Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{5}\right) +\left(\frac{-8}{8}\right) -\left(\frac{6}{-12}\right)\\= \frac{4}{5}- \frac{8}{8}+\frac{6}{12}\\=\frac{4}{5}-\frac{1}{1}+\frac{1}{2}\\=\frac{8}{10}-\frac{10}{10}+\frac{5}{10}\\=\frac{8-10+5}{10}\\=\frac{3}{10}\)
2. \(+\left(\frac{-3}{2}\right) -\left(\frac{2}{8}\right) -\left(\frac{-2}{-6}\right)\\= \frac{-3}{2}- \frac{2}{8}-\frac{2}{6}\\=\frac{-3}{2}-\frac{1}{4}-\frac{1}{3}\\=\frac{-18}{12}-\frac{3}{12}-\frac{4}{12}\\=\frac{-18-3-4}{12}\\=\frac{-25}{12}\)
3. \(+\left(\frac{-10}{-3}\right) -\left(\frac{-6}{-7}\right) +\left(\frac{-6}{12}\right)\\= \frac{10}{3}- \frac{6}{7}-\frac{6}{12}\\=\frac{10}{3}-\frac{6}{7}-\frac{1}{2}\\=\frac{140}{42}-\frac{36}{42}-\frac{21}{42}\\=\frac{140-36-21}{42}\\=\frac{83}{42}\)
4. \(+\left(\frac{-9}{-8}\right) -\left(\frac{2}{-7}\right) +\left(\frac{7}{-8}\right)\\= \frac{9}{8}+ \frac{2}{7}-\frac{7}{8}\\=\frac{63}{56}+\frac{16}{56}-\frac{49}{56}\\=\frac{63+16-49}{56}\\=\frac{30}{56}\\=\frac{15}{28}\)
5. \(-\left(\frac{6}{5}\right) +\left(\frac{2}{-10}\right) -\left(\frac{4}{10}\right)\\= \frac{-6}{5}- \frac{2}{10}-\frac{4}{10}\\=\frac{-6}{5}-\frac{1}{5}-\frac{2}{5}\\=\frac{-6-1-2}{5}\\=\frac{-9}{5}\)
6. \(-\left(\frac{-5}{6}\right) -\left(\frac{-7}{4}\right) +\left(\frac{-3}{10}\right)\\= \frac{5}{6}+ \frac{7}{4}-\frac{3}{10}\\=\frac{50}{60}+\frac{105}{60}-\frac{18}{60}\\=\frac{50+105-18}{60}\\=\frac{137}{60}\)
7. \(+\left(\frac{8}{7}\right) -\left(\frac{-2}{-3}\right) -\left(\frac{-4}{-11}\right)\\= \frac{8}{7}- \frac{2}{3}-\frac{4}{11}\\=\frac{264}{231}-\frac{154}{231}-\frac{84}{231}\\=\frac{264-154-84}{231}\\=\frac{26}{231}\)
8. \(+\left(\frac{5}{-8}\right) -\left(\frac{-5}{-2}\right) +\left(\frac{-6}{-3}\right)\\= \frac{-5}{8}- \frac{5}{2}+\frac{6}{3}\\=\frac{-5}{8}-\frac{5}{2}+\frac{2}{1}\\=\frac{-5-5+2}{8}\\=\frac{-8}{8}\\=\frac{-1}{1}\)
9. \(+\left(\frac{10}{7}\right) +\left(\frac{9}{-10}\right) +\left(\frac{-9}{9}\right)\\= \frac{10}{7}- \frac{9}{10}-\frac{9}{9}\\=\frac{10}{7}-\frac{9}{10}-\frac{1}{1}\\=\frac{100}{70}-\frac{63}{70}-\frac{70}{70}\\=\frac{100-63-70}{70}\\=\frac{-33}{70}\)
10. \(+\left(\frac{10}{3}\right) -\left(\frac{8}{6}\right) +\left(\frac{-9}{-10}\right)\\= \frac{10}{3}- \frac{8}{6}+\frac{9}{10}\\=\frac{10}{3}-\frac{4}{3}+\frac{9}{10}\\=\frac{100}{30}-\frac{40}{30}+\frac{27}{30}\\=\frac{100-40+27}{30}\\=\frac{87}{30}\\=\frac{29}{10}\)
11. \(-\left(\frac{6}{-5}\right) +\left(\frac{-7}{10}\right) +\left(\frac{-2}{-4}\right)\\= \frac{6}{5}- \frac{7}{10}+\frac{2}{4}\\=\frac{6}{5}-\frac{7}{10}+\frac{1}{2}\\=\frac{12}{10}-\frac{7}{10}+\frac{5}{10}\\=\frac{12-7+5}{10}\\=\frac{10}{10}\\=\frac{1}{1}\)
12. \(-\left(\frac{-5}{2}\right) +\left(\frac{8}{-10}\right) +\left(\frac{10}{3}\right)\\= \frac{5}{2}- \frac{8}{10}+\frac{10}{3}\\=\frac{5}{2}-\frac{4}{5}+\frac{10}{3}\\=\frac{75}{30}-\frac{24}{30}+\frac{100}{30}\\=\frac{75-24+100}{30}\\=\frac{151}{30}\)