{45}\\=\frac{4}{9}\)
10. \(-\left(\frac{7}{9}\right) +\left(\frac{6}{7}\right) -\left(\frac{-5}{5}\right)\\= \frac{-7}{9}+ \frac{6}{7}+\frac{5}{5}\\=\frac{-7}{9}+\frac{6}{7}+\frac{1}{1}\\=\frac{-49}{63}+\frac{54}{63}+\frac{63}{63}\\=\frac{-49+54+63}{63}\\=\frac{68}{63}\)
11. \(-\left(\frac{-6}{-5}\right) +\left(\frac{2}{-2}\right) +\left(\frac{6}{-12}\right)\\= \frac{-6}{5}- \frac{2}{2}-\frac{6}{12}\\=\frac{-6}{5}-\frac{1}{1}-\frac{1}{2}\\=\frac{-12}{10}-\frac{10}{10}-\frac{5}{10}\\=\frac{-12-10-5}{10}\\=\frac{-27}{10}\)
12. \(+\left(\frac{-4}{9}\right) +\left(\frac{2}{10}\right) +\left(\frac{-8}{-10}\right)\\= \frac{-4}{9}+ \frac{2}{10}+\frac{8}{10}\\=\frac{-4}{9}+\frac{1}{5}+\frac{4}{5}\\=\frac{-20}{45}+\frac{9}{45}+\frac{36}{45}\\=\frac{-20+9+36}{45}\\=\frac{25}{45}\\=\frac{5}{9}\)