Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{-7}\right) +\left(\frac{10}{9}\right) +\left(\frac{8}{-10}\right)\\= \frac{9}{7}+ \frac{10}{9}-\frac{8}{10}\\=\frac{9}{7}+\frac{10}{9}-\frac{4}{5}\\=\frac{405}{315}+\frac{350}{315}-\frac{252}{315}\\=\frac{405+350-252}{315}\\=\frac{503}{315}\)
2. \(+\left(\frac{-7}{-2}\right) -\left(\frac{4}{3}\right) +\left(\frac{10}{-7}\right)\\= \frac{7}{2}- \frac{4}{3}-\frac{10}{7}\\=\frac{147}{42}-\frac{56}{42}-\frac{60}{42}\\=\frac{147-56-60}{42}\\=\frac{31}{42}\)
3. \(+\left(\frac{-7}{5}\right) +\left(\frac{-3}{-6}\right) -\left(\frac{-6}{2}\right)\\= \frac{-7}{5}+ \frac{3}{6}+\frac{6}{2}\\=\frac{-7}{5}+\frac{1}{2}+\frac{3}{1}\\=\frac{-14}{10}+\frac{5}{10}+\frac{30}{10}\\=\frac{-14+5+30}{10}\\=\frac{21}{10}\)
4. \(-\left(\frac{8}{-3}\right) +\left(\frac{-9}{2}\right) +\left(\frac{8}{-8}\right)\\= \frac{8}{3}- \frac{9}{2}-\frac{8}{8}\\=\frac{8}{3}-\frac{9}{2}-\frac{1}{1}\\=\frac{16}{6}-\frac{27}{6}-\frac{6}{6}\\=\frac{16-27-6}{6}\\=\frac{-17}{6}\)
5. \(+\left(\frac{4}{3}\right) +\left(\frac{-5}{-4}\right) +\left(\frac{11}{-7}\right)\\= \frac{4}{3}+ \frac{5}{4}-\frac{11}{7}\\=\frac{112}{84}+\frac{105}{84}-\frac{132}{84}\\=\frac{112+105-132}{84}\\=\frac{85}{84}\)
6. \(-\left(\frac{9}{2}\right) -\left(\frac{2}{8}\right) +\left(\frac{-11}{-10}\right)\\= \frac{-9}{2}- \frac{2}{8}+\frac{11}{10}\\=\frac{-9}{2}-\frac{1}{4}+\frac{11}{10}\\=\frac{-90}{20}-\frac{5}{20}+\frac{22}{20}\\=\frac{-90-5+22}{20}\\=\frac{-73}{20}\)
7. \(+\left(\frac{4}{5}\right) -\left(\frac{-5}{-2}\right) +\left(\frac{-8}{12}\right)\\= \frac{4}{5}- \frac{5}{2}-\frac{8}{12}\\=\frac{4}{5}-\frac{5}{2}-\frac{2}{3}\\=\frac{24}{30}-\frac{75}{30}-\frac{20}{30}\\=\frac{24-75-20}{30}\\=\frac{-71}{30}\)
8. \(+\left(\frac{7}{9}\right) +\left(\frac{-5}{10}\right) +\left(\frac{6}{-6}\right)\\= \frac{7}{9}- \frac{5}{10}-\frac{6}{6}\\=\frac{7}{9}-\frac{1}{2}-\frac{1}{1}\\=\frac{14}{18}-\frac{9}{18}-\frac{18}{18}\\=\frac{14-9-18}{18}\\=\frac{-13}{18}\)
9. \(+\left(\frac{5}{-3}\right) -\left(\frac{-2}{-7}\right) +\left(\frac{-3}{-2}\right)\\= \frac{-5}{3}- \frac{2}{7}+\frac{3}{2}\\=\frac{-70}{42}-\frac{12}{42}+\frac{63}{42}\\=\frac{-70-12+63}{42}\\=\frac{-19}{42}\)
10. \(-\left(\frac{6}{7}\right) -\left(\frac{8}{-8}\right) -\left(\frac{7}{3}\right)\\= \frac{-6}{7}+ \frac{8}{8}-\frac{7}{3}\\=\frac{-6}{7}+\frac{1}{1}-\frac{7}{3}\\=\frac{-18}{21}+\frac{21}{21}-\frac{49}{21}\\=\frac{-18+21-49}{21}\\=\frac{-46}{21}\)
11. \(+\left(\frac{-5}{-9}\right) +\left(\frac{-8}{-2}\right) -\left(\frac{-9}{12}\right)\\= \frac{5}{9}+ \frac{8}{2}+\frac{9}{12}\\=\frac{5}{9}+\frac{4}{1}+\frac{3}{4}\\=\frac{20}{36}+\frac{144}{36}+\frac{27}{36}\\=\frac{20+144+27}{36}\\=\frac{191}{36}\)
12. \(+\left(\frac{8}{3}\right) -\left(\frac{-5}{-6}\right) +\left(\frac{8}{10}\right)\\= \frac{8}{3}- \frac{5}{6}+\frac{8}{10}\\=\frac{8}{3}-\frac{5}{6}+\frac{4}{5}\\=\frac{80}{30}-\frac{25}{30}+\frac{24}{30}\\=\frac{80-25+24}{30}\\=\frac{79}{30}\)