Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-7}\right) +\left(\frac{-6}{-6}\right) -\left(\frac{-3}{5}\right)\\= \frac{10}{7}+ \frac{6}{6}+\frac{3}{5}\\=\frac{10}{7}+\frac{1}{1}+\frac{3}{5}\\=\frac{50}{35}+\frac{35}{35}+\frac{21}{35}\\=\frac{50+35+21}{35}\\=\frac{106}{35}\)
2. \(-\left(\frac{4}{3}\right) -\left(\frac{6}{4}\right) +\left(\frac{-12}{-6}\right)\\= \frac{-4}{3}- \frac{6}{4}+\frac{12}{6}\\=\frac{-4}{3}-\frac{3}{2}+\frac{2}{1}\\=\frac{-8}{6}-\frac{9}{6}+\frac{12}{6}\\=\frac{-8-9+12}{6}\\=\frac{-5}{6}\)
3. \(-\left(\frac{3}{-7}\right) +\left(\frac{5}{-9}\right) -\left(\frac{-5}{7}\right)\\= \frac{3}{7}- \frac{5}{9}+\frac{5}{7}\\=\frac{27}{63}-\frac{35}{63}+\frac{45}{63}\\=\frac{27-35+45}{63}\\=\frac{37}{63}\)
4. \(-\left(\frac{2}{5}\right) +\left(\frac{4}{3}\right) +\left(\frac{6}{5}\right)\\= \frac{-2}{5}+ \frac{4}{3}+\frac{6}{5}\\=\frac{-6}{15}+\frac{20}{15}+\frac{18}{15}\\=\frac{-6+20+18}{15}\\=\frac{32}{15}\)
5. \(-\left(\frac{-2}{-3}\right) +\left(\frac{-4}{3}\right) -\left(\frac{-9}{-5}\right)\\= \frac{-2}{3}- \frac{4}{3}-\frac{9}{5}\\=\frac{-10}{15}-\frac{20}{15}-\frac{27}{15}\\=\frac{-10-20-27}{15}\\=\frac{-57}{15}\\=\frac{-19}{5}\)
6. \(+\left(\frac{-5}{3}\right) -\left(\frac{-4}{7}\right) +\left(\frac{-2}{-9}\right)\\= \frac{-5}{3}+ \frac{4}{7}+\frac{2}{9}\\=\frac{-105}{63}+\frac{36}{63}+\frac{14}{63}\\=\frac{-105+36+14}{63}\\=\frac{-55}{63}\)
7. \(-\left(\frac{-8}{-7}\right) +\left(\frac{4}{-3}\right) -\left(\frac{12}{11}\right)\\= \frac{-8}{7}- \frac{4}{3}-\frac{12}{11}\\=\frac{-264}{231}-\frac{308}{231}-\frac{252}{231}\\=\frac{-264-308-252}{231}\\=\frac{-824}{231}\)
8. \(-\left(\frac{-10}{-9}\right) +\left(\frac{-6}{-5}\right) +\left(\frac{-4}{-7}\right)\\= \frac{-10}{9}+ \frac{6}{5}+\frac{4}{7}\\=\frac{-350}{315}+\frac{378}{315}+\frac{180}{315}\\=\frac{-350+378+180}{315}\\=\frac{208}{315}\)
9. \(-\left(\frac{5}{-6}\right) -\left(\frac{-7}{-7}\right) +\left(\frac{3}{2}\right)\\= \frac{5}{6}- \frac{7}{7}+\frac{3}{2}\\=\frac{5}{6}-\frac{1}{1}+\frac{3}{2}\\=\frac{5-1+3}{6}\\=\frac{7}{6}\)
10. \(+\left(\frac{10}{-3}\right) -\left(\frac{5}{5}\right) +\left(\frac{8}{4}\right)\\= \frac{-10}{3}- \frac{5}{5}+\frac{8}{4}\\=\frac{-10}{3}-\frac{1}{1}+\frac{2}{1}\\=\frac{-10-1+2}{3}\\=\frac{-9}{3}\\=\frac{-3}{1}\)
11. \(+\left(\frac{2}{7}\right) +\left(\frac{-3}{7}\right) -\left(\frac{-5}{-6}\right)\\= \frac{2}{7}- \frac{3}{7}-\frac{5}{6}\\=\frac{12}{42}-\frac{18}{42}-\frac{35}{42}\\=\frac{12-18-35}{42}\\=\frac{-41}{42}\)
12. \(-\left(\frac{-4}{9}\right) -\left(\frac{2}{7}\right) -\left(\frac{-8}{-11}\right)\\= \frac{4}{9}- \frac{2}{7}-\frac{8}{11}\\=\frac{308}{693}-\frac{198}{693}-\frac{504}{693}\\=\frac{308-198-504}{693}\\=\frac{-394}{693}\)