Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{10}{-7}\right) +\left(\frac{8}{-6}\right) -\left(\frac{3}{-5}\right)\\= \frac{-10}{7}- \frac{8}{6}+\frac{3}{5}\\=\frac{-10}{7}-\frac{4}{3}+\frac{3}{5}\\=\frac{-150}{105}-\frac{140}{105}+\frac{63}{105}\\=\frac{-150-140+63}{105}\\=\frac{-227}{105}\)
2. \(-\left(\frac{6}{-5}\right) +\left(\frac{9}{6}\right) +\left(\frac{-11}{5}\right)\\= \frac{6}{5}+ \frac{9}{6}-\frac{11}{5}\\=\frac{6}{5}+\frac{3}{2}-\frac{11}{5}\\=\frac{12}{10}+\frac{15}{10}-\frac{22}{10}\\=\frac{12+15-22}{10}\\=\frac{5}{10}\\=\frac{1}{2}\)
3. \(-\left(\frac{-5}{2}\right) -\left(\frac{4}{8}\right) +\left(\frac{-5}{-10}\right)\\= \frac{5}{2}- \frac{4}{8}+\frac{5}{10}\\=\frac{5}{2}-\frac{1}{2}+\frac{1}{2}\\=\frac{5-1+1}{2}\\=\frac{5}{2}\)
4. \(+\left(\frac{2}{3}\right) -\left(\frac{10}{8}\right) +\left(\frac{6}{-9}\right)\\= \frac{2}{3}- \frac{10}{8}-\frac{6}{9}\\=\frac{2}{3}-\frac{5}{4}-\frac{2}{3}\\=\frac{8}{12}-\frac{15}{12}-\frac{8}{12}\\=\frac{8-15-8}{12}\\=\frac{-15}{12}\\=\frac{-5}{4}\)
5. \(+\left(\frac{7}{2}\right) +\left(\frac{8}{-3}\right) +\left(\frac{-9}{-5}\right)\\= \frac{7}{2}- \frac{8}{3}+\frac{9}{5}\\=\frac{105}{30}-\frac{80}{30}+\frac{54}{30}\\=\frac{105-80+54}{30}\\=\frac{79}{30}\)
6. \(-\left(\frac{2}{3}\right) +\left(\frac{-10}{-9}\right) +\left(\frac{-11}{2}\right)\\= \frac{-2}{3}+ \frac{10}{9}-\frac{11}{2}\\=\frac{-12}{18}+\frac{20}{18}-\frac{99}{18}\\=\frac{-12+20-99}{18}\\=\frac{-91}{18}\)
7. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-3}{-6}\right) +\left(\frac{3}{2}\right)\\= \frac{6}{5}- \frac{3}{6}+\frac{3}{2}\\=\frac{6}{5}-\frac{1}{2}+\frac{3}{2}\\=\frac{12}{10}-\frac{5}{10}+\frac{15}{10}\\=\frac{12-5+15}{10}\\=\frac{22}{10}\\=\frac{11}{5}\)
8. \(+\left(\frac{10}{3}\right) +\left(\frac{7}{2}\right) -\left(\frac{9}{-6}\right)\\= \frac{10}{3}+ \frac{7}{2}+\frac{9}{6}\\=\frac{10}{3}+\frac{7}{2}+\frac{3}{2}\\=\frac{20}{6}+\frac{21}{6}+\frac{9}{6}\\=\frac{20+21+9}{6}\\=\frac{50}{6}\\=\frac{25}{3}\)
9. \(+\left(\frac{-8}{-3}\right) -\left(\frac{-3}{-3}\right) +\left(\frac{6}{-6}\right)\\= \frac{8}{3}- \frac{3}{3}-\frac{6}{6}\\=\frac{8}{3}-\frac{1}{1}-\frac{1}{1}\\=\frac{8-1-1}{3}\\=\frac{6}{3}\\=\frac{2}{1}\)
10. \(-\left(\frac{4}{-7}\right) -\left(\frac{6}{-6}\right) +\left(\frac{12}{-10}\right)\\= \frac{4}{7}+ \frac{6}{6}-\frac{12}{10}\\=\frac{4}{7}+\frac{1}{1}-\frac{6}{5}\\=\frac{20}{35}+\frac{35}{35}-\frac{42}{35}\\=\frac{20+35-42}{35}\\=\frac{13}{35}\)
11. \(-\left(\frac{3}{-2}\right) +\left(\frac{-6}{4}\right) -\left(\frac{3}{-11}\right)\\= \frac{3}{2}- \frac{6}{4}+\frac{3}{11}\\=\frac{3}{2}-\frac{3}{2}+\frac{3}{11}\\=\frac{33}{22}-\frac{33}{22}+\frac{6}{22}\\=\frac{33-33+6}{22}\\=\frac{6}{22}\\=\frac{3}{11}\)
12. \(-\left(\frac{2}{9}\right) +\left(\frac{-7}{9}\right) -\left(\frac{6}{7}\right)\\= \frac{-2}{9}- \frac{7}{9}-\frac{6}{7}\\=\frac{-14}{63}-\frac{49}{63}-\frac{54}{63}\\=\frac{-14-49-54}{63}\\=\frac{-117}{63}\\=\frac{-13}{7}\)