Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{-5}\right) -\left(\frac{3}{-5}\right) -\left(\frac{4}{-3}\right)\\= \frac{8}{5}+ \frac{3}{5}+\frac{4}{3}\\=\frac{24}{15}+\frac{9}{15}+\frac{20}{15}\\=\frac{24+9+20}{15}\\=\frac{53}{15}\)
2. \(+\left(\frac{5}{7}\right) -\left(\frac{6}{-5}\right) -\left(\frac{12}{6}\right)\\= \frac{5}{7}+ \frac{6}{5}-\frac{12}{6}\\=\frac{5}{7}+\frac{6}{5}-\frac{2}{1}\\=\frac{25}{35}+\frac{42}{35}-\frac{70}{35}\\=\frac{25+42-70}{35}\\=\frac{-3}{35}\)
3. \(+\left(\frac{7}{4}\right) +\left(\frac{-3}{-4}\right) -\left(\frac{7}{-2}\right)\\= \frac{7}{4}+ \frac{3}{4}+\frac{7}{2}\\=\frac{7+3+7}{4}\\=\frac{17}{4}\)
4. \(+\left(\frac{-2}{-9}\right) -\left(\frac{2}{-3}\right) -\left(\frac{5}{-11}\right)\\= \frac{2}{9}+ \frac{2}{3}+\frac{5}{11}\\=\frac{22}{99}+\frac{66}{99}+\frac{45}{99}\\=\frac{22+66+45}{99}\\=\frac{133}{99}\)
5. \(-\left(\frac{4}{-7}\right) +\left(\frac{10}{7}\right) +\left(\frac{-12}{2}\right)\\= \frac{4}{7}+ \frac{10}{7}-\frac{12}{2}\\=\frac{4}{7}+\frac{10}{7}-\frac{6}{1}\\=\frac{4+10-6}{7}\\=\frac{8}{7}\)
6. \(-\left(\frac{-3}{-2}\right) -\left(\frac{-5}{-2}\right) -\left(\frac{-3}{-7}\right)\\= \frac{-3}{2}- \frac{5}{2}-\frac{3}{7}\\=\frac{-21}{14}-\frac{35}{14}-\frac{6}{14}\\=\frac{-21-35-6}{14}\\=\frac{-62}{14}\\=\frac{-31}{7}\)
7. \(-\left(\frac{2}{-3}\right) -\left(\frac{-9}{-3}\right) +\left(\frac{6}{9}\right)\\= \frac{2}{3}- \frac{9}{3}+\frac{6}{9}\\=\frac{2}{3}-\frac{3}{1}+\frac{2}{3}\\=\frac{2-3+2}{3}\\=\frac{1}{3}\)
8. \(-\left(\frac{-4}{-3}\right) +\left(\frac{10}{-4}\right) -\left(\frac{2}{11}\right)\\= \frac{-4}{3}- \frac{10}{4}-\frac{2}{11}\\=\frac{-4}{3}-\frac{5}{2}-\frac{2}{11}\\=\frac{-88}{66}-\frac{165}{66}-\frac{12}{66}\\=\frac{-88-165-12}{66}\\=\frac{-265}{66}\)
9. \(-\left(\frac{-4}{-3}\right) +\left(\frac{-10}{5}\right) +\left(\frac{-11}{11}\right)\\= \frac{-4}{3}- \frac{10}{5}-\frac{11}{11}\\=\frac{-4}{3}-\frac{2}{1}-\frac{1}{1}\\=\frac{-4-2-1}{3}\\=\frac{-7}{3}\)
10. \(+\left(\frac{-2}{-3}\right) -\left(\frac{9}{5}\right) +\left(\frac{-5}{12}\right)\\= \frac{2}{3}- \frac{9}{5}-\frac{5}{12}\\=\frac{40}{60}-\frac{108}{60}-\frac{25}{60}\\=\frac{40-108-25}{60}\\=\frac{-93}{60}\\=\frac{-31}{20}\)
11. \(+\left(\frac{-3}{-8}\right) -\left(\frac{-8}{-6}\right) +\left(\frac{-12}{8}\right)\\= \frac{3}{8}- \frac{8}{6}-\frac{12}{8}\\=\frac{3}{8}-\frac{4}{3}-\frac{3}{2}\\=\frac{9}{24}-\frac{32}{24}-\frac{36}{24}\\=\frac{9-32-36}{24}\\=\frac{-59}{24}\)
12. \(-\left(\frac{6}{-5}\right) +\left(\frac{2}{5}\right) +\left(\frac{-10}{3}\right)\\= \frac{6}{5}+ \frac{2}{5}-\frac{10}{3}\\=\frac{18}{15}+\frac{6}{15}-\frac{50}{15}\\=\frac{18+6-50}{15}\\=\frac{-26}{15}\)