Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{-7}\right) -\left(\frac{-2}{5}\right) -\left(\frac{8}{12}\right)\\= \frac{-3}{7}+ \frac{2}{5}-\frac{8}{12}\\=\frac{-3}{7}+\frac{2}{5}-\frac{2}{3}\\=\frac{-45}{105}+\frac{42}{105}-\frac{70}{105}\\=\frac{-45+42-70}{105}\\=\frac{-73}{105}\)
2. \(-\left(\frac{6}{5}\right) -\left(\frac{10}{-6}\right) -\left(\frac{7}{-9}\right)\\= \frac{-6}{5}+ \frac{10}{6}+\frac{7}{9}\\=\frac{-6}{5}+\frac{5}{3}+\frac{7}{9}\\=\frac{-54}{45}+\frac{75}{45}+\frac{35}{45}\\=\frac{-54+75+35}{45}\\=\frac{56}{45}\)
3. \(+\left(\frac{-2}{-3}\right) -\left(\frac{-4}{5}\right) -\left(\frac{6}{-9}\right)\\= \frac{2}{3}+ \frac{4}{5}+\frac{6}{9}\\=\frac{2}{3}+\frac{4}{5}+\frac{2}{3}\\=\frac{10}{15}+\frac{12}{15}+\frac{10}{15}\\=\frac{10+12+10}{15}\\=\frac{32}{15}\)
4. \(+\left(\frac{-4}{-3}\right) +\left(\frac{7}{-5}\right) -\left(\frac{-12}{4}\right)\\= \frac{4}{3}- \frac{7}{5}+\frac{12}{4}\\=\frac{4}{3}-\frac{7}{5}+\frac{3}{1}\\=\frac{20}{15}-\frac{21}{15}+\frac{45}{15}\\=\frac{20-21+45}{15}\\=\frac{44}{15}\)
5. \(+\left(\frac{-10}{-3}\right) +\left(\frac{3}{8}\right) +\left(\frac{3}{-6}\right)\\= \frac{10}{3}+ \frac{3}{8}-\frac{3}{6}\\=\frac{10}{3}+\frac{3}{8}-\frac{1}{2}\\=\frac{80}{24}+\frac{9}{24}-\frac{12}{24}\\=\frac{80+9-12}{24}\\=\frac{77}{24}\)
6. \(+\left(\frac{-5}{2}\right) -\left(\frac{8}{10}\right) +\left(\frac{5}{8}\right)\\= \frac{-5}{2}- \frac{8}{10}+\frac{5}{8}\\=\frac{-5}{2}-\frac{4}{5}+\frac{5}{8}\\=\frac{-100}{40}-\frac{32}{40}+\frac{25}{40}\\=\frac{-100-32+25}{40}\\=\frac{-107}{40}\)
7. \(+\left(\frac{-2}{-5}\right) +\left(\frac{7}{6}\right) -\left(\frac{-3}{9}\right)\\= \frac{2}{5}+ \frac{7}{6}+\frac{3}{9}\\=\frac{2}{5}+\frac{7}{6}+\frac{1}{3}\\=\frac{12}{30}+\frac{35}{30}+\frac{10}{30}\\=\frac{12+35+10}{30}\\=\frac{57}{30}\\=\frac{19}{10}\)
8. \(+\left(\frac{10}{7}\right) +\left(\frac{9}{6}\right) +\left(\frac{-8}{11}\right)\\= \frac{10}{7}+ \frac{9}{6}-\frac{8}{11}\\=\frac{10}{7}+\frac{3}{2}-\frac{8}{11}\\=\frac{220}{154}+\frac{231}{154}-\frac{112}{154}\\=\frac{220+231-112}{154}\\=\frac{339}{154}\)
9. \(+\left(\frac{-9}{-2}\right) +\left(\frac{3}{-7}\right) -\left(\frac{-3}{-6}\right)\\= \frac{9}{2}- \frac{3}{7}-\frac{3}{6}\\=\frac{9}{2}-\frac{3}{7}-\frac{1}{2}\\=\frac{63}{14}-\frac{6}{14}-\frac{7}{14}\\=\frac{63-6-7}{14}\\=\frac{50}{14}\\=\frac{25}{7}\)
10. \(-\left(\frac{3}{-4}\right) -\left(\frac{2}{3}\right) -\left(\frac{-4}{-12}\right)\\= \frac{3}{4}- \frac{2}{3}-\frac{4}{12}\\=\frac{3}{4}-\frac{2}{3}-\frac{1}{3}\\=\frac{9}{12}-\frac{8}{12}-\frac{4}{12}\\=\frac{9-8-4}{12}\\=\frac{-3}{12}\\=\frac{-1}{4}\)
11. \(-\left(\frac{2}{5}\right) +\left(\frac{9}{2}\right) -\left(\frac{-12}{2}\right)\\= \frac{-2}{5}+ \frac{9}{2}+\frac{12}{2}\\=\frac{-2}{5}+\frac{9}{2}+\frac{6}{1}\\=\frac{-4}{10}+\frac{45}{10}+\frac{60}{10}\\=\frac{-4+45+60}{10}\\=\frac{101}{10}\)
12. \(-\left(\frac{-3}{-5}\right) -\left(\frac{4}{-7}\right) +\left(\frac{-5}{-9}\right)\\= \frac{-3}{5}+ \frac{4}{7}+\frac{5}{9}\\=\frac{-189}{315}+\frac{180}{315}+\frac{175}{315}\\=\frac{-189+180+175}{315}\\=\frac{166}{315}\)