Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{-2}\right) +\left(\frac{2}{-4}\right) -\left(\frac{5}{6}\right)\\= \frac{3}{2}- \frac{2}{4}-\frac{5}{6}\\=\frac{3}{2}-\frac{1}{2}-\frac{5}{6}\\=\frac{9}{6}-\frac{3}{6}-\frac{5}{6}\\=\frac{9-3-5}{6}\\=\frac{1}{6}\)
2. \(+\left(\frac{-5}{2}\right) +\left(\frac{-6}{-5}\right) +\left(\frac{-7}{8}\right)\\= \frac{-5}{2}+ \frac{6}{5}-\frac{7}{8}\\=\frac{-100}{40}+\frac{48}{40}-\frac{35}{40}\\=\frac{-100+48-35}{40}\\=\frac{-87}{40}\)
3. \(+\left(\frac{-3}{-4}\right) +\left(\frac{3}{-2}\right) +\left(\frac{-12}{-11}\right)\\= \frac{3}{4}- \frac{3}{2}+\frac{12}{11}\\=\frac{33}{44}-\frac{66}{44}+\frac{48}{44}\\=\frac{33-66+48}{44}\\=\frac{15}{44}\)
4. \(+\left(\frac{4}{-9}\right) -\left(\frac{3}{-8}\right) +\left(\frac{12}{-5}\right)\\= \frac{-4}{9}+ \frac{3}{8}-\frac{12}{5}\\=\frac{-160}{360}+\frac{135}{360}-\frac{864}{360}\\=\frac{-160+135-864}{360}\\=\frac{-889}{360}\)
5. \(+\left(\frac{-4}{-3}\right) -\left(\frac{5}{8}\right) -\left(\frac{11}{3}\right)\\= \frac{4}{3}- \frac{5}{8}-\frac{11}{3}\\=\frac{32}{24}-\frac{15}{24}-\frac{88}{24}\\=\frac{32-15-88}{24}\\=\frac{-71}{24}\)
6. \(+\left(\frac{2}{3}\right) -\left(\frac{5}{2}\right) +\left(\frac{-3}{7}\right)\\= \frac{2}{3}- \frac{5}{2}-\frac{3}{7}\\=\frac{28}{42}-\frac{105}{42}-\frac{18}{42}\\=\frac{28-105-18}{42}\\=\frac{-95}{42}\)
7. \(-\left(\frac{3}{-8}\right) -\left(\frac{6}{9}\right) -\left(\frac{-8}{10}\right)\\= \frac{3}{8}- \frac{6}{9}+\frac{8}{10}\\=\frac{3}{8}-\frac{2}{3}+\frac{4}{5}\\=\frac{45}{120}-\frac{80}{120}+\frac{96}{120}\\=\frac{45-80+96}{120}\\=\frac{61}{120}\)
8. \(-\left(\frac{8}{-3}\right) -\left(\frac{8}{3}\right) -\left(\frac{2}{3}\right)\\= \frac{8}{3}- \frac{8}{3}-\frac{2}{3}\\=\frac{8-8-2}{3}\\=\frac{-2}{3}\)
9. \(-\left(\frac{-2}{-7}\right) -\left(\frac{10}{7}\right) +\left(\frac{3}{-10}\right)\\= \frac{-2}{7}- \frac{10}{7}-\frac{3}{10}\\=\frac{-20}{70}-\frac{100}{70}-\frac{21}{70}\\=\frac{-20-100-21}{70}\\=\frac{-141}{70}\)
10. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-4}{3}\right) -\left(\frac{-11}{-7}\right)\\= \frac{-6}{5}- \frac{4}{3}-\frac{11}{7}\\=\frac{-126}{105}-\frac{140}{105}-\frac{165}{105}\\=\frac{-126-140-165}{105}\\=\frac{-431}{105}\)
11. \(+\left(\frac{-5}{2}\right) +\left(\frac{-9}{-5}\right) -\left(\frac{3}{6}\right)\\= \frac{-5}{2}+ \frac{9}{5}-\frac{3}{6}\\=\frac{-5}{2}+\frac{9}{5}-\frac{1}{2}\\=\frac{-25}{10}+\frac{18}{10}-\frac{5}{10}\\=\frac{-25+18-5}{10}\\=\frac{-12}{10}\\=\frac{-6}{5}\)
12. \(-\left(\frac{8}{-7}\right) +\left(\frac{4}{4}\right) +\left(\frac{-2}{12}\right)\\= \frac{8}{7}+ \frac{4}{4}-\frac{2}{12}\\=\frac{8}{7}+\frac{1}{1}-\frac{1}{6}\\=\frac{48}{42}+\frac{42}{42}-\frac{7}{42}\\=\frac{48+42-7}{42}\\=\frac{83}{42}\)