Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{2}\right) +\left(\frac{2}{-8}\right) -\left(\frac{-5}{-6}\right)\\= \frac{-5}{2}- \frac{2}{8}-\frac{5}{6}\\=\frac{-5}{2}-\frac{1}{4}-\frac{5}{6}\\=\frac{-30}{12}-\frac{3}{12}-\frac{10}{12}\\=\frac{-30-3-10}{12}\\=\frac{-43}{12}\)
2. \(-\left(\frac{-2}{-7}\right) -\left(\frac{10}{8}\right) -\left(\frac{10}{5}\right)\\= \frac{-2}{7}- \frac{10}{8}-\frac{10}{5}\\=\frac{-2}{7}-\frac{5}{4}-\frac{2}{1}\\=\frac{-8}{28}-\frac{35}{28}-\frac{56}{28}\\=\frac{-8-35-56}{28}\\=\frac{-99}{28}\)
3. \(+\left(\frac{4}{-7}\right) -\left(\frac{9}{-8}\right) +\left(\frac{-6}{-3}\right)\\= \frac{-4}{7}+ \frac{9}{8}+\frac{6}{3}\\=\frac{-4}{7}+\frac{9}{8}+\frac{2}{1}\\=\frac{-32}{56}+\frac{63}{56}+\frac{112}{56}\\=\frac{-32+63+112}{56}\\=\frac{143}{56}\)
4. \(+\left(\frac{-6}{7}\right) -\left(\frac{7}{3}\right) +\left(\frac{11}{10}\right)\\= \frac{-6}{7}- \frac{7}{3}+\frac{11}{10}\\=\frac{-180}{210}-\frac{490}{210}+\frac{231}{210}\\=\frac{-180-490+231}{210}\\=\frac{-439}{210}\)
5. \(-\left(\frac{3}{8}\right) -\left(\frac{-3}{-5}\right) +\left(\frac{10}{4}\right)\\= \frac{-3}{8}- \frac{3}{5}+\frac{10}{4}\\=\frac{-3}{8}-\frac{3}{5}+\frac{5}{2}\\=\frac{-15}{40}-\frac{24}{40}+\frac{100}{40}\\=\frac{-15-24+100}{40}\\=\frac{61}{40}\)
6. \(-\left(\frac{-9}{4}\right) -\left(\frac{10}{5}\right) -\left(\frac{2}{8}\right)\\= \frac{9}{4}- \frac{10}{5}-\frac{2}{8}\\=\frac{9}{4}-\frac{2}{1}-\frac{1}{4}\\=\frac{9-2-1}{4}\\=\frac{6}{4}\\=\frac{3}{2}\)
7. \(+\left(\frac{-8}{-3}\right) -\left(\frac{8}{-6}\right) -\left(\frac{-6}{-3}\right)\\= \frac{8}{3}+ \frac{8}{6}-\frac{6}{3}\\=\frac{8}{3}+\frac{4}{3}-\frac{2}{1}\\=\frac{8+4-2}{3}\\=\frac{10}{3}\)
8. \(-\left(\frac{-5}{-8}\right) -\left(\frac{-8}{10}\right) -\left(\frac{10}{-10}\right)\\= \frac{-5}{8}+ \frac{8}{10}+\frac{10}{10}\\=\frac{-5}{8}+\frac{4}{5}+\frac{1}{1}\\=\frac{-25}{40}+\frac{32}{40}+\frac{40}{40}\\=\frac{-25+32+40}{40}\\=\frac{47}{40}\)
9. \(+\left(\frac{-7}{5}\right) +\left(\frac{9}{-2}\right) -\left(\frac{8}{8}\right)\\= \frac{-7}{5}- \frac{9}{2}-\frac{8}{8}\\=\frac{-7}{5}-\frac{9}{2}-\frac{1}{1}\\=\frac{-14}{10}-\frac{45}{10}-\frac{10}{10}\\=\frac{-14-45-10}{10}\\=\frac{-69}{10}\)
10. \(-\left(\frac{10}{-7}\right) +\left(\frac{3}{-6}\right) +\left(\frac{-3}{8}\right)\\= \frac{10}{7}- \frac{3}{6}-\frac{3}{8}\\=\frac{10}{7}-\frac{1}{2}-\frac{3}{8}\\=\frac{80}{56}-\frac{28}{56}-\frac{21}{56}\\=\frac{80-28-21}{56}\\=\frac{31}{56}\)
11. \(-\left(\frac{7}{6}\right) -\left(\frac{-10}{9}\right) +\left(\frac{8}{-7}\right)\\= \frac{-7}{6}+ \frac{10}{9}-\frac{8}{7}\\=\frac{-147}{126}+\frac{140}{126}-\frac{144}{126}\\=\frac{-147+140-144}{126}\\=\frac{-151}{126}\)
12. \(+\left(\frac{-2}{5}\right) +\left(\frac{-8}{-3}\right) +\left(\frac{-6}{3}\right)\\= \frac{-2}{5}+ \frac{8}{3}-\frac{6}{3}\\=\frac{-2}{5}+\frac{8}{3}-\frac{2}{1}\\=\frac{-6}{15}+\frac{40}{15}-\frac{30}{15}\\=\frac{-6+40-30}{15}\\=\frac{4}{15}\)