Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{-2}\right) -\left(\frac{-9}{-3}\right) +\left(\frac{5}{12}\right)\\= \frac{7}{2}- \frac{9}{3}+\frac{5}{12}\\=\frac{7}{2}-\frac{3}{1}+\frac{5}{12}\\=\frac{42}{12}-\frac{36}{12}+\frac{5}{12}\\=\frac{42-36+5}{12}\\=\frac{11}{12}\)
2. \(-\left(\frac{10}{-7}\right) -\left(\frac{6}{4}\right) +\left(\frac{-12}{-3}\right)\\= \frac{10}{7}- \frac{6}{4}+\frac{12}{3}\\=\frac{10}{7}-\frac{3}{2}+\frac{4}{1}\\=\frac{20}{14}-\frac{21}{14}+\frac{56}{14}\\=\frac{20-21+56}{14}\\=\frac{55}{14}\)
3. \(-\left(\frac{4}{-5}\right) +\left(\frac{-5}{-6}\right) +\left(\frac{-6}{5}\right)\\= \frac{4}{5}+ \frac{5}{6}-\frac{6}{5}\\=\frac{24}{30}+\frac{25}{30}-\frac{36}{30}\\=\frac{24+25-36}{30}\\=\frac{13}{30}\)
4. \(+\left(\frac{3}{-2}\right) -\left(\frac{-3}{10}\right) -\left(\frac{-11}{-6}\right)\\= \frac{-3}{2}+ \frac{3}{10}-\frac{11}{6}\\=\frac{-45}{30}+\frac{9}{30}-\frac{55}{30}\\=\frac{-45+9-55}{30}\\=\frac{-91}{30}\)
5. \(-\left(\frac{-4}{5}\right) +\left(\frac{-6}{-7}\right) -\left(\frac{10}{-10}\right)\\= \frac{4}{5}+ \frac{6}{7}+\frac{10}{10}\\=\frac{4}{5}+\frac{6}{7}+\frac{1}{1}\\=\frac{28}{35}+\frac{30}{35}+\frac{35}{35}\\=\frac{28+30+35}{35}\\=\frac{93}{35}\)
6. \(+\left(\frac{9}{5}\right) +\left(\frac{3}{6}\right) +\left(\frac{-9}{11}\right)\\= \frac{9}{5}+ \frac{3}{6}-\frac{9}{11}\\=\frac{9}{5}+\frac{1}{2}-\frac{9}{11}\\=\frac{198}{110}+\frac{55}{110}-\frac{90}{110}\\=\frac{198+55-90}{110}\\=\frac{163}{110}\)
7. \(+\left(\frac{-4}{-5}\right) -\left(\frac{6}{-3}\right) -\left(\frac{-2}{8}\right)\\= \frac{4}{5}+ \frac{6}{3}+\frac{2}{8}\\=\frac{4}{5}+\frac{2}{1}+\frac{1}{4}\\=\frac{16}{20}+\frac{40}{20}+\frac{5}{20}\\=\frac{16+40+5}{20}\\=\frac{61}{20}\)
8. \(+\left(\frac{-7}{-6}\right) +\left(\frac{-10}{-10}\right) +\left(\frac{-7}{-12}\right)\\= \frac{7}{6}+ \frac{10}{10}+\frac{7}{12}\\=\frac{7}{6}+\frac{1}{1}+\frac{7}{12}\\=\frac{14}{12}+\frac{12}{12}+\frac{7}{12}\\=\frac{14+12+7}{12}\\=\frac{33}{12}\\=\frac{11}{4}\)
9. \(-\left(\frac{-7}{-3}\right) +\left(\frac{-8}{10}\right) -\left(\frac{3}{-3}\right)\\= \frac{-7}{3}- \frac{8}{10}+\frac{3}{3}\\=\frac{-7}{3}-\frac{4}{5}+\frac{1}{1}\\=\frac{-35}{15}-\frac{12}{15}+\frac{15}{15}\\=\frac{-35-12+15}{15}\\=\frac{-32}{15}\)
10. \(-\left(\frac{4}{-7}\right) +\left(\frac{-7}{5}\right) -\left(\frac{-11}{-11}\right)\\= \frac{4}{7}- \frac{7}{5}-\frac{11}{11}\\=\frac{4}{7}-\frac{7}{5}-\frac{1}{1}\\=\frac{20}{35}-\frac{49}{35}-\frac{35}{35}\\=\frac{20-49-35}{35}\\=\frac{-64}{35}\)
11. \(+\left(\frac{2}{9}\right) -\left(\frac{9}{-6}\right) -\left(\frac{-8}{-9}\right)\\= \frac{2}{9}+ \frac{9}{6}-\frac{8}{9}\\=\frac{2}{9}+\frac{3}{2}-\frac{8}{9}\\=\frac{4}{18}+\frac{27}{18}-\frac{16}{18}\\=\frac{4+27-16}{18}\\=\frac{15}{18}\\=\frac{5}{6}\)
12. \(+\left(\frac{-8}{-3}\right) -\left(\frac{6}{-10}\right) -\left(\frac{3}{4}\right)\\= \frac{8}{3}+ \frac{6}{10}-\frac{3}{4}\\=\frac{8}{3}+\frac{3}{5}-\frac{3}{4}\\=\frac{160}{60}+\frac{36}{60}-\frac{45}{60}\\=\frac{160+36-45}{60}\\=\frac{151}{60}\)