Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{-4}\right) +\left(\frac{-8}{7}\right) -\left(\frac{-2}{6}\right)\\= \frac{5}{4}- \frac{8}{7}+\frac{2}{6}\\=\frac{5}{4}-\frac{8}{7}+\frac{1}{3}\\=\frac{105}{84}-\frac{96}{84}+\frac{28}{84}\\=\frac{105-96+28}{84}\\=\frac{37}{84}\)
2. \(+\left(\frac{-10}{9}\right) -\left(\frac{-9}{2}\right) +\left(\frac{-11}{-4}\right)\\= \frac{-10}{9}+ \frac{9}{2}+\frac{11}{4}\\=\frac{-40}{36}+\frac{162}{36}+\frac{99}{36}\\=\frac{-40+162+99}{36}\\=\frac{221}{36}\)
3. \(+\left(\frac{2}{-9}\right) -\left(\frac{-3}{9}\right) -\left(\frac{-4}{-3}\right)\\= \frac{-2}{9}+ \frac{3}{9}-\frac{4}{3}\\=\frac{-2}{9}+\frac{1}{3}-\frac{4}{3}\\=\frac{-2+1-4}{9}\\=\frac{-5}{9}\)
4. \(+\left(\frac{-4}{3}\right) -\left(\frac{-6}{-6}\right) -\left(\frac{-4}{-11}\right)\\= \frac{-4}{3}- \frac{6}{6}-\frac{4}{11}\\=\frac{-4}{3}-\frac{1}{1}-\frac{4}{11}\\=\frac{-44}{33}-\frac{33}{33}-\frac{12}{33}\\=\frac{-44-33-12}{33}\\=\frac{-89}{33}\)
5. \(-\left(\frac{5}{9}\right) -\left(\frac{6}{-3}\right) -\left(\frac{2}{-8}\right)\\= \frac{-5}{9}+ \frac{6}{3}+\frac{2}{8}\\=\frac{-5}{9}+\frac{2}{1}+\frac{1}{4}\\=\frac{-20}{36}+\frac{72}{36}+\frac{9}{36}\\=\frac{-20+72+9}{36}\\=\frac{61}{36}\)
6. \(-\left(\frac{-10}{7}\right) +\left(\frac{-10}{4}\right) +\left(\frac{-10}{-4}\right)\\= \frac{10}{7}- \frac{10}{4}+\frac{10}{4}\\=\frac{10}{7}-\frac{5}{2}+\frac{5}{2}\\=\frac{20}{14}-\frac{35}{14}+\frac{35}{14}\\=\frac{20-35+35}{14}\\=\frac{20}{14}\\=\frac{10}{7}\)
7. \(-\left(\frac{7}{-8}\right) +\left(\frac{3}{2}\right) -\left(\frac{11}{3}\right)\\= \frac{7}{8}+ \frac{3}{2}-\frac{11}{3}\\=\frac{21}{24}+\frac{36}{24}-\frac{88}{24}\\=\frac{21+36-88}{24}\\=\frac{-31}{24}\)
8. \(+\left(\frac{-7}{3}\right) +\left(\frac{-4}{-3}\right) +\left(\frac{-4}{-2}\right)\\= \frac{-7}{3}+ \frac{4}{3}+\frac{4}{2}\\=\frac{-7}{3}+\frac{4}{3}+\frac{2}{1}\\=\frac{-7+4+2}{3}\\=\frac{-1}{3}\)
9. \(+\left(\frac{-3}{-2}\right) -\left(\frac{6}{4}\right) +\left(\frac{-10}{-5}\right)\\= \frac{3}{2}- \frac{6}{4}+\frac{10}{5}\\=\frac{3}{2}-\frac{3}{2}+\frac{2}{1}\\=\frac{3-3+2}{2}\\=\frac{2}{2}\\=\frac{1}{1}\)
10. \(-\left(\frac{-7}{4}\right) -\left(\frac{-8}{-10}\right) +\left(\frac{8}{4}\right)\\= \frac{7}{4}- \frac{8}{10}+\frac{8}{4}\\=\frac{7}{4}-\frac{4}{5}+\frac{2}{1}\\=\frac{35}{20}-\frac{16}{20}+\frac{40}{20}\\=\frac{35-16+40}{20}\\=\frac{59}{20}\)
11. \(-\left(\frac{9}{-7}\right) +\left(\frac{-8}{-10}\right) +\left(\frac{8}{9}\right)\\= \frac{9}{7}+ \frac{8}{10}+\frac{8}{9}\\=\frac{9}{7}+\frac{4}{5}+\frac{8}{9}\\=\frac{405}{315}+\frac{252}{315}+\frac{280}{315}\\=\frac{405+252+280}{315}\\=\frac{937}{315}\)
12. \(+\left(\frac{-9}{7}\right) +\left(\frac{-7}{-4}\right) -\left(\frac{10}{-4}\right)\\= \frac{-9}{7}+ \frac{7}{4}+\frac{10}{4}\\=\frac{-9}{7}+\frac{7}{4}+\frac{5}{2}\\=\frac{-36}{28}+\frac{49}{28}+\frac{70}{28}\\=\frac{-36+49+70}{28}\\=\frac{83}{28}\)