Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{8}\right) +\left(\frac{10}{6}\right) +\left(\frac{6}{-7}\right)\\= \frac{9}{8}+ \frac{10}{6}-\frac{6}{7}\\=\frac{9}{8}+\frac{5}{3}-\frac{6}{7}\\=\frac{189}{168}+\frac{280}{168}-\frac{144}{168}\\=\frac{189+280-144}{168}\\=\frac{325}{168}\)
2. \(+\left(\frac{-5}{4}\right) +\left(\frac{-3}{-8}\right) +\left(\frac{4}{-6}\right)\\= \frac{-5}{4}+ \frac{3}{8}-\frac{4}{6}\\=\frac{-5}{4}+\frac{3}{8}-\frac{2}{3}\\=\frac{-30}{24}+\frac{9}{24}-\frac{16}{24}\\=\frac{-30+9-16}{24}\\=\frac{-37}{24}\)
3. \(+\left(\frac{-2}{7}\right) -\left(\frac{-8}{5}\right) -\left(\frac{-2}{-6}\right)\\= \frac{-2}{7}+ \frac{8}{5}-\frac{2}{6}\\=\frac{-2}{7}+\frac{8}{5}-\frac{1}{3}\\=\frac{-30}{105}+\frac{168}{105}-\frac{35}{105}\\=\frac{-30+168-35}{105}\\=\frac{103}{105}\)
4. \(-\left(\frac{-2}{-7}\right) +\left(\frac{4}{10}\right) -\left(\frac{-8}{4}\right)\\= \frac{-2}{7}+ \frac{4}{10}+\frac{8}{4}\\=\frac{-2}{7}+\frac{2}{5}+\frac{2}{1}\\=\frac{-10}{35}+\frac{14}{35}+\frac{70}{35}\\=\frac{-10+14+70}{35}\\=\frac{74}{35}\)
5. \(-\left(\frac{-6}{5}\right) +\left(\frac{-10}{4}\right) -\left(\frac{12}{-7}\right)\\= \frac{6}{5}- \frac{10}{4}+\frac{12}{7}\\=\frac{6}{5}-\frac{5}{2}+\frac{12}{7}\\=\frac{84}{70}-\frac{175}{70}+\frac{120}{70}\\=\frac{84-175+120}{70}\\=\frac{29}{70}\)
6. \(-\left(\frac{-7}{8}\right) +\left(\frac{7}{9}\right) +\left(\frac{6}{-4}\right)\\= \frac{7}{8}+ \frac{7}{9}-\frac{6}{4}\\=\frac{7}{8}+\frac{7}{9}-\frac{3}{2}\\=\frac{63}{72}+\frac{56}{72}-\frac{108}{72}\\=\frac{63+56-108}{72}\\=\frac{11}{72}\)
7. \(+\left(\frac{-2}{-3}\right) +\left(\frac{8}{-8}\right) -\left(\frac{-5}{-11}\right)\\= \frac{2}{3}- \frac{8}{8}-\frac{5}{11}\\=\frac{2}{3}-\frac{1}{1}-\frac{5}{11}\\=\frac{22}{33}-\frac{33}{33}-\frac{15}{33}\\=\frac{22-33-15}{33}\\=\frac{-26}{33}\)
8. \(-\left(\frac{-10}{7}\right) -\left(\frac{-3}{6}\right) -\left(\frac{11}{8}\right)\\= \frac{10}{7}+ \frac{3}{6}-\frac{11}{8}\\=\frac{10}{7}+\frac{1}{2}-\frac{11}{8}\\=\frac{80}{56}+\frac{28}{56}-\frac{77}{56}\\=\frac{80+28-77}{56}\\=\frac{31}{56}\)
9. \(-\left(\frac{6}{5}\right) -\left(\frac{-3}{7}\right) -\left(\frac{11}{2}\right)\\= \frac{-6}{5}+ \frac{3}{7}-\frac{11}{2}\\=\frac{-84}{70}+\frac{30}{70}-\frac{385}{70}\\=\frac{-84+30-385}{70}\\=\frac{-439}{70}\)
10. \(-\left(\frac{7}{-5}\right) +\left(\frac{3}{-9}\right) +\left(\frac{9}{-10}\right)\\= \frac{7}{5}- \frac{3}{9}-\frac{9}{10}\\=\frac{7}{5}-\frac{1}{3}-\frac{9}{10}\\=\frac{42}{30}-\frac{10}{30}-\frac{27}{30}\\=\frac{42-10-27}{30}\\=\frac{5}{30}\\=\frac{1}{6}\)
11. \(-\left(\frac{-10}{3}\right) +\left(\frac{3}{-7}\right) +\left(\frac{10}{-12}\right)\\= \frac{10}{3}- \frac{3}{7}-\frac{10}{12}\\=\frac{10}{3}-\frac{3}{7}-\frac{5}{6}\\=\frac{140}{42}-\frac{18}{42}-\frac{35}{42}\\=\frac{140-18-35}{42}\\=\frac{87}{42}\\=\frac{29}{14}\)
12. \(+\left(\frac{-5}{-3}\right) -\left(\frac{-2}{8}\right) +\left(\frac{-11}{-3}\right)\\= \frac{5}{3}+ \frac{2}{8}+\frac{11}{3}\\=\frac{5}{3}+\frac{1}{4}+\frac{11}{3}\\=\frac{20}{12}+\frac{3}{12}+\frac{44}{12}\\=\frac{20+3+44}{12}\\=\frac{67}{12}\)