Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{7}\right) -\left(\frac{-5}{6}\right) +\left(\frac{-5}{-4}\right)\\= \frac{2}{7}+ \frac{5}{6}+\frac{5}{4}\\=\frac{24}{84}+\frac{70}{84}+\frac{105}{84}\\=\frac{24+70+105}{84}\\=\frac{199}{84}\)
2. \(-\left(\frac{10}{7}\right) +\left(\frac{3}{-9}\right) +\left(\frac{11}{-6}\right)\\= \frac{-10}{7}- \frac{3}{9}-\frac{11}{6}\\=\frac{-10}{7}-\frac{1}{3}-\frac{11}{6}\\=\frac{-60}{42}-\frac{14}{42}-\frac{77}{42}\\=\frac{-60-14-77}{42}\\=\frac{-151}{42}\)
3. \(+\left(\frac{9}{7}\right) +\left(\frac{6}{8}\right) -\left(\frac{-8}{12}\right)\\= \frac{9}{7}+ \frac{6}{8}+\frac{8}{12}\\=\frac{9}{7}+\frac{3}{4}+\frac{2}{3}\\=\frac{108}{84}+\frac{63}{84}+\frac{56}{84}\\=\frac{108+63+56}{84}\\=\frac{227}{84}\)
4. \(-\left(\frac{-6}{5}\right) +\left(\frac{7}{-6}\right) +\left(\frac{5}{-8}\right)\\= \frac{6}{5}- \frac{7}{6}-\frac{5}{8}\\=\frac{144}{120}-\frac{140}{120}-\frac{75}{120}\\=\frac{144-140-75}{120}\\=\frac{-71}{120}\)
5. \(+\left(\frac{-3}{-7}\right) +\left(\frac{-6}{5}\right) +\left(\frac{-11}{12}\right)\\= \frac{3}{7}- \frac{6}{5}-\frac{11}{12}\\=\frac{180}{420}-\frac{504}{420}-\frac{385}{420}\\=\frac{180-504-385}{420}\\=\frac{-709}{420}\)
6. \(+\left(\frac{7}{5}\right) +\left(\frac{-9}{9}\right) +\left(\frac{-7}{-11}\right)\\= \frac{7}{5}- \frac{9}{9}+\frac{7}{11}\\=\frac{7}{5}-\frac{1}{1}+\frac{7}{11}\\=\frac{77}{55}-\frac{55}{55}+\frac{35}{55}\\=\frac{77-55+35}{55}\\=\frac{57}{55}\)
7. \(+\left(\frac{-2}{-3}\right) -\left(\frac{8}{4}\right) +\left(\frac{-7}{-2}\right)\\= \frac{2}{3}- \frac{8}{4}+\frac{7}{2}\\=\frac{2}{3}-\frac{2}{1}+\frac{7}{2}\\=\frac{4}{6}-\frac{12}{6}+\frac{21}{6}\\=\frac{4-12+21}{6}\\=\frac{13}{6}\)
8. \(-\left(\frac{-5}{-6}\right) -\left(\frac{-9}{9}\right) +\left(\frac{-8}{-8}\right)\\= \frac{-5}{6}+ \frac{9}{9}+\frac{8}{8}\\=\frac{-5}{6}+\frac{1}{1}+\frac{1}{1}\\=\frac{-5+1+1}{6}\\=\frac{-3}{6}\\=\frac{-1}{2}\)
9. \(+\left(\frac{8}{3}\right) +\left(\frac{2}{-6}\right) -\left(\frac{6}{-3}\right)\\= \frac{8}{3}- \frac{2}{6}+\frac{6}{3}\\=\frac{8}{3}-\frac{1}{3}+\frac{2}{1}\\=\frac{8-1+2}{3}\\=\frac{9}{3}\\=\frac{3}{1}\)
10. \(+\left(\frac{-6}{-5}\right) -\left(\frac{4}{-6}\right) +\left(\frac{-5}{7}\right)\\= \frac{6}{5}+ \frac{4}{6}-\frac{5}{7}\\=\frac{6}{5}+\frac{2}{3}-\frac{5}{7}\\=\frac{126}{105}+\frac{70}{105}-\frac{75}{105}\\=\frac{126+70-75}{105}\\=\frac{121}{105}\)
11. \(-\left(\frac{7}{2}\right) -\left(\frac{9}{3}\right) +\left(\frac{10}{4}\right)\\= \frac{-7}{2}- \frac{9}{3}+\frac{10}{4}\\=\frac{-7}{2}-\frac{3}{1}+\frac{5}{2}\\=\frac{-7-3+5}{2}\\=\frac{-5}{2}\)
12. \(-\left(\frac{8}{3}\right) +\left(\frac{-6}{7}\right) +\left(\frac{-9}{8}\right)\\= \frac{-8}{3}- \frac{6}{7}-\frac{9}{8}\\=\frac{-448}{168}-\frac{144}{168}-\frac{189}{168}\\=\frac{-448-144-189}{168}\\=\frac{-781}{168}\)