Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{7}\right) +\left(\frac{4}{9}\right) -\left(\frac{10}{-6}\right)\\= \frac{-10}{7}+ \frac{4}{9}+\frac{10}{6}\\=\frac{-10}{7}+\frac{4}{9}+\frac{5}{3}\\=\frac{-90}{63}+\frac{28}{63}+\frac{105}{63}\\=\frac{-90+28+105}{63}\\=\frac{43}{63}\)
2. \(+\left(\frac{-5}{-2}\right) +\left(\frac{5}{7}\right) -\left(\frac{3}{2}\right)\\= \frac{5}{2}+ \frac{5}{7}-\frac{3}{2}\\=\frac{35}{14}+\frac{10}{14}-\frac{21}{14}\\=\frac{35+10-21}{14}\\=\frac{24}{14}\\=\frac{12}{7}\)
3. \(-\left(\frac{-7}{4}\right) -\left(\frac{-6}{-4}\right) +\left(\frac{4}{5}\right)\\= \frac{7}{4}- \frac{6}{4}+\frac{4}{5}\\=\frac{7}{4}-\frac{3}{2}+\frac{4}{5}\\=\frac{35}{20}-\frac{30}{20}+\frac{16}{20}\\=\frac{35-30+16}{20}\\=\frac{21}{20}\)
4. \(+\left(\frac{-8}{-9}\right) +\left(\frac{-7}{-5}\right) +\left(\frac{12}{5}\right)\\= \frac{8}{9}+ \frac{7}{5}+\frac{12}{5}\\=\frac{40}{45}+\frac{63}{45}+\frac{108}{45}\\=\frac{40+63+108}{45}\\=\frac{211}{45}\)
5. \(-\left(\frac{-2}{-5}\right) -\left(\frac{-5}{3}\right) -\left(\frac{5}{4}\right)\\= \frac{-2}{5}+ \frac{5}{3}-\frac{5}{4}\\=\frac{-24}{60}+\frac{100}{60}-\frac{75}{60}\\=\frac{-24+100-75}{60}\\=\frac{1}{60}\)
6. \(+\left(\frac{-3}{-2}\right) -\left(\frac{-9}{-10}\right) +\left(\frac{-4}{-2}\right)\\= \frac{3}{2}- \frac{9}{10}+\frac{4}{2}\\=\frac{3}{2}-\frac{9}{10}+\frac{2}{1}\\=\frac{15}{10}-\frac{9}{10}+\frac{20}{10}\\=\frac{15-9+20}{10}\\=\frac{26}{10}\\=\frac{13}{5}\)
7. \(+\left(\frac{-7}{6}\right) +\left(\frac{7}{-9}\right) +\left(\frac{3}{6}\right)\\= \frac{-7}{6}- \frac{7}{9}+\frac{3}{6}\\=\frac{-7}{6}-\frac{7}{9}+\frac{1}{2}\\=\frac{-21}{18}-\frac{14}{18}+\frac{9}{18}\\=\frac{-21-14+9}{18}\\=\frac{-26}{18}\\=\frac{-13}{9}\)
8. \(-\left(\frac{-9}{7}\right) -\left(\frac{8}{-3}\right) +\left(\frac{9}{2}\right)\\= \frac{9}{7}+ \frac{8}{3}+\frac{9}{2}\\=\frac{54}{42}+\frac{112}{42}+\frac{189}{42}\\=\frac{54+112+189}{42}\\=\frac{355}{42}\)
9. \(-\left(\frac{-5}{-3}\right) -\left(\frac{6}{-3}\right) -\left(\frac{-12}{8}\right)\\= \frac{-5}{3}+ \frac{6}{3}+\frac{12}{8}\\=\frac{-5}{3}+\frac{2}{1}+\frac{3}{2}\\=\frac{-10}{6}+\frac{12}{6}+\frac{9}{6}\\=\frac{-10+12+9}{6}\\=\frac{11}{6}\)
10. \(-\left(\frac{8}{-5}\right) -\left(\frac{-3}{5}\right) +\left(\frac{-4}{-7}\right)\\= \frac{8}{5}+ \frac{3}{5}+\frac{4}{7}\\=\frac{56}{35}+\frac{21}{35}+\frac{20}{35}\\=\frac{56+21+20}{35}\\=\frac{97}{35}\)
11. \(-\left(\frac{-8}{3}\right) -\left(\frac{6}{-3}\right) -\left(\frac{2}{-2}\right)\\= \frac{8}{3}+ \frac{6}{3}+\frac{2}{2}\\=\frac{8}{3}+\frac{2}{1}+\frac{1}{1}\\=\frac{8+2+1}{3}\\=\frac{11}{3}\)
12. \(-\left(\frac{-6}{5}\right) -\left(\frac{-3}{4}\right) +\left(\frac{2}{3}\right)\\= \frac{6}{5}+ \frac{3}{4}+\frac{2}{3}\\=\frac{72}{60}+\frac{45}{60}+\frac{40}{60}\\=\frac{72+45+40}{60}\\=\frac{157}{60}\)