Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{2}\right) +\left(\frac{-4}{-10}\right) +\left(\frac{3}{-5}\right)\\= \frac{3}{2}+ \frac{4}{10}-\frac{3}{5}\\=\frac{3}{2}+\frac{2}{5}-\frac{3}{5}\\=\frac{15}{10}+\frac{4}{10}-\frac{6}{10}\\=\frac{15+4-6}{10}\\=\frac{13}{10}\)
2. \(-\left(\frac{4}{-3}\right) -\left(\frac{4}{4}\right) +\left(\frac{-9}{-2}\right)\\= \frac{4}{3}- \frac{4}{4}+\frac{9}{2}\\=\frac{4}{3}-\frac{1}{1}+\frac{9}{2}\\=\frac{8}{6}-\frac{6}{6}+\frac{27}{6}\\=\frac{8-6+27}{6}\\=\frac{29}{6}\)
3. \(+\left(\frac{2}{9}\right) +\left(\frac{-2}{6}\right) -\left(\frac{9}{5}\right)\\= \frac{2}{9}- \frac{2}{6}-\frac{9}{5}\\=\frac{2}{9}-\frac{1}{3}-\frac{9}{5}\\=\frac{10}{45}-\frac{15}{45}-\frac{81}{45}\\=\frac{10-15-81}{45}\\=\frac{-86}{45}\)
4. \(+\left(\frac{5}{3}\right) -\left(\frac{-2}{9}\right) -\left(\frac{-2}{7}\right)\\= \frac{5}{3}+ \frac{2}{9}+\frac{2}{7}\\=\frac{105}{63}+\frac{14}{63}+\frac{18}{63}\\=\frac{105+14+18}{63}\\=\frac{137}{63}\)
5. \(-\left(\frac{4}{7}\right) +\left(\frac{-8}{7}\right) +\left(\frac{12}{8}\right)\\= \frac{-4}{7}- \frac{8}{7}+\frac{12}{8}\\=\frac{-4}{7}-\frac{8}{7}+\frac{3}{2}\\=\frac{-8}{14}-\frac{16}{14}+\frac{21}{14}\\=\frac{-8-16+21}{14}\\=\frac{-3}{14}\)
6. \(-\left(\frac{10}{3}\right) +\left(\frac{2}{-4}\right) -\left(\frac{5}{-6}\right)\\= \frac{-10}{3}- \frac{2}{4}+\frac{5}{6}\\=\frac{-10}{3}-\frac{1}{2}+\frac{5}{6}\\=\frac{-20}{6}-\frac{3}{6}+\frac{5}{6}\\=\frac{-20-3+5}{6}\\=\frac{-18}{6}\\=\frac{-3}{1}\)
7. \(+\left(\frac{4}{-9}\right) +\left(\frac{4}{-10}\right) +\left(\frac{-12}{-3}\right)\\= \frac{-4}{9}- \frac{4}{10}+\frac{12}{3}\\=\frac{-4}{9}-\frac{2}{5}+\frac{4}{1}\\=\frac{-20}{45}-\frac{18}{45}+\frac{180}{45}\\=\frac{-20-18+180}{45}\\=\frac{142}{45}\)
8. \(+\left(\frac{8}{3}\right) +\left(\frac{-9}{7}\right) -\left(\frac{-10}{-5}\right)\\= \frac{8}{3}- \frac{9}{7}-\frac{10}{5}\\=\frac{8}{3}-\frac{9}{7}-\frac{2}{1}\\=\frac{56}{21}-\frac{27}{21}-\frac{42}{21}\\=\frac{56-27-42}{21}\\=\frac{-13}{21}\)
9. \(+\left(\frac{-10}{-3}\right) +\left(\frac{-4}{-6}\right) +\left(\frac{-9}{8}\right)\\= \frac{10}{3}+ \frac{4}{6}-\frac{9}{8}\\=\frac{10}{3}+\frac{2}{3}-\frac{9}{8}\\=\frac{80}{24}+\frac{16}{24}-\frac{27}{24}\\=\frac{80+16-27}{24}\\=\frac{69}{24}\\=\frac{23}{8}\)
10. \(+\left(\frac{-4}{7}\right) +\left(\frac{-8}{3}\right) +\left(\frac{12}{6}\right)\\= \frac{-4}{7}- \frac{8}{3}+\frac{12}{6}\\=\frac{-4}{7}-\frac{8}{3}+\frac{2}{1}\\=\frac{-12}{21}-\frac{56}{21}+\frac{42}{21}\\=\frac{-12-56+42}{21}\\=\frac{-26}{21}\)
11. \(+\left(\frac{9}{4}\right) +\left(\frac{7}{10}\right) +\left(\frac{-5}{-2}\right)\\= \frac{9}{4}+ \frac{7}{10}+\frac{5}{2}\\=\frac{45}{20}+\frac{14}{20}+\frac{50}{20}\\=\frac{45+14+50}{20}\\=\frac{109}{20}\)
12. \(-\left(\frac{-7}{2}\right) -\left(\frac{3}{6}\right) -\left(\frac{-8}{-10}\right)\\= \frac{7}{2}- \frac{3}{6}-\frac{8}{10}\\=\frac{7}{2}-\frac{1}{2}-\frac{4}{5}\\=\frac{35}{10}-\frac{5}{10}-\frac{8}{10}\\=\frac{35-5-8}{10}\\=\frac{22}{10}\\=\frac{11}{5}\)