Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{7}\right) +\left(\frac{9}{2}\right) -\left(\frac{-6}{-7}\right)\\= \frac{2}{7}+ \frac{9}{2}-\frac{6}{7}\\=\frac{4}{14}+\frac{63}{14}-\frac{12}{14}\\=\frac{4+63-12}{14}\\=\frac{55}{14}\)
2. \(+\left(\frac{5}{-9}\right) -\left(\frac{-8}{6}\right) +\left(\frac{8}{-7}\right)\\= \frac{-5}{9}+ \frac{8}{6}-\frac{8}{7}\\=\frac{-5}{9}+\frac{4}{3}-\frac{8}{7}\\=\frac{-35}{63}+\frac{84}{63}-\frac{72}{63}\\=\frac{-35+84-72}{63}\\=\frac{-23}{63}\)
3. \(-\left(\frac{-4}{-3}\right) -\left(\frac{-6}{2}\right) +\left(\frac{9}{4}\right)\\= \frac{-4}{3}+ \frac{6}{2}+\frac{9}{4}\\=\frac{-4}{3}+\frac{3}{1}+\frac{9}{4}\\=\frac{-16}{12}+\frac{36}{12}+\frac{27}{12}\\=\frac{-16+36+27}{12}\\=\frac{47}{12}\)
4. \(-\left(\frac{5}{9}\right) +\left(\frac{6}{-9}\right) -\left(\frac{2}{5}\right)\\= \frac{-5}{9}- \frac{6}{9}-\frac{2}{5}\\=\frac{-5}{9}-\frac{2}{3}-\frac{2}{5}\\=\frac{-25}{45}-\frac{30}{45}-\frac{18}{45}\\=\frac{-25-30-18}{45}\\=\frac{-73}{45}\)
5. \(+\left(\frac{4}{3}\right) +\left(\frac{2}{-9}\right) +\left(\frac{-7}{-3}\right)\\= \frac{4}{3}- \frac{2}{9}+\frac{7}{3}\\=\frac{12}{9}-\frac{2}{9}+\frac{21}{9}\\=\frac{12-2+21}{9}\\=\frac{31}{9}\)
6. \(+\left(\frac{-2}{3}\right) +\left(\frac{-7}{8}\right) +\left(\frac{-12}{5}\right)\\= \frac{-2}{3}- \frac{7}{8}-\frac{12}{5}\\=\frac{-80}{120}-\frac{105}{120}-\frac{288}{120}\\=\frac{-80-105-288}{120}\\=\frac{-473}{120}\)
7. \(-\left(\frac{-8}{-5}\right) -\left(\frac{-10}{4}\right) -\left(\frac{7}{8}\right)\\= \frac{-8}{5}+ \frac{10}{4}-\frac{7}{8}\\=\frac{-8}{5}+\frac{5}{2}-\frac{7}{8}\\=\frac{-64}{40}+\frac{100}{40}-\frac{35}{40}\\=\frac{-64+100-35}{40}\\=\frac{1}{40}\)
8. \(-\left(\frac{4}{-7}\right) -\left(\frac{8}{-2}\right) +\left(\frac{-5}{8}\right)\\= \frac{4}{7}+ \frac{8}{2}-\frac{5}{8}\\=\frac{4}{7}+\frac{4}{1}-\frac{5}{8}\\=\frac{32}{56}+\frac{224}{56}-\frac{35}{56}\\=\frac{32+224-35}{56}\\=\frac{221}{56}\)
9. \(-\left(\frac{-10}{-3}\right) +\left(\frac{-2}{-2}\right) +\left(\frac{-4}{5}\right)\\= \frac{-10}{3}+ \frac{2}{2}-\frac{4}{5}\\=\frac{-10}{3}+\frac{1}{1}-\frac{4}{5}\\=\frac{-50}{15}+\frac{15}{15}-\frac{12}{15}\\=\frac{-50+15-12}{15}\\=\frac{-47}{15}\)
10. \(-\left(\frac{-5}{3}\right) +\left(\frac{-8}{3}\right) -\left(\frac{-7}{-3}\right)\\= \frac{5}{3}- \frac{8}{3}-\frac{7}{3}\\=\frac{5-8-7}{3}\\=\frac{-10}{3}\)
11. \(-\left(\frac{-7}{-2}\right) -\left(\frac{7}{7}\right) +\left(\frac{-9}{7}\right)\\= \frac{-7}{2}- \frac{7}{7}-\frac{9}{7}\\=\frac{-7}{2}-\frac{1}{1}-\frac{9}{7}\\=\frac{-49}{14}-\frac{14}{14}-\frac{18}{14}\\=\frac{-49-14-18}{14}\\=\frac{-81}{14}\)
12. \(+\left(\frac{-9}{7}\right) +\left(\frac{6}{5}\right) +\left(\frac{2}{-5}\right)\\= \frac{-9}{7}+ \frac{6}{5}-\frac{2}{5}\\=\frac{-45}{35}+\frac{42}{35}-\frac{14}{35}\\=\frac{-45+42-14}{35}\\=\frac{-17}{35}\)