Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-7}\right) +\left(\frac{-8}{-6}\right) +\left(\frac{-8}{9}\right)\\= \frac{10}{7}+ \frac{8}{6}-\frac{8}{9}\\=\frac{10}{7}+\frac{4}{3}-\frac{8}{9}\\=\frac{90}{63}+\frac{84}{63}-\frac{56}{63}\\=\frac{90+84-56}{63}\\=\frac{118}{63}\)
2. \(-\left(\frac{-4}{3}\right) -\left(\frac{-6}{-8}\right) -\left(\frac{-12}{3}\right)\\= \frac{4}{3}- \frac{6}{8}+\frac{12}{3}\\=\frac{4}{3}-\frac{3}{4}+\frac{4}{1}\\=\frac{16}{12}-\frac{9}{12}+\frac{48}{12}\\=\frac{16-9+48}{12}\\=\frac{55}{12}\)
3. \(+\left(\frac{-3}{-7}\right) +\left(\frac{10}{9}\right) +\left(\frac{-6}{-3}\right)\\= \frac{3}{7}+ \frac{10}{9}+\frac{6}{3}\\=\frac{3}{7}+\frac{10}{9}+\frac{2}{1}\\=\frac{27}{63}+\frac{70}{63}+\frac{126}{63}\\=\frac{27+70+126}{63}\\=\frac{223}{63}\)
4. \(-\left(\frac{6}{-5}\right) -\left(\frac{7}{2}\right) -\left(\frac{4}{-6}\right)\\= \frac{6}{5}- \frac{7}{2}+\frac{4}{6}\\=\frac{6}{5}-\frac{7}{2}+\frac{2}{3}\\=\frac{36}{30}-\frac{105}{30}+\frac{20}{30}\\=\frac{36-105+20}{30}\\=\frac{-49}{30}\)
5. \(-\left(\frac{-3}{2}\right) -\left(\frac{10}{-5}\right) -\left(\frac{3}{7}\right)\\= \frac{3}{2}+ \frac{10}{5}-\frac{3}{7}\\=\frac{3}{2}+\frac{2}{1}-\frac{3}{7}\\=\frac{21}{14}+\frac{28}{14}-\frac{6}{14}\\=\frac{21+28-6}{14}\\=\frac{43}{14}\)
6. \(+\left(\frac{10}{3}\right) -\left(\frac{4}{2}\right) -\left(\frac{-2}{9}\right)\\= \frac{10}{3}- \frac{4}{2}+\frac{2}{9}\\=\frac{10}{3}-\frac{2}{1}+\frac{2}{9}\\=\frac{30}{9}-\frac{18}{9}+\frac{2}{9}\\=\frac{30-18+2}{9}\\=\frac{14}{9}\)
7. \(-\left(\frac{-4}{3}\right) +\left(\frac{-3}{-4}\right) +\left(\frac{8}{-11}\right)\\= \frac{4}{3}+ \frac{3}{4}-\frac{8}{11}\\=\frac{176}{132}+\frac{99}{132}-\frac{96}{132}\\=\frac{176+99-96}{132}\\=\frac{179}{132}\)
8. \(+\left(\frac{-8}{-3}\right) +\left(\frac{3}{-8}\right) -\left(\frac{-6}{12}\right)\\= \frac{8}{3}- \frac{3}{8}+\frac{6}{12}\\=\frac{8}{3}-\frac{3}{8}+\frac{1}{2}\\=\frac{64}{24}-\frac{9}{24}+\frac{12}{24}\\=\frac{64-9+12}{24}\\=\frac{67}{24}\)
9. \(+\left(\frac{7}{5}\right) +\left(\frac{8}{3}\right) +\left(\frac{-7}{-4}\right)\\= \frac{7}{5}+ \frac{8}{3}+\frac{7}{4}\\=\frac{84}{60}+\frac{160}{60}+\frac{105}{60}\\=\frac{84+160+105}{60}\\=\frac{349}{60}\)
10. \(-\left(\frac{-2}{5}\right) -\left(\frac{-5}{2}\right) -\left(\frac{-12}{-9}\right)\\= \frac{2}{5}+ \frac{5}{2}-\frac{12}{9}\\=\frac{2}{5}+\frac{5}{2}-\frac{4}{3}\\=\frac{12}{30}+\frac{75}{30}-\frac{40}{30}\\=\frac{12+75-40}{30}\\=\frac{47}{30}\)
11. \(+\left(\frac{-7}{-8}\right) +\left(\frac{-10}{10}\right) -\left(\frac{-7}{-8}\right)\\= \frac{7}{8}- \frac{10}{10}-\frac{7}{8}\\=\frac{7}{8}-\frac{1}{1}-\frac{7}{8}\\=\frac{7-1-7}{8}\\=\frac{-1}{8}\)
12. \(-\left(\frac{-10}{3}\right) +\left(\frac{-7}{-6}\right) -\left(\frac{-12}{5}\right)\\= \frac{10}{3}+ \frac{7}{6}+\frac{12}{5}\\=\frac{100}{30}+\frac{35}{30}+\frac{72}{30}\\=\frac{100+35+72}{30}\\=\frac{207}{30}\\=\frac{69}{10}\)