Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{8}{5}\right) -\left(\frac{-3}{2}\right) -\left(\frac{7}{9}\right)\\= \frac{8}{5}+ \frac{3}{2}-\frac{7}{9}\\=\frac{144}{90}+\frac{135}{90}-\frac{70}{90}\\=\frac{144+135-70}{90}\\=\frac{209}{90}\)
2. \(-\left(\frac{-9}{7}\right) +\left(\frac{-8}{-10}\right) -\left(\frac{9}{-7}\right)\\= \frac{9}{7}+ \frac{8}{10}+\frac{9}{7}\\=\frac{9}{7}+\frac{4}{5}+\frac{9}{7}\\=\frac{45}{35}+\frac{28}{35}+\frac{45}{35}\\=\frac{45+28+45}{35}\\=\frac{118}{35}\)
3. \(+\left(\frac{4}{7}\right) +\left(\frac{-10}{-2}\right) -\left(\frac{11}{11}\right)\\= \frac{4}{7}+ \frac{10}{2}-\frac{11}{11}\\=\frac{4}{7}+\frac{5}{1}-\frac{1}{1}\\=\frac{4+5-1}{7}\\=\frac{8}{7}\)
4. \(-\left(\frac{-6}{5}\right) -\left(\frac{-2}{-2}\right) +\left(\frac{11}{12}\right)\\= \frac{6}{5}- \frac{2}{2}+\frac{11}{12}\\=\frac{6}{5}-\frac{1}{1}+\frac{11}{12}\\=\frac{72}{60}-\frac{60}{60}+\frac{55}{60}\\=\frac{72-60+55}{60}\\=\frac{67}{60}\)
5. \(-\left(\frac{-5}{-8}\right) -\left(\frac{7}{3}\right) +\left(\frac{5}{8}\right)\\= \frac{-5}{8}- \frac{7}{3}+\frac{5}{8}\\=\frac{-15}{24}-\frac{56}{24}+\frac{15}{24}\\=\frac{-15-56+15}{24}\\=\frac{-56}{24}\\=\frac{-7}{3}\)
6. \(+\left(\frac{-4}{-3}\right) +\left(\frac{-7}{4}\right) +\left(\frac{-4}{2}\right)\\= \frac{4}{3}- \frac{7}{4}-\frac{4}{2}\\=\frac{4}{3}-\frac{7}{4}-\frac{2}{1}\\=\frac{16}{12}-\frac{21}{12}-\frac{24}{12}\\=\frac{16-21-24}{12}\\=\frac{-29}{12}\)
7. \(-\left(\frac{-2}{-7}\right) -\left(\frac{-5}{10}\right) +\left(\frac{-8}{-8}\right)\\= \frac{-2}{7}+ \frac{5}{10}+\frac{8}{8}\\=\frac{-2}{7}+\frac{1}{2}+\frac{1}{1}\\=\frac{-4}{14}+\frac{7}{14}+\frac{14}{14}\\=\frac{-4+7+14}{14}\\=\frac{17}{14}\)
8. \(-\left(\frac{-5}{6}\right) +\left(\frac{-7}{5}\right) +\left(\frac{10}{9}\right)\\= \frac{5}{6}- \frac{7}{5}+\frac{10}{9}\\=\frac{75}{90}-\frac{126}{90}+\frac{100}{90}\\=\frac{75-126+100}{90}\\=\frac{49}{90}\)
9. \(-\left(\frac{-2}{5}\right) +\left(\frac{-6}{5}\right) -\left(\frac{9}{6}\right)\\= \frac{2}{5}- \frac{6}{5}-\frac{9}{6}\\=\frac{2}{5}-\frac{6}{5}-\frac{3}{2}\\=\frac{4}{10}-\frac{12}{10}-\frac{15}{10}\\=\frac{4-12-15}{10}\\=\frac{-23}{10}\)
10. \(+\left(\frac{-5}{-4}\right) +\left(\frac{10}{-8}\right) -\left(\frac{6}{3}\right)\\= \frac{5}{4}- \frac{10}{8}-\frac{6}{3}\\=\frac{5}{4}-\frac{5}{4}-\frac{2}{1}\\=\frac{5-5-2}{4}\\=\frac{-2}{4}\\=\frac{-1}{2}\)
11. \(+\left(\frac{9}{-7}\right) -\left(\frac{-4}{-5}\right) -\left(\frac{8}{-9}\right)\\= \frac{-9}{7}- \frac{4}{5}+\frac{8}{9}\\=\frac{-405}{315}-\frac{252}{315}+\frac{280}{315}\\=\frac{-405-252+280}{315}\\=\frac{-377}{315}\)
12. \(+\left(\frac{-9}{-2}\right) +\left(\frac{-8}{-2}\right) +\left(\frac{9}{10}\right)\\= \frac{9}{2}+ \frac{8}{2}+\frac{9}{10}\\=\frac{9}{2}+\frac{4}{1}+\frac{9}{10}\\=\frac{45}{10}+\frac{40}{10}+\frac{9}{10}\\=\frac{45+40+9}{10}\\=\frac{94}{10}\\=\frac{47}{5}\)