Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{9}\right) -\left(\frac{2}{-10}\right) -\left(\frac{10}{-5}\right)\\= \frac{-4}{9}+ \frac{2}{10}+\frac{10}{5}\\=\frac{-4}{9}+\frac{1}{5}+\frac{2}{1}\\=\frac{-20}{45}+\frac{9}{45}+\frac{90}{45}\\=\frac{-20+9+90}{45}\\=\frac{79}{45}\)
2. \(-\left(\frac{-9}{7}\right) -\left(\frac{3}{4}\right) -\left(\frac{7}{-12}\right)\\= \frac{9}{7}- \frac{3}{4}+\frac{7}{12}\\=\frac{108}{84}-\frac{63}{84}+\frac{49}{84}\\=\frac{108-63+49}{84}\\=\frac{94}{84}\\=\frac{47}{42}\)
3. \(+\left(\frac{3}{7}\right) -\left(\frac{8}{-4}\right) +\left(\frac{8}{5}\right)\\= \frac{3}{7}+ \frac{8}{4}+\frac{8}{5}\\=\frac{3}{7}+\frac{2}{1}+\frac{8}{5}\\=\frac{15}{35}+\frac{70}{35}+\frac{56}{35}\\=\frac{15+70+56}{35}\\=\frac{141}{35}\)
4. \(+\left(\frac{2}{5}\right) +\left(\frac{3}{3}\right) -\left(\frac{7}{-6}\right)\\= \frac{2}{5}+ \frac{3}{3}+\frac{7}{6}\\=\frac{2}{5}+\frac{1}{1}+\frac{7}{6}\\=\frac{12}{30}+\frac{30}{30}+\frac{35}{30}\\=\frac{12+30+35}{30}\\=\frac{77}{30}\)
5. \(+\left(\frac{-9}{-2}\right) +\left(\frac{4}{-9}\right) -\left(\frac{-2}{9}\right)\\= \frac{9}{2}- \frac{4}{9}+\frac{2}{9}\\=\frac{81}{18}-\frac{8}{18}+\frac{4}{18}\\=\frac{81-8+4}{18}\\=\frac{77}{18}\)
6. \(-\left(\frac{-4}{-7}\right) -\left(\frac{-4}{8}\right) -\left(\frac{-12}{4}\right)\\= \frac{-4}{7}+ \frac{4}{8}+\frac{12}{4}\\=\frac{-4}{7}+\frac{1}{2}+\frac{3}{1}\\=\frac{-8}{14}+\frac{7}{14}+\frac{42}{14}\\=\frac{-8+7+42}{14}\\=\frac{41}{14}\)
7. \(-\left(\frac{9}{8}\right) -\left(\frac{3}{-5}\right) +\left(\frac{8}{-7}\right)\\= \frac{-9}{8}+ \frac{3}{5}-\frac{8}{7}\\=\frac{-315}{280}+\frac{168}{280}-\frac{320}{280}\\=\frac{-315+168-320}{280}\\=\frac{-467}{280}\)
8. \(-\left(\frac{8}{9}\right) +\left(\frac{4}{-3}\right) +\left(\frac{-7}{-2}\right)\\= \frac{-8}{9}- \frac{4}{3}+\frac{7}{2}\\=\frac{-16}{18}-\frac{24}{18}+\frac{63}{18}\\=\frac{-16-24+63}{18}\\=\frac{23}{18}\)
9. \(+\left(\frac{-9}{-7}\right) +\left(\frac{-3}{8}\right) +\left(\frac{7}{-8}\right)\\= \frac{9}{7}- \frac{3}{8}-\frac{7}{8}\\=\frac{72}{56}-\frac{21}{56}-\frac{49}{56}\\=\frac{72-21-49}{56}\\=\frac{2}{56}\\=\frac{1}{28}\)
10. \(+\left(\frac{6}{-5}\right) -\left(\frac{5}{7}\right) -\left(\frac{12}{-9}\right)\\= \frac{-6}{5}- \frac{5}{7}+\frac{12}{9}\\=\frac{-6}{5}-\frac{5}{7}+\frac{4}{3}\\=\frac{-126}{105}-\frac{75}{105}+\frac{140}{105}\\=\frac{-126-75+140}{105}\\=\frac{-61}{105}\)
11. \(-\left(\frac{5}{4}\right) -\left(\frac{-2}{-8}\right) +\left(\frac{4}{-12}\right)\\= \frac{-5}{4}- \frac{2}{8}-\frac{4}{12}\\=\frac{-5}{4}-\frac{1}{4}-\frac{1}{3}\\=\frac{-15}{12}-\frac{3}{12}-\frac{4}{12}\\=\frac{-15-3-4}{12}\\=\frac{-22}{12}\\=\frac{-11}{6}\)
12. \(+\left(\frac{8}{-3}\right) +\left(\frac{3}{10}\right) +\left(\frac{6}{-12}\right)\\= \frac{-8}{3}+ \frac{3}{10}-\frac{6}{12}\\=\frac{-8}{3}+\frac{3}{10}-\frac{1}{2}\\=\frac{-80}{30}+\frac{9}{30}-\frac{15}{30}\\=\frac{-80+9-15}{30}\\=\frac{-86}{30}\\=\frac{-43}{15}\)