Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{-8}\right) -\left(\frac{8}{8}\right) -\left(\frac{-12}{-11}\right)\\= \frac{7}{8}- \frac{8}{8}-\frac{12}{11}\\=\frac{7}{8}-\frac{1}{1}-\frac{12}{11}\\=\frac{77}{88}-\frac{88}{88}-\frac{96}{88}\\=\frac{77-88-96}{88}\\=\frac{-107}{88}\)
2. \(-\left(\frac{-8}{-9}\right) +\left(\frac{7}{3}\right) +\left(\frac{4}{-11}\right)\\= \frac{-8}{9}+ \frac{7}{3}-\frac{4}{11}\\=\frac{-88}{99}+\frac{231}{99}-\frac{36}{99}\\=\frac{-88+231-36}{99}\\=\frac{107}{99}\)
3. \(+\left(\frac{10}{-3}\right) +\left(\frac{2}{5}\right) -\left(\frac{-12}{9}\right)\\= \frac{-10}{3}+ \frac{2}{5}+\frac{12}{9}\\=\frac{-10}{3}+\frac{2}{5}+\frac{4}{3}\\=\frac{-50}{15}+\frac{6}{15}+\frac{20}{15}\\=\frac{-50+6+20}{15}\\=\frac{-24}{15}\\=\frac{-8}{5}\)
4. \(-\left(\frac{-5}{-6}\right) -\left(\frac{-8}{7}\right) +\left(\frac{-3}{11}\right)\\= \frac{-5}{6}+ \frac{8}{7}-\frac{3}{11}\\=\frac{-385}{462}+\frac{528}{462}-\frac{126}{462}\\=\frac{-385+528-126}{462}\\=\frac{17}{462}\)
5. \(+\left(\frac{-9}{-8}\right) +\left(\frac{-4}{-3}\right) -\left(\frac{-12}{6}\right)\\= \frac{9}{8}+ \frac{4}{3}+\frac{12}{6}\\=\frac{9}{8}+\frac{4}{3}+\frac{2}{1}\\=\frac{27}{24}+\frac{32}{24}+\frac{48}{24}\\=\frac{27+32+48}{24}\\=\frac{107}{24}\)
6. \(+\left(\frac{-4}{-9}\right) -\left(\frac{-5}{7}\right) -\left(\frac{8}{-12}\right)\\= \frac{4}{9}+ \frac{5}{7}+\frac{8}{12}\\=\frac{4}{9}+\frac{5}{7}+\frac{2}{3}\\=\frac{28}{63}+\frac{45}{63}+\frac{42}{63}\\=\frac{28+45+42}{63}\\=\frac{115}{63}\)
7. \(-\left(\frac{-3}{4}\right) -\left(\frac{6}{4}\right) +\left(\frac{10}{8}\right)\\= \frac{3}{4}- \frac{6}{4}+\frac{10}{8}\\=\frac{3}{4}-\frac{3}{2}+\frac{5}{4}\\=\frac{3-3+5}{4}\\=\frac{5}{4}\)
8. \(+\left(\frac{-3}{2}\right) +\left(\frac{-3}{8}\right) +\left(\frac{12}{-11}\right)\\= \frac{-3}{2}- \frac{3}{8}-\frac{12}{11}\\=\frac{-132}{88}-\frac{33}{88}-\frac{96}{88}\\=\frac{-132-33-96}{88}\\=\frac{-261}{88}\)
9. \(+\left(\frac{-2}{-5}\right) +\left(\frac{-10}{3}\right) +\left(\frac{-5}{7}\right)\\= \frac{2}{5}- \frac{10}{3}-\frac{5}{7}\\=\frac{42}{105}-\frac{350}{105}-\frac{75}{105}\\=\frac{42-350-75}{105}\\=\frac{-383}{105}\)
10. \(-\left(\frac{10}{-9}\right) -\left(\frac{10}{-4}\right) +\left(\frac{2}{12}\right)\\= \frac{10}{9}+ \frac{10}{4}+\frac{2}{12}\\=\frac{10}{9}+\frac{5}{2}+\frac{1}{6}\\=\frac{20}{18}+\frac{45}{18}+\frac{3}{18}\\=\frac{20+45+3}{18}\\=\frac{68}{18}\\=\frac{34}{9}\)
11. \(+\left(\frac{7}{5}\right) -\left(\frac{-8}{-7}\right) -\left(\frac{-12}{9}\right)\\= \frac{7}{5}- \frac{8}{7}+\frac{12}{9}\\=\frac{7}{5}-\frac{8}{7}+\frac{4}{3}\\=\frac{147}{105}-\frac{120}{105}+\frac{140}{105}\\=\frac{147-120+140}{105}\\=\frac{167}{105}\)
12. \(-\left(\frac{6}{-5}\right) +\left(\frac{-9}{-10}\right) -\left(\frac{10}{-8}\right)\\= \frac{6}{5}+ \frac{9}{10}+\frac{10}{8}\\=\frac{6}{5}+\frac{9}{10}+\frac{5}{4}\\=\frac{24}{20}+\frac{18}{20}+\frac{25}{20}\\=\frac{24+18+25}{20}\\=\frac{67}{20}\)