Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{-9}\right) -\left(\frac{10}{2}\right) -\left(\frac{-4}{-2}\right)\\= \frac{-2}{9}- \frac{10}{2}-\frac{4}{2}\\=\frac{-2}{9}-\frac{5}{1}-\frac{2}{1}\\=\frac{-2-5-2}{9}\\=\frac{-9}{9}\\=\frac{-1}{1}\)
2. \(+\left(\frac{-6}{5}\right) -\left(\frac{4}{-10}\right) +\left(\frac{3}{-5}\right)\\= \frac{-6}{5}+ \frac{4}{10}-\frac{3}{5}\\=\frac{-6}{5}+\frac{2}{5}-\frac{3}{5}\\=\frac{-6+2-3}{5}\\=\frac{-7}{5}\)
3. \(-\left(\frac{-2}{7}\right) +\left(\frac{5}{-2}\right) +\left(\frac{-11}{-8}\right)\\= \frac{2}{7}- \frac{5}{2}+\frac{11}{8}\\=\frac{16}{56}-\frac{140}{56}+\frac{77}{56}\\=\frac{16-140+77}{56}\\=\frac{-47}{56}\)
4. \(-\left(\frac{5}{-2}\right) +\left(\frac{-5}{-8}\right) -\left(\frac{-3}{6}\right)\\= \frac{5}{2}+ \frac{5}{8}+\frac{3}{6}\\=\frac{5}{2}+\frac{5}{8}+\frac{1}{2}\\=\frac{20}{8}+\frac{5}{8}+\frac{4}{8}\\=\frac{20+5+4}{8}\\=\frac{29}{8}\)
5. \(+\left(\frac{3}{-7}\right) +\left(\frac{2}{3}\right) +\left(\frac{4}{5}\right)\\= \frac{-3}{7}+ \frac{2}{3}+\frac{4}{5}\\=\frac{-45}{105}+\frac{70}{105}+\frac{84}{105}\\=\frac{-45+70+84}{105}\\=\frac{109}{105}\)
6. \(+\left(\frac{-2}{-3}\right) -\left(\frac{6}{-5}\right) +\left(\frac{-6}{4}\right)\\= \frac{2}{3}+ \frac{6}{5}-\frac{6}{4}\\=\frac{2}{3}+\frac{6}{5}-\frac{3}{2}\\=\frac{20}{30}+\frac{36}{30}-\frac{45}{30}\\=\frac{20+36-45}{30}\\=\frac{11}{30}\)
7. \(+\left(\frac{4}{5}\right) +\left(\frac{-7}{5}\right) -\left(\frac{-11}{-9}\right)\\= \frac{4}{5}- \frac{7}{5}-\frac{11}{9}\\=\frac{36}{45}-\frac{63}{45}-\frac{55}{45}\\=\frac{36-63-55}{45}\\=\frac{-82}{45}\)
8. \(-\left(\frac{-7}{-9}\right) +\left(\frac{4}{-3}\right) +\left(\frac{10}{-7}\right)\\= \frac{-7}{9}- \frac{4}{3}-\frac{10}{7}\\=\frac{-49}{63}-\frac{84}{63}-\frac{90}{63}\\=\frac{-49-84-90}{63}\\=\frac{-223}{63}\)
9. \(+\left(\frac{6}{-7}\right) +\left(\frac{-10}{10}\right) -\left(\frac{12}{6}\right)\\= \frac{-6}{7}- \frac{10}{10}-\frac{12}{6}\\=\frac{-6}{7}-\frac{1}{1}-\frac{2}{1}\\=\frac{-6-1-2}{7}\\=\frac{-9}{7}\)
10. \(+\left(\frac{7}{-3}\right) +\left(\frac{-2}{5}\right) +\left(\frac{11}{-4}\right)\\= \frac{-7}{3}- \frac{2}{5}-\frac{11}{4}\\=\frac{-140}{60}-\frac{24}{60}-\frac{165}{60}\\=\frac{-140-24-165}{60}\\=\frac{-329}{60}\)
11. \(+\left(\frac{7}{-6}\right) +\left(\frac{-6}{-8}\right) -\left(\frac{-8}{-12}\right)\\= \frac{-7}{6}+ \frac{6}{8}-\frac{8}{12}\\=\frac{-7}{6}+\frac{3}{4}-\frac{2}{3}\\=\frac{-14}{12}+\frac{9}{12}-\frac{8}{12}\\=\frac{-14+9-8}{12}\\=\frac{-13}{12}\)
12. \(-\left(\frac{-5}{7}\right) -\left(\frac{-7}{-10}\right) +\left(\frac{-8}{-10}\right)\\= \frac{5}{7}- \frac{7}{10}+\frac{8}{10}\\=\frac{5}{7}-\frac{7}{10}+\frac{4}{5}\\=\frac{50}{70}-\frac{49}{70}+\frac{56}{70}\\=\frac{50-49+56}{70}\\=\frac{57}{70}\)