Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{-2}\right) +\left(\frac{2}{3}\right) +\left(\frac{-10}{9}\right)\\= \frac{5}{2}+ \frac{2}{3}-\frac{10}{9}\\=\frac{45}{18}+\frac{12}{18}-\frac{20}{18}\\=\frac{45+12-20}{18}\\=\frac{37}{18}\)
2. \(+\left(\frac{8}{-5}\right) +\left(\frac{-2}{7}\right) -\left(\frac{12}{-3}\right)\\= \frac{-8}{5}- \frac{2}{7}+\frac{12}{3}\\=\frac{-8}{5}-\frac{2}{7}+\frac{4}{1}\\=\frac{-56}{35}-\frac{10}{35}+\frac{140}{35}\\=\frac{-56-10+140}{35}\\=\frac{74}{35}\)
3. \(-\left(\frac{3}{-2}\right) -\left(\frac{-9}{-6}\right) +\left(\frac{12}{4}\right)\\= \frac{3}{2}- \frac{9}{6}+\frac{12}{4}\\=\frac{3}{2}-\frac{3}{2}+\frac{3}{1}\\=\frac{3-3+3}{2}\\=\frac{3}{2}\)
4. \(+\left(\frac{-6}{-5}\right) -\left(\frac{9}{2}\right) -\left(\frac{8}{4}\right)\\= \frac{6}{5}- \frac{9}{2}-\frac{8}{4}\\=\frac{6}{5}-\frac{9}{2}-\frac{2}{1}\\=\frac{12}{10}-\frac{45}{10}-\frac{20}{10}\\=\frac{12-45-20}{10}\\=\frac{-53}{10}\)
5. \(+\left(\frac{4}{-9}\right) +\left(\frac{10}{-8}\right) -\left(\frac{-7}{12}\right)\\= \frac{-4}{9}- \frac{10}{8}+\frac{7}{12}\\=\frac{-4}{9}-\frac{5}{4}+\frac{7}{12}\\=\frac{-16}{36}-\frac{45}{36}+\frac{21}{36}\\=\frac{-16-45+21}{36}\\=\frac{-40}{36}\\=\frac{-10}{9}\)
6. \(+\left(\frac{3}{4}\right) +\left(\frac{-5}{-9}\right) +\left(\frac{-10}{9}\right)\\= \frac{3}{4}+ \frac{5}{9}-\frac{10}{9}\\=\frac{27}{36}+\frac{20}{36}-\frac{40}{36}\\=\frac{27+20-40}{36}\\=\frac{7}{36}\)
7. \(-\left(\frac{4}{-9}\right) +\left(\frac{-6}{-10}\right) +\left(\frac{-10}{8}\right)\\= \frac{4}{9}+ \frac{6}{10}-\frac{10}{8}\\=\frac{4}{9}+\frac{3}{5}-\frac{5}{4}\\=\frac{80}{180}+\frac{108}{180}-\frac{225}{180}\\=\frac{80+108-225}{180}\\=\frac{-37}{180}\)
8. \(+\left(\frac{5}{4}\right) +\left(\frac{2}{-4}\right) +\left(\frac{-2}{-4}\right)\\= \frac{5}{4}- \frac{2}{4}+\frac{2}{4}\\=\frac{5}{4}-\frac{1}{2}+\frac{1}{2}\\=\frac{5-1+1}{4}\\=\frac{5}{4}\)
9. \(-\left(\frac{-5}{3}\right) -\left(\frac{2}{-10}\right) -\left(\frac{10}{-8}\right)\\= \frac{5}{3}+ \frac{2}{10}+\frac{10}{8}\\=\frac{5}{3}+\frac{1}{5}+\frac{5}{4}\\=\frac{100}{60}+\frac{12}{60}+\frac{75}{60}\\=\frac{100+12+75}{60}\\=\frac{187}{60}\)
10. \(+\left(\frac{-5}{6}\right) +\left(\frac{-5}{-6}\right) -\left(\frac{-9}{-10}\right)\\= \frac{-5}{6}+ \frac{5}{6}-\frac{9}{10}\\=\frac{-25}{30}+\frac{25}{30}-\frac{27}{30}\\=\frac{-25+25-27}{30}\\=\frac{-27}{30}\\=\frac{-9}{10}\)
11. \(-\left(\frac{7}{-2}\right) -\left(\frac{-2}{-5}\right) -\left(\frac{-9}{11}\right)\\= \frac{7}{2}- \frac{2}{5}+\frac{9}{11}\\=\frac{385}{110}-\frac{44}{110}+\frac{90}{110}\\=\frac{385-44+90}{110}\\=\frac{431}{110}\)
12. \(-\left(\frac{-6}{-5}\right) +\left(\frac{7}{-6}\right) -\left(\frac{-7}{-4}\right)\\= \frac{-6}{5}- \frac{7}{6}-\frac{7}{4}\\=\frac{-72}{60}-\frac{70}{60}-\frac{105}{60}\\=\frac{-72-70-105}{60}\\=\frac{-247}{60}\)