Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{2}\right) -\left(\frac{4}{4}\right) -\left(\frac{9}{-6}\right)\\= \frac{9}{2}- \frac{4}{4}+\frac{9}{6}\\=\frac{9}{2}-\frac{1}{1}+\frac{3}{2}\\=\frac{9-1+3}{2}\\=\frac{11}{2}\)
2. \(+\left(\frac{-2}{9}\right) +\left(\frac{-5}{7}\right) +\left(\frac{8}{11}\right)\\= \frac{-2}{9}- \frac{5}{7}+\frac{8}{11}\\=\frac{-154}{693}-\frac{495}{693}+\frac{504}{693}\\=\frac{-154-495+504}{693}\\=\frac{-145}{693}\)
3. \(-\left(\frac{2}{7}\right) +\left(\frac{5}{-3}\right) +\left(\frac{-9}{3}\right)\\= \frac{-2}{7}- \frac{5}{3}-\frac{9}{3}\\=\frac{-2}{7}-\frac{5}{3}-\frac{3}{1}\\=\frac{-6}{21}-\frac{35}{21}-\frac{63}{21}\\=\frac{-6-35-63}{21}\\=\frac{-104}{21}\)
4. \(+\left(\frac{5}{8}\right) -\left(\frac{7}{6}\right) -\left(\frac{-2}{5}\right)\\= \frac{5}{8}- \frac{7}{6}+\frac{2}{5}\\=\frac{75}{120}-\frac{140}{120}+\frac{48}{120}\\=\frac{75-140+48}{120}\\=\frac{-17}{120}\)
5. \(+\left(\frac{-5}{3}\right) +\left(\frac{-10}{10}\right) -\left(\frac{-2}{-11}\right)\\= \frac{-5}{3}- \frac{10}{10}-\frac{2}{11}\\=\frac{-5}{3}-\frac{1}{1}-\frac{2}{11}\\=\frac{-55}{33}-\frac{33}{33}-\frac{6}{33}\\=\frac{-55-33-6}{33}\\=\frac{-94}{33}\)
6. \(+\left(\frac{6}{-5}\right) +\left(\frac{-8}{2}\right) -\left(\frac{-7}{-3}\right)\\= \frac{-6}{5}- \frac{8}{2}-\frac{7}{3}\\=\frac{-6}{5}-\frac{4}{1}-\frac{7}{3}\\=\frac{-18}{15}-\frac{60}{15}-\frac{35}{15}\\=\frac{-18-60-35}{15}\\=\frac{-113}{15}\)
7. \(-\left(\frac{10}{-3}\right) -\left(\frac{9}{6}\right) -\left(\frac{-8}{-10}\right)\\= \frac{10}{3}- \frac{9}{6}-\frac{8}{10}\\=\frac{10}{3}-\frac{3}{2}-\frac{4}{5}\\=\frac{100}{30}-\frac{45}{30}-\frac{24}{30}\\=\frac{100-45-24}{30}\\=\frac{31}{30}\)
8. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-6}{6}\right) +\left(\frac{-4}{2}\right)\\= \frac{6}{5}+ \frac{6}{6}-\frac{4}{2}\\=\frac{6}{5}+\frac{1}{1}-\frac{2}{1}\\=\frac{6+1-2}{5}\\=\frac{5}{5}\\=\frac{1}{1}\)
9. \(+\left(\frac{5}{2}\right) -\left(\frac{3}{4}\right) +\left(\frac{-2}{2}\right)\\= \frac{5}{2}- \frac{3}{4}-\frac{2}{2}\\=\frac{5}{2}-\frac{3}{4}-\frac{1}{1}\\=\frac{10}{4}-\frac{3}{4}-\frac{4}{4}\\=\frac{10-3-4}{4}\\=\frac{3}{4}\)
10. \(+\left(\frac{-5}{9}\right) -\left(\frac{-8}{-6}\right) -\left(\frac{-3}{-7}\right)\\= \frac{-5}{9}- \frac{8}{6}-\frac{3}{7}\\=\frac{-5}{9}-\frac{4}{3}-\frac{3}{7}\\=\frac{-35}{63}-\frac{84}{63}-\frac{27}{63}\\=\frac{-35-84-27}{63}\\=\frac{-146}{63}\)
11. \(+\left(\frac{3}{-2}\right) +\left(\frac{7}{-8}\right) +\left(\frac{-9}{7}\right)\\= \frac{-3}{2}- \frac{7}{8}-\frac{9}{7}\\=\frac{-84}{56}-\frac{49}{56}-\frac{72}{56}\\=\frac{-84-49-72}{56}\\=\frac{-205}{56}\)
12. \(-\left(\frac{5}{2}\right) +\left(\frac{3}{-2}\right) +\left(\frac{8}{4}\right)\\= \frac{-5}{2}- \frac{3}{2}+\frac{8}{4}\\=\frac{-5}{2}-\frac{3}{2}+\frac{2}{1}\\=\frac{-5-3+2}{2}\\=\frac{-6}{2}\\=\frac{-3}{1}\)