Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{-7}\right) -\left(\frac{-2}{6}\right) +\left(\frac{9}{11}\right)\\= \frac{-5}{7}+ \frac{2}{6}+\frac{9}{11}\\=\frac{-5}{7}+\frac{1}{3}+\frac{9}{11}\\=\frac{-165}{231}+\frac{77}{231}+\frac{189}{231}\\=\frac{-165+77+189}{231}\\=\frac{101}{231}\)
2. \(+\left(\frac{7}{-5}\right) +\left(\frac{8}{-7}\right) +\left(\frac{-5}{8}\right)\\= \frac{-7}{5}- \frac{8}{7}-\frac{5}{8}\\=\frac{-392}{280}-\frac{320}{280}-\frac{175}{280}\\=\frac{-392-320-175}{280}\\=\frac{-887}{280}\)
3. \(+\left(\frac{-2}{3}\right) -\left(\frac{-2}{-5}\right) +\left(\frac{-8}{11}\right)\\= \frac{-2}{3}- \frac{2}{5}-\frac{8}{11}\\=\frac{-110}{165}-\frac{66}{165}-\frac{120}{165}\\=\frac{-110-66-120}{165}\\=\frac{-296}{165}\)
4. \(-\left(\frac{7}{-8}\right) -\left(\frac{-5}{-9}\right) -\left(\frac{-6}{-10}\right)\\= \frac{7}{8}- \frac{5}{9}-\frac{6}{10}\\=\frac{7}{8}-\frac{5}{9}-\frac{3}{5}\\=\frac{315}{360}-\frac{200}{360}-\frac{216}{360}\\=\frac{315-200-216}{360}\\=\frac{-101}{360}\)
5. \(-\left(\frac{2}{5}\right) -\left(\frac{-8}{2}\right) +\left(\frac{-10}{12}\right)\\= \frac{-2}{5}+ \frac{8}{2}-\frac{10}{12}\\=\frac{-2}{5}+\frac{4}{1}-\frac{5}{6}\\=\frac{-12}{30}+\frac{120}{30}-\frac{25}{30}\\=\frac{-12+120-25}{30}\\=\frac{83}{30}\)
6. \(+\left(\frac{2}{3}\right) +\left(\frac{6}{-8}\right) -\left(\frac{-3}{8}\right)\\= \frac{2}{3}- \frac{6}{8}+\frac{3}{8}\\=\frac{2}{3}-\frac{3}{4}+\frac{3}{8}\\=\frac{16}{24}-\frac{18}{24}+\frac{9}{24}\\=\frac{16-18+9}{24}\\=\frac{7}{24}\)
7. \(-\left(\frac{10}{9}\right) -\left(\frac{5}{-8}\right) -\left(\frac{2}{3}\right)\\= \frac{-10}{9}+ \frac{5}{8}-\frac{2}{3}\\=\frac{-80}{72}+\frac{45}{72}-\frac{48}{72}\\=\frac{-80+45-48}{72}\\=\frac{-83}{72}\)
8. \(+\left(\frac{-10}{7}\right) -\left(\frac{10}{-9}\right) -\left(\frac{-7}{-3}\right)\\= \frac{-10}{7}+ \frac{10}{9}-\frac{7}{3}\\=\frac{-90}{63}+\frac{70}{63}-\frac{147}{63}\\=\frac{-90+70-147}{63}\\=\frac{-167}{63}\)
9. \(-\left(\frac{-6}{-7}\right) +\left(\frac{-6}{8}\right) -\left(\frac{5}{12}\right)\\= \frac{-6}{7}- \frac{6}{8}-\frac{5}{12}\\=\frac{-6}{7}-\frac{3}{4}-\frac{5}{12}\\=\frac{-72}{84}-\frac{63}{84}-\frac{35}{84}\\=\frac{-72-63-35}{84}\\=\frac{-170}{84}\\=\frac{-85}{42}\)
10. \(-\left(\frac{-2}{-9}\right) +\left(\frac{-3}{-5}\right) -\left(\frac{-10}{-4}\right)\\= \frac{-2}{9}+ \frac{3}{5}-\frac{10}{4}\\=\frac{-2}{9}+\frac{3}{5}-\frac{5}{2}\\=\frac{-20}{90}+\frac{54}{90}-\frac{225}{90}\\=\frac{-20+54-225}{90}\\=\frac{-191}{90}\)
11. \(-\left(\frac{5}{-6}\right) +\left(\frac{-3}{5}\right) +\left(\frac{11}{2}\right)\\= \frac{5}{6}- \frac{3}{5}+\frac{11}{2}\\=\frac{25}{30}-\frac{18}{30}+\frac{165}{30}\\=\frac{25-18+165}{30}\\=\frac{172}{30}\\=\frac{86}{15}\)
12. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-8}{10}\right) +\left(\frac{-11}{9}\right)\\= \frac{6}{5}- \frac{8}{10}-\frac{11}{9}\\=\frac{6}{5}-\frac{4}{5}-\frac{11}{9}\\=\frac{54}{45}-\frac{36}{45}-\frac{55}{45}\\=\frac{54-36-55}{45}\\=\frac{-37}{45}\)