Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{3}\right) +\left(\frac{-3}{-8}\right) +\left(\frac{2}{-3}\right)\\= \frac{-4}{3}+ \frac{3}{8}-\frac{2}{3}\\=\frac{-32}{24}+\frac{9}{24}-\frac{16}{24}\\=\frac{-32+9-16}{24}\\=\frac{-39}{24}\\=\frac{-13}{8}\)
2. \(+\left(\frac{-8}{-3}\right) -\left(\frac{-7}{-5}\right) -\left(\frac{-4}{10}\right)\\= \frac{8}{3}- \frac{7}{5}+\frac{4}{10}\\=\frac{8}{3}-\frac{7}{5}+\frac{2}{5}\\=\frac{40}{15}-\frac{21}{15}+\frac{6}{15}\\=\frac{40-21+6}{15}\\=\frac{25}{15}\\=\frac{5}{3}\)
3. \(-\left(\frac{7}{-5}\right) +\left(\frac{9}{-6}\right) +\left(\frac{-11}{-11}\right)\\= \frac{7}{5}- \frac{9}{6}+\frac{11}{11}\\=\frac{7}{5}-\frac{3}{2}+\frac{1}{1}\\=\frac{14}{10}-\frac{15}{10}+\frac{10}{10}\\=\frac{14-15+10}{10}\\=\frac{9}{10}\)
4. \(+\left(\frac{-9}{-2}\right) +\left(\frac{-5}{-8}\right) +\left(\frac{9}{-3}\right)\\= \frac{9}{2}+ \frac{5}{8}-\frac{9}{3}\\=\frac{9}{2}+\frac{5}{8}-\frac{3}{1}\\=\frac{36}{8}+\frac{5}{8}-\frac{24}{8}\\=\frac{36+5-24}{8}\\=\frac{17}{8}\)
5. \(-\left(\frac{-9}{-8}\right) +\left(\frac{3}{-4}\right) +\left(\frac{-6}{-3}\right)\\= \frac{-9}{8}- \frac{3}{4}+\frac{6}{3}\\=\frac{-9}{8}-\frac{3}{4}+\frac{2}{1}\\=\frac{-9-3+2}{8}\\=\frac{-10}{8}\\=\frac{-5}{4}\)
6. \(+\left(\frac{3}{-8}\right) +\left(\frac{-5}{-6}\right) +\left(\frac{4}{-11}\right)\\= \frac{-3}{8}+ \frac{5}{6}-\frac{4}{11}\\=\frac{-99}{264}+\frac{220}{264}-\frac{96}{264}\\=\frac{-99+220-96}{264}\\=\frac{25}{264}\)
7. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-10}{3}\right) +\left(\frac{-3}{4}\right)\\= \frac{-6}{5}- \frac{10}{3}-\frac{3}{4}\\=\frac{-72}{60}-\frac{200}{60}-\frac{45}{60}\\=\frac{-72-200-45}{60}\\=\frac{-317}{60}\)
8. \(-\left(\frac{6}{-5}\right) +\left(\frac{-10}{-8}\right) +\left(\frac{-2}{-6}\right)\\= \frac{6}{5}+ \frac{10}{8}+\frac{2}{6}\\=\frac{6}{5}+\frac{5}{4}+\frac{1}{3}\\=\frac{72}{60}+\frac{75}{60}+\frac{20}{60}\\=\frac{72+75+20}{60}\\=\frac{167}{60}\)
9. \(+\left(\frac{5}{-7}\right) +\left(\frac{2}{-6}\right) +\left(\frac{3}{11}\right)\\= \frac{-5}{7}- \frac{2}{6}+\frac{3}{11}\\=\frac{-5}{7}-\frac{1}{3}+\frac{3}{11}\\=\frac{-165}{231}-\frac{77}{231}+\frac{63}{231}\\=\frac{-165-77+63}{231}\\=\frac{-179}{231}\)
10. \(-\left(\frac{-4}{-3}\right) +\left(\frac{-2}{-4}\right) +\left(\frac{4}{-4}\right)\\= \frac{-4}{3}+ \frac{2}{4}-\frac{4}{4}\\=\frac{-4}{3}+\frac{1}{2}-\frac{1}{1}\\=\frac{-8}{6}+\frac{3}{6}-\frac{6}{6}\\=\frac{-8+3-6}{6}\\=\frac{-11}{6}\)
11. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-4}{-10}\right) +\left(\frac{-5}{-8}\right)\\= \frac{-6}{5}+ \frac{4}{10}+\frac{5}{8}\\=\frac{-6}{5}+\frac{2}{5}+\frac{5}{8}\\=\frac{-48}{40}+\frac{16}{40}+\frac{25}{40}\\=\frac{-48+16+25}{40}\\=\frac{-7}{40}\)
12. \(+\left(\frac{-4}{3}\right) +\left(\frac{-3}{4}\right) -\left(\frac{-9}{5}\right)\\= \frac{-4}{3}- \frac{3}{4}+\frac{9}{5}\\=\frac{-80}{60}-\frac{45}{60}+\frac{108}{60}\\=\frac{-80-45+108}{60}\\=\frac{-17}{60}\)