Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{3}\right) -\left(\frac{-10}{-6}\right) +\left(\frac{-9}{-2}\right)\\= \frac{-2}{3}- \frac{10}{6}+\frac{9}{2}\\=\frac{-2}{3}-\frac{5}{3}+\frac{9}{2}\\=\frac{-4}{6}-\frac{10}{6}+\frac{27}{6}\\=\frac{-4-10+27}{6}\\=\frac{13}{6}\)
2. \(-\left(\frac{6}{5}\right) -\left(\frac{-7}{-3}\right) -\left(\frac{-7}{5}\right)\\= \frac{-6}{5}- \frac{7}{3}+\frac{7}{5}\\=\frac{-18}{15}-\frac{35}{15}+\frac{21}{15}\\=\frac{-18-35+21}{15}\\=\frac{-32}{15}\)
3. \(+\left(\frac{9}{-2}\right) +\left(\frac{4}{-6}\right) -\left(\frac{-5}{-7}\right)\\= \frac{-9}{2}- \frac{4}{6}-\frac{5}{7}\\=\frac{-9}{2}-\frac{2}{3}-\frac{5}{7}\\=\frac{-189}{42}-\frac{28}{42}-\frac{30}{42}\\=\frac{-189-28-30}{42}\\=\frac{-247}{42}\)
4. \(-\left(\frac{-6}{5}\right) +\left(\frac{7}{6}\right) +\left(\frac{11}{-11}\right)\\= \frac{6}{5}+ \frac{7}{6}-\frac{11}{11}\\=\frac{6}{5}+\frac{7}{6}-\frac{1}{1}\\=\frac{36}{30}+\frac{35}{30}-\frac{30}{30}\\=\frac{36+35-30}{30}\\=\frac{41}{30}\)
5. \(-\left(\frac{-7}{2}\right) +\left(\frac{7}{-7}\right) -\left(\frac{8}{4}\right)\\= \frac{7}{2}- \frac{7}{7}-\frac{8}{4}\\=\frac{7}{2}-\frac{1}{1}-\frac{2}{1}\\=\frac{7-1-2}{2}\\=\frac{4}{2}\\=\frac{2}{1}\)
6. \(+\left(\frac{4}{-3}\right) +\left(\frac{-10}{9}\right) +\left(\frac{11}{4}\right)\\= \frac{-4}{3}- \frac{10}{9}+\frac{11}{4}\\=\frac{-48}{36}-\frac{40}{36}+\frac{99}{36}\\=\frac{-48-40+99}{36}\\=\frac{11}{36}\)
7. \(+\left(\frac{8}{-7}\right) +\left(\frac{-2}{3}\right) +\left(\frac{-3}{-11}\right)\\= \frac{-8}{7}- \frac{2}{3}+\frac{3}{11}\\=\frac{-264}{231}-\frac{154}{231}+\frac{63}{231}\\=\frac{-264-154+63}{231}\\=\frac{-355}{231}\)
8. \(+\left(\frac{4}{-5}\right) -\left(\frac{-8}{-10}\right) -\left(\frac{4}{-10}\right)\\= \frac{-4}{5}- \frac{8}{10}+\frac{4}{10}\\=\frac{-4}{5}-\frac{4}{5}+\frac{2}{5}\\=\frac{-4-4+2}{5}\\=\frac{-6}{5}\)
9. \(+\left(\frac{-4}{-3}\right) -\left(\frac{-6}{-9}\right) +\left(\frac{-6}{-9}\right)\\= \frac{4}{3}- \frac{6}{9}+\frac{6}{9}\\=\frac{4}{3}-\frac{2}{3}+\frac{2}{3}\\=\frac{4-2+2}{3}\\=\frac{4}{3}\)
10. \(+\left(\frac{-2}{9}\right) +\left(\frac{-10}{-2}\right) +\left(\frac{-8}{-2}\right)\\= \frac{-2}{9}+ \frac{10}{2}+\frac{8}{2}\\=\frac{-2}{9}+\frac{5}{1}+\frac{4}{1}\\=\frac{-2+5+4}{9}\\=\frac{7}{9}\)
11. \(+\left(\frac{3}{4}\right) +\left(\frac{-3}{-5}\right) +\left(\frac{9}{4}\right)\\= \frac{3}{4}+ \frac{3}{5}+\frac{9}{4}\\=\frac{15}{20}+\frac{12}{20}+\frac{45}{20}\\=\frac{15+12+45}{20}\\=\frac{72}{20}\\=\frac{18}{5}\)
12. \(+\left(\frac{-5}{-8}\right) +\left(\frac{7}{-10}\right) +\left(\frac{-12}{6}\right)\\= \frac{5}{8}- \frac{7}{10}-\frac{12}{6}\\=\frac{5}{8}-\frac{7}{10}-\frac{2}{1}\\=\frac{25}{40}-\frac{28}{40}-\frac{80}{40}\\=\frac{25-28-80}{40}\\=\frac{-83}{40}\)