Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{-2}\right) +\left(\frac{-3}{-2}\right) +\left(\frac{-2}{11}\right)\\= \frac{9}{2}+ \frac{3}{2}-\frac{2}{11}\\=\frac{99}{22}+\frac{33}{22}-\frac{4}{22}\\=\frac{99+33-4}{22}\\=\frac{128}{22}\\=\frac{64}{11}\)
2. \(+\left(\frac{-2}{-3}\right) +\left(\frac{6}{-7}\right) +\left(\frac{-3}{10}\right)\\= \frac{2}{3}- \frac{6}{7}-\frac{3}{10}\\=\frac{140}{210}-\frac{180}{210}-\frac{63}{210}\\=\frac{140-180-63}{210}\\=\frac{-103}{210}\)
3. \(-\left(\frac{-10}{-7}\right) -\left(\frac{9}{-9}\right) +\left(\frac{5}{2}\right)\\= \frac{-10}{7}+ \frac{9}{9}+\frac{5}{2}\\=\frac{-10}{7}+\frac{1}{1}+\frac{5}{2}\\=\frac{-20}{14}+\frac{14}{14}+\frac{35}{14}\\=\frac{-20+14+35}{14}\\=\frac{29}{14}\)
4. \(-\left(\frac{-2}{-3}\right) +\left(\frac{7}{2}\right) -\left(\frac{-11}{10}\right)\\= \frac{-2}{3}+ \frac{7}{2}+\frac{11}{10}\\=\frac{-20}{30}+\frac{105}{30}+\frac{33}{30}\\=\frac{-20+105+33}{30}\\=\frac{118}{30}\\=\frac{59}{15}\)
5. \(-\left(\frac{-10}{7}\right) +\left(\frac{-5}{-5}\right) -\left(\frac{-6}{9}\right)\\= \frac{10}{7}+ \frac{5}{5}+\frac{6}{9}\\=\frac{10}{7}+\frac{1}{1}+\frac{2}{3}\\=\frac{30}{21}+\frac{21}{21}+\frac{14}{21}\\=\frac{30+21+14}{21}\\=\frac{65}{21}\)
6. \(+\left(\frac{6}{-7}\right) +\left(\frac{6}{-8}\right) -\left(\frac{12}{11}\right)\\= \frac{-6}{7}- \frac{6}{8}-\frac{12}{11}\\=\frac{-6}{7}-\frac{3}{4}-\frac{12}{11}\\=\frac{-264}{308}-\frac{231}{308}-\frac{336}{308}\\=\frac{-264-231-336}{308}\\=\frac{-831}{308}\)
7. \(-\left(\frac{9}{2}\right) +\left(\frac{-10}{-3}\right) -\left(\frac{-2}{2}\right)\\= \frac{-9}{2}+ \frac{10}{3}+\frac{2}{2}\\=\frac{-9}{2}+\frac{10}{3}+\frac{1}{1}\\=\frac{-27}{6}+\frac{20}{6}+\frac{6}{6}\\=\frac{-27+20+6}{6}\\=\frac{-1}{6}\)
8. \(+\left(\frac{6}{-5}\right) +\left(\frac{6}{10}\right) -\left(\frac{-2}{-5}\right)\\= \frac{-6}{5}+ \frac{6}{10}-\frac{2}{5}\\=\frac{-6}{5}+\frac{3}{5}-\frac{2}{5}\\=\frac{-6+3-2}{5}\\=\frac{-5}{5}\\=\frac{-1}{1}\)
9. \(-\left(\frac{2}{-3}\right) +\left(\frac{-10}{9}\right) +\left(\frac{-3}{8}\right)\\= \frac{2}{3}- \frac{10}{9}-\frac{3}{8}\\=\frac{48}{72}-\frac{80}{72}-\frac{27}{72}\\=\frac{48-80-27}{72}\\=\frac{-59}{72}\)
10. \(+\left(\frac{7}{8}\right) +\left(\frac{-6}{9}\right) +\left(\frac{9}{-10}\right)\\= \frac{7}{8}- \frac{6}{9}-\frac{9}{10}\\=\frac{7}{8}-\frac{2}{3}-\frac{9}{10}\\=\frac{105}{120}-\frac{80}{120}-\frac{108}{120}\\=\frac{105-80-108}{120}\\=\frac{-83}{120}\)
11. \(-\left(\frac{10}{-9}\right) +\left(\frac{-3}{7}\right) -\left(\frac{5}{-11}\right)\\= \frac{10}{9}- \frac{3}{7}+\frac{5}{11}\\=\frac{770}{693}-\frac{297}{693}+\frac{315}{693}\\=\frac{770-297+315}{693}\\=\frac{788}{693}\)
12. \(-\left(\frac{5}{3}\right) -\left(\frac{-7}{5}\right) +\left(\frac{-9}{6}\right)\\= \frac{-5}{3}+ \frac{7}{5}-\frac{9}{6}\\=\frac{-5}{3}+\frac{7}{5}-\frac{3}{2}\\=\frac{-50}{30}+\frac{42}{30}-\frac{45}{30}\\=\frac{-50+42-45}{30}\\=\frac{-53}{30}\)