Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{-7}\right) +\left(\frac{5}{3}\right) -\left(\frac{6}{10}\right)\\= \frac{-3}{7}+ \frac{5}{3}-\frac{6}{10}\\=\frac{-3}{7}+\frac{5}{3}-\frac{3}{5}\\=\frac{-45}{105}+\frac{175}{105}-\frac{63}{105}\\=\frac{-45+175-63}{105}\\=\frac{67}{105}\)
2. \(+\left(\frac{-7}{-9}\right) +\left(\frac{6}{9}\right) -\left(\frac{-5}{-7}\right)\\= \frac{7}{9}+ \frac{6}{9}-\frac{5}{7}\\=\frac{7}{9}+\frac{2}{3}-\frac{5}{7}\\=\frac{49}{63}+\frac{42}{63}-\frac{45}{63}\\=\frac{49+42-45}{63}\\=\frac{46}{63}\)
3. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-3}{2}\right) +\left(\frac{-4}{11}\right)\\= \frac{-6}{5}- \frac{3}{2}-\frac{4}{11}\\=\frac{-132}{110}-\frac{165}{110}-\frac{40}{110}\\=\frac{-132-165-40}{110}\\=\frac{-337}{110}\)
4. \(+\left(\frac{8}{5}\right) -\left(\frac{-4}{-2}\right) +\left(\frac{3}{-3}\right)\\= \frac{8}{5}- \frac{4}{2}-\frac{3}{3}\\=\frac{8}{5}-\frac{2}{1}-\frac{1}{1}\\=\frac{8-2-1}{5}\\=\frac{5}{5}\\=\frac{1}{1}\)
5. \(-\left(\frac{-2}{9}\right) +\left(\frac{-3}{-3}\right) +\left(\frac{7}{8}\right)\\= \frac{2}{9}+ \frac{3}{3}+\frac{7}{8}\\=\frac{2}{9}+\frac{1}{1}+\frac{7}{8}\\=\frac{16}{72}+\frac{72}{72}+\frac{63}{72}\\=\frac{16+72+63}{72}\\=\frac{151}{72}\)
6. \(-\left(\frac{-6}{5}\right) +\left(\frac{-9}{3}\right) -\left(\frac{-9}{6}\right)\\= \frac{6}{5}- \frac{9}{3}+\frac{9}{6}\\=\frac{6}{5}-\frac{3}{1}+\frac{3}{2}\\=\frac{12}{10}-\frac{30}{10}+\frac{15}{10}\\=\frac{12-30+15}{10}\\=\frac{-3}{10}\)
7. \(+\left(\frac{-5}{-4}\right) +\left(\frac{3}{-10}\right) -\left(\frac{6}{-7}\right)\\= \frac{5}{4}- \frac{3}{10}+\frac{6}{7}\\=\frac{175}{140}-\frac{42}{140}+\frac{120}{140}\\=\frac{175-42+120}{140}\\=\frac{253}{140}\)
8. \(+\left(\frac{6}{-5}\right) +\left(\frac{8}{-3}\right) +\left(\frac{-5}{11}\right)\\= \frac{-6}{5}- \frac{8}{3}-\frac{5}{11}\\=\frac{-198}{165}-\frac{440}{165}-\frac{75}{165}\\=\frac{-198-440-75}{165}\\=\frac{-713}{165}\)
9. \(+\left(\frac{-3}{-2}\right) -\left(\frac{-3}{3}\right) -\left(\frac{11}{2}\right)\\= \frac{3}{2}+ \frac{3}{3}-\frac{11}{2}\\=\frac{3}{2}+\frac{1}{1}-\frac{11}{2}\\=\frac{3+1-11}{2}\\=\frac{-7}{2}\)
10. \(+\left(\frac{-8}{7}\right) +\left(\frac{-8}{-8}\right) +\left(\frac{2}{11}\right)\\= \frac{-8}{7}+ \frac{8}{8}+\frac{2}{11}\\=\frac{-8}{7}+\frac{1}{1}+\frac{2}{11}\\=\frac{-88}{77}+\frac{77}{77}+\frac{14}{77}\\=\frac{-88+77+14}{77}\\=\frac{3}{77}\)
11. \(-\left(\frac{2}{-3}\right) +\left(\frac{3}{-8}\right) -\left(\frac{5}{8}\right)\\= \frac{2}{3}- \frac{3}{8}-\frac{5}{8}\\=\frac{16}{24}-\frac{9}{24}-\frac{15}{24}\\=\frac{16-9-15}{24}\\=\frac{-8}{24}\\=\frac{-1}{3}\)
12. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-8}{9}\right) -\left(\frac{-7}{-6}\right)\\= \frac{-10}{7}- \frac{8}{9}-\frac{7}{6}\\=\frac{-180}{126}-\frac{112}{126}-\frac{147}{126}\\=\frac{-180-112-147}{126}\\=\frac{-439}{126}\)