Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{2}\right) +\left(\frac{2}{-3}\right) +\left(\frac{-11}{3}\right)\\= \frac{3}{2}- \frac{2}{3}-\frac{11}{3}\\=\frac{9}{6}-\frac{4}{6}-\frac{22}{6}\\=\frac{9-4-22}{6}\\=\frac{-17}{6}\)
2. \(-\left(\frac{-2}{-5}\right) -\left(\frac{-5}{-5}\right) +\left(\frac{-2}{7}\right)\\= \frac{-2}{5}- \frac{5}{5}-\frac{2}{7}\\=\frac{-2}{5}-\frac{1}{1}-\frac{2}{7}\\=\frac{-14}{35}-\frac{35}{35}-\frac{10}{35}\\=\frac{-14-35-10}{35}\\=\frac{-59}{35}\)
3. \(+\left(\frac{-7}{-3}\right) +\left(\frac{10}{-3}\right) +\left(\frac{9}{-4}\right)\\= \frac{7}{3}- \frac{10}{3}-\frac{9}{4}\\=\frac{28}{12}-\frac{40}{12}-\frac{27}{12}\\=\frac{28-40-27}{12}\\=\frac{-39}{12}\\=\frac{-13}{4}\)
4. \(+\left(\frac{-10}{7}\right) +\left(\frac{8}{-3}\right) +\left(\frac{2}{-5}\right)\\= \frac{-10}{7}- \frac{8}{3}-\frac{2}{5}\\=\frac{-150}{105}-\frac{280}{105}-\frac{42}{105}\\=\frac{-150-280-42}{105}\\=\frac{-472}{105}\)
5. \(-\left(\frac{-10}{-9}\right) -\left(\frac{-6}{7}\right) -\left(\frac{3}{4}\right)\\= \frac{-10}{9}+ \frac{6}{7}-\frac{3}{4}\\=\frac{-280}{252}+\frac{216}{252}-\frac{189}{252}\\=\frac{-280+216-189}{252}\\=\frac{-253}{252}\)
6. \(-\left(\frac{-2}{9}\right) -\left(\frac{6}{6}\right) +\left(\frac{7}{11}\right)\\= \frac{2}{9}- \frac{6}{6}+\frac{7}{11}\\=\frac{2}{9}-\frac{1}{1}+\frac{7}{11}\\=\frac{22}{99}-\frac{99}{99}+\frac{63}{99}\\=\frac{22-99+63}{99}\\=\frac{-14}{99}\)
7. \(-\left(\frac{4}{9}\right) +\left(\frac{3}{10}\right) +\left(\frac{11}{4}\right)\\= \frac{-4}{9}+ \frac{3}{10}+\frac{11}{4}\\=\frac{-80}{180}+\frac{54}{180}+\frac{495}{180}\\=\frac{-80+54+495}{180}\\=\frac{469}{180}\)
8. \(+\left(\frac{-9}{7}\right) -\left(\frac{10}{-2}\right) -\left(\frac{-9}{-4}\right)\\= \frac{-9}{7}+ \frac{10}{2}-\frac{9}{4}\\=\frac{-9}{7}+\frac{5}{1}-\frac{9}{4}\\=\frac{-36}{28}+\frac{140}{28}-\frac{63}{28}\\=\frac{-36+140-63}{28}\\=\frac{41}{28}\)
9. \(-\left(\frac{5}{6}\right) -\left(\frac{-6}{6}\right) -\left(\frac{4}{-11}\right)\\= \frac{-5}{6}+ \frac{6}{6}+\frac{4}{11}\\=\frac{-5}{6}+\frac{1}{1}+\frac{4}{11}\\=\frac{-55}{66}+\frac{66}{66}+\frac{24}{66}\\=\frac{-55+66+24}{66}\\=\frac{35}{66}\)
10. \(-\left(\frac{6}{7}\right) +\left(\frac{4}{3}\right) +\left(\frac{8}{10}\right)\\= \frac{-6}{7}+ \frac{4}{3}+\frac{8}{10}\\=\frac{-6}{7}+\frac{4}{3}+\frac{4}{5}\\=\frac{-90}{105}+\frac{140}{105}+\frac{84}{105}\\=\frac{-90+140+84}{105}\\=\frac{134}{105}\)
11. \(-\left(\frac{-8}{5}\right) +\left(\frac{-5}{6}\right) +\left(\frac{-6}{-3}\right)\\= \frac{8}{5}- \frac{5}{6}+\frac{6}{3}\\=\frac{8}{5}-\frac{5}{6}+\frac{2}{1}\\=\frac{48}{30}-\frac{25}{30}+\frac{60}{30}\\=\frac{48-25+60}{30}\\=\frac{83}{30}\)
12. \(-\left(\frac{2}{7}\right) -\left(\frac{3}{5}\right) -\left(\frac{-10}{2}\right)\\= \frac{-2}{7}- \frac{3}{5}+\frac{10}{2}\\=\frac{-2}{7}-\frac{3}{5}+\frac{5}{1}\\=\frac{-10}{35}-\frac{21}{35}+\frac{175}{35}\\=\frac{-10-21+175}{35}\\=\frac{144}{35}\)