Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{9}\right) -\left(\frac{7}{-2}\right) +\left(\frac{9}{-8}\right)\\= \frac{-10}{9}+ \frac{7}{2}-\frac{9}{8}\\=\frac{-80}{72}+\frac{252}{72}-\frac{81}{72}\\=\frac{-80+252-81}{72}\\=\frac{91}{72}\)
2. \(-\left(\frac{-3}{8}\right) +\left(\frac{4}{-2}\right) -\left(\frac{9}{11}\right)\\= \frac{3}{8}- \frac{4}{2}-\frac{9}{11}\\=\frac{3}{8}-\frac{2}{1}-\frac{9}{11}\\=\frac{33}{88}-\frac{176}{88}-\frac{72}{88}\\=\frac{33-176-72}{88}\\=\frac{-215}{88}\)
3. \(+\left(\frac{7}{3}\right) +\left(\frac{-9}{-9}\right) -\left(\frac{-10}{9}\right)\\= \frac{7}{3}+ \frac{9}{9}+\frac{10}{9}\\=\frac{7}{3}+\frac{1}{1}+\frac{10}{9}\\=\frac{21}{9}+\frac{9}{9}+\frac{10}{9}\\=\frac{21+9+10}{9}\\=\frac{40}{9}\)
4. \(-\left(\frac{3}{2}\right) +\left(\frac{-6}{2}\right) -\left(\frac{3}{6}\right)\\= \frac{-3}{2}- \frac{6}{2}-\frac{3}{6}\\=\frac{-3}{2}-\frac{3}{1}-\frac{1}{2}\\=\frac{-3-3-1}{2}\\=\frac{-7}{2}\)
5. \(-\left(\frac{5}{-2}\right) -\left(\frac{7}{6}\right) -\left(\frac{-7}{8}\right)\\= \frac{5}{2}- \frac{7}{6}+\frac{7}{8}\\=\frac{60}{24}-\frac{28}{24}+\frac{21}{24}\\=\frac{60-28+21}{24}\\=\frac{53}{24}\)
6. \(+\left(\frac{9}{-2}\right) -\left(\frac{-4}{3}\right) +\left(\frac{4}{6}\right)\\= \frac{-9}{2}+ \frac{4}{3}+\frac{4}{6}\\=\frac{-9}{2}+\frac{4}{3}+\frac{2}{3}\\=\frac{-27}{6}+\frac{8}{6}+\frac{4}{6}\\=\frac{-27+8+4}{6}\\=\frac{-15}{6}\\=\frac{-5}{2}\)
7. \(+\left(\frac{8}{-5}\right) -\left(\frac{7}{5}\right) -\left(\frac{3}{6}\right)\\= \frac{-8}{5}- \frac{7}{5}-\frac{3}{6}\\=\frac{-8}{5}-\frac{7}{5}-\frac{1}{2}\\=\frac{-16}{10}-\frac{14}{10}-\frac{5}{10}\\=\frac{-16-14-5}{10}\\=\frac{-35}{10}\\=\frac{-7}{2}\)
8. \(+\left(\frac{3}{7}\right) -\left(\frac{-7}{-9}\right) -\left(\frac{3}{8}\right)\\= \frac{3}{7}- \frac{7}{9}-\frac{3}{8}\\=\frac{216}{504}-\frac{392}{504}-\frac{189}{504}\\=\frac{216-392-189}{504}\\=\frac{-365}{504}\)
9. \(-\left(\frac{8}{-3}\right) +\left(\frac{-7}{-8}\right) +\left(\frac{-12}{-3}\right)\\= \frac{8}{3}+ \frac{7}{8}+\frac{12}{3}\\=\frac{8}{3}+\frac{7}{8}+\frac{4}{1}\\=\frac{64}{24}+\frac{21}{24}+\frac{96}{24}\\=\frac{64+21+96}{24}\\=\frac{181}{24}\)
10. \(-\left(\frac{-5}{6}\right) +\left(\frac{-10}{-9}\right) -\left(\frac{-2}{-10}\right)\\= \frac{5}{6}+ \frac{10}{9}-\frac{2}{10}\\=\frac{5}{6}+\frac{10}{9}-\frac{1}{5}\\=\frac{75}{90}+\frac{100}{90}-\frac{18}{90}\\=\frac{75+100-18}{90}\\=\frac{157}{90}\)
11. \(-\left(\frac{2}{-3}\right) -\left(\frac{-5}{7}\right) +\left(\frac{5}{2}\right)\\= \frac{2}{3}+ \frac{5}{7}+\frac{5}{2}\\=\frac{28}{42}+\frac{30}{42}+\frac{105}{42}\\=\frac{28+30+105}{42}\\=\frac{163}{42}\)
12. \(-\left(\frac{-10}{9}\right) -\left(\frac{-7}{-4}\right) -\left(\frac{8}{-11}\right)\\= \frac{10}{9}- \frac{7}{4}+\frac{8}{11}\\=\frac{440}{396}-\frac{693}{396}+\frac{288}{396}\\=\frac{440-693+288}{396}\\=\frac{35}{396}\)