Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{-7}\right) +\left(\frac{3}{10}\right) +\left(\frac{7}{-4}\right)\\= \frac{-3}{7}+ \frac{3}{10}-\frac{7}{4}\\=\frac{-60}{140}+\frac{42}{140}-\frac{245}{140}\\=\frac{-60+42-245}{140}\\=\frac{-263}{140}\)
2. \(+\left(\frac{-8}{-7}\right) -\left(\frac{-5}{-2}\right) +\left(\frac{-3}{8}\right)\\= \frac{8}{7}- \frac{5}{2}-\frac{3}{8}\\=\frac{64}{56}-\frac{140}{56}-\frac{21}{56}\\=\frac{64-140-21}{56}\\=\frac{-97}{56}\)
3. \(+\left(\frac{-6}{5}\right) -\left(\frac{7}{-2}\right) +\left(\frac{-2}{-4}\right)\\= \frac{-6}{5}+ \frac{7}{2}+\frac{2}{4}\\=\frac{-6}{5}+\frac{7}{2}+\frac{1}{2}\\=\frac{-12}{10}+\frac{35}{10}+\frac{5}{10}\\=\frac{-12+35+5}{10}\\=\frac{28}{10}\\=\frac{14}{5}\)
4. \(+\left(\frac{8}{-7}\right) +\left(\frac{-6}{-3}\right) -\left(\frac{-11}{-10}\right)\\= \frac{-8}{7}+ \frac{6}{3}-\frac{11}{10}\\=\frac{-8}{7}+\frac{2}{1}-\frac{11}{10}\\=\frac{-80}{70}+\frac{140}{70}-\frac{77}{70}\\=\frac{-80+140-77}{70}\\=\frac{-17}{70}\)
5. \(-\left(\frac{8}{5}\right) -\left(\frac{-5}{-5}\right) +\left(\frac{12}{11}\right)\\= \frac{-8}{5}- \frac{5}{5}+\frac{12}{11}\\=\frac{-8}{5}-\frac{1}{1}+\frac{12}{11}\\=\frac{-88}{55}-\frac{55}{55}+\frac{60}{55}\\=\frac{-88-55+60}{55}\\=\frac{-83}{55}\)
6. \(-\left(\frac{-3}{8}\right) +\left(\frac{4}{-6}\right) +\left(\frac{-5}{6}\right)\\= \frac{3}{8}- \frac{4}{6}-\frac{5}{6}\\=\frac{3}{8}-\frac{2}{3}-\frac{5}{6}\\=\frac{9}{24}-\frac{16}{24}-\frac{20}{24}\\=\frac{9-16-20}{24}\\=\frac{-27}{24}\\=\frac{-9}{8}\)
7. \(-\left(\frac{9}{2}\right) +\left(\frac{-9}{8}\right) -\left(\frac{11}{8}\right)\\= \frac{-9}{2}- \frac{9}{8}-\frac{11}{8}\\=\frac{-36}{8}-\frac{9}{8}-\frac{11}{8}\\=\frac{-36-9-11}{8}\\=\frac{-56}{8}\\=\frac{-7}{1}\)
8. \(-\left(\frac{7}{-2}\right) -\left(\frac{-5}{5}\right) -\left(\frac{2}{-8}\right)\\= \frac{7}{2}+ \frac{5}{5}+\frac{2}{8}\\=\frac{7}{2}+\frac{1}{1}+\frac{1}{4}\\=\frac{14}{4}+\frac{4}{4}+\frac{1}{4}\\=\frac{14+4+1}{4}\\=\frac{19}{4}\)
9. \(+\left(\frac{-5}{-7}\right) -\left(\frac{-7}{-10}\right) +\left(\frac{-4}{-11}\right)\\= \frac{5}{7}- \frac{7}{10}+\frac{4}{11}\\=\frac{550}{770}-\frac{539}{770}+\frac{280}{770}\\=\frac{550-539+280}{770}\\=\frac{291}{770}\)
10. \(-\left(\frac{-3}{-2}\right) +\left(\frac{4}{2}\right) +\left(\frac{-11}{8}\right)\\= \frac{-3}{2}+ \frac{4}{2}-\frac{11}{8}\\=\frac{-3}{2}+\frac{2}{1}-\frac{11}{8}\\=\frac{-12}{8}+\frac{16}{8}-\frac{11}{8}\\=\frac{-12+16-11}{8}\\=\frac{-7}{8}\)
11. \(+\left(\frac{7}{3}\right) +\left(\frac{3}{4}\right) +\left(\frac{11}{6}\right)\\= \frac{7}{3}+ \frac{3}{4}+\frac{11}{6}\\=\frac{28}{12}+\frac{9}{12}+\frac{22}{12}\\=\frac{28+9+22}{12}\\=\frac{59}{12}\)
12. \(-\left(\frac{9}{-2}\right) -\left(\frac{-3}{6}\right) -\left(\frac{5}{-11}\right)\\= \frac{9}{2}+ \frac{3}{6}+\frac{5}{11}\\=\frac{9}{2}+\frac{1}{2}+\frac{5}{11}\\=\frac{99}{22}+\frac{11}{22}+\frac{10}{22}\\=\frac{99+11+10}{22}\\=\frac{120}{22}\\=\frac{60}{11}\)