Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{7}\right) -\left(\frac{-9}{-8}\right) -\left(\frac{5}{-12}\right)\\= \frac{9}{7}- \frac{9}{8}+\frac{5}{12}\\=\frac{216}{168}-\frac{189}{168}+\frac{70}{168}\\=\frac{216-189+70}{168}\\=\frac{97}{168}\)
2. \(-\left(\frac{-4}{-3}\right) -\left(\frac{-2}{7}\right) -\left(\frac{-2}{5}\right)\\= \frac{-4}{3}+ \frac{2}{7}+\frac{2}{5}\\=\frac{-140}{105}+\frac{30}{105}+\frac{42}{105}\\=\frac{-140+30+42}{105}\\=\frac{-68}{105}\)
3. \(+\left(\frac{-9}{7}\right) +\left(\frac{4}{5}\right) +\left(\frac{-7}{-12}\right)\\= \frac{-9}{7}+ \frac{4}{5}+\frac{7}{12}\\=\frac{-540}{420}+\frac{336}{420}+\frac{245}{420}\\=\frac{-540+336+245}{420}\\=\frac{41}{420}\)
4. \(+\left(\frac{-9}{-4}\right) -\left(\frac{4}{-4}\right) +\left(\frac{-4}{3}\right)\\= \frac{9}{4}+ \frac{4}{4}-\frac{4}{3}\\=\frac{9}{4}+\frac{1}{1}-\frac{4}{3}\\=\frac{27}{12}+\frac{12}{12}-\frac{16}{12}\\=\frac{27+12-16}{12}\\=\frac{23}{12}\)
5. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-7}{-10}\right) +\left(\frac{2}{6}\right)\\= \frac{3}{2}+ \frac{7}{10}+\frac{2}{6}\\=\frac{3}{2}+\frac{7}{10}+\frac{1}{3}\\=\frac{45}{30}+\frac{21}{30}+\frac{10}{30}\\=\frac{45+21+10}{30}\\=\frac{76}{30}\\=\frac{38}{15}\)
6. \(+\left(\frac{-6}{5}\right) +\left(\frac{10}{2}\right) -\left(\frac{5}{12}\right)\\= \frac{-6}{5}+ \frac{10}{2}-\frac{5}{12}\\=\frac{-6}{5}+\frac{5}{1}-\frac{5}{12}\\=\frac{-72}{60}+\frac{300}{60}-\frac{25}{60}\\=\frac{-72+300-25}{60}\\=\frac{203}{60}\)
7. \(-\left(\frac{-7}{8}\right) -\left(\frac{-2}{-9}\right) +\left(\frac{-10}{7}\right)\\= \frac{7}{8}- \frac{2}{9}-\frac{10}{7}\\=\frac{441}{504}-\frac{112}{504}-\frac{720}{504}\\=\frac{441-112-720}{504}\\=\frac{-391}{504}\)
8. \(-\left(\frac{-9}{-2}\right) +\left(\frac{7}{10}\right) +\left(\frac{-2}{-2}\right)\\= \frac{-9}{2}+ \frac{7}{10}+\frac{2}{2}\\=\frac{-9}{2}+\frac{7}{10}+\frac{1}{1}\\=\frac{-45}{10}+\frac{7}{10}+\frac{10}{10}\\=\frac{-45+7+10}{10}\\=\frac{-28}{10}\\=\frac{-14}{5}\)
9. \(+\left(\frac{-10}{-9}\right) +\left(\frac{-8}{-10}\right) -\left(\frac{-4}{-2}\right)\\= \frac{10}{9}+ \frac{8}{10}-\frac{4}{2}\\=\frac{10}{9}+\frac{4}{5}-\frac{2}{1}\\=\frac{50}{45}+\frac{36}{45}-\frac{90}{45}\\=\frac{50+36-90}{45}\\=\frac{-4}{45}\)
10. \(-\left(\frac{-7}{8}\right) +\left(\frac{9}{6}\right) +\left(\frac{6}{-4}\right)\\= \frac{7}{8}+ \frac{9}{6}-\frac{6}{4}\\=\frac{7}{8}+\frac{3}{2}-\frac{3}{2}\\=\frac{7+3-3}{8}\\=\frac{7}{8}\)
11. \(+\left(\frac{-6}{7}\right) +\left(\frac{-2}{-8}\right) +\left(\frac{4}{6}\right)\\= \frac{-6}{7}+ \frac{2}{8}+\frac{4}{6}\\=\frac{-6}{7}+\frac{1}{4}+\frac{2}{3}\\=\frac{-72}{84}+\frac{21}{84}+\frac{56}{84}\\=\frac{-72+21+56}{84}\\=\frac{5}{84}\)
12. \(-\left(\frac{6}{-5}\right) -\left(\frac{9}{8}\right) -\left(\frac{8}{-6}\right)\\= \frac{6}{5}- \frac{9}{8}+\frac{8}{6}\\=\frac{6}{5}-\frac{9}{8}+\frac{4}{3}\\=\frac{144}{120}-\frac{135}{120}+\frac{160}{120}\\=\frac{144-135+160}{120}\\=\frac{169}{120}\)