Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{-5}\right) -\left(\frac{9}{6}\right) -\left(\frac{8}{-2}\right)\\= \frac{-6}{5}- \frac{9}{6}+\frac{8}{2}\\=\frac{-6}{5}-\frac{3}{2}+\frac{4}{1}\\=\frac{-12}{10}-\frac{15}{10}+\frac{40}{10}\\=\frac{-12-15+40}{10}\\=\frac{13}{10}\)
2. \(-\left(\frac{-9}{2}\right) -\left(\frac{-2}{-3}\right) -\left(\frac{-2}{7}\right)\\= \frac{9}{2}- \frac{2}{3}+\frac{2}{7}\\=\frac{189}{42}-\frac{28}{42}+\frac{12}{42}\\=\frac{189-28+12}{42}\\=\frac{173}{42}\)
3. \(+\left(\frac{-2}{-9}\right) -\left(\frac{-2}{6}\right) +\left(\frac{5}{-4}\right)\\= \frac{2}{9}+ \frac{2}{6}-\frac{5}{4}\\=\frac{2}{9}+\frac{1}{3}-\frac{5}{4}\\=\frac{8}{36}+\frac{12}{36}-\frac{45}{36}\\=\frac{8+12-45}{36}\\=\frac{-25}{36}\)
4. \(-\left(\frac{-8}{3}\right) -\left(\frac{-7}{3}\right) +\left(\frac{-10}{8}\right)\\= \frac{8}{3}+ \frac{7}{3}-\frac{10}{8}\\=\frac{8}{3}+\frac{7}{3}-\frac{5}{4}\\=\frac{32}{12}+\frac{28}{12}-\frac{15}{12}\\=\frac{32+28-15}{12}\\=\frac{45}{12}\\=\frac{15}{4}\)
5. \(+\left(\frac{2}{7}\right) +\left(\frac{10}{-2}\right) +\left(\frac{10}{6}\right)\\= \frac{2}{7}- \frac{10}{2}+\frac{10}{6}\\=\frac{2}{7}-\frac{5}{1}+\frac{5}{3}\\=\frac{6}{21}-\frac{105}{21}+\frac{35}{21}\\=\frac{6-105+35}{21}\\=\frac{-64}{21}\)
6. \(-\left(\frac{2}{-5}\right) +\left(\frac{-10}{9}\right) +\left(\frac{-2}{8}\right)\\= \frac{2}{5}- \frac{10}{9}-\frac{2}{8}\\=\frac{2}{5}-\frac{10}{9}-\frac{1}{4}\\=\frac{72}{180}-\frac{200}{180}-\frac{45}{180}\\=\frac{72-200-45}{180}\\=\frac{-173}{180}\)
7. \(-\left(\frac{4}{7}\right) -\left(\frac{-2}{4}\right) +\left(\frac{10}{-12}\right)\\= \frac{-4}{7}+ \frac{2}{4}-\frac{10}{12}\\=\frac{-4}{7}+\frac{1}{2}-\frac{5}{6}\\=\frac{-24}{42}+\frac{21}{42}-\frac{35}{42}\\=\frac{-24+21-35}{42}\\=\frac{-38}{42}\\=\frac{-19}{21}\)
8. \(+\left(\frac{-2}{9}\right) +\left(\frac{-2}{7}\right) +\left(\frac{8}{-7}\right)\\= \frac{-2}{9}- \frac{2}{7}-\frac{8}{7}\\=\frac{-14}{63}-\frac{18}{63}-\frac{72}{63}\\=\frac{-14-18-72}{63}\\=\frac{-104}{63}\)
9. \(-\left(\frac{7}{2}\right) +\left(\frac{6}{-6}\right) +\left(\frac{2}{8}\right)\\= \frac{-7}{2}- \frac{6}{6}+\frac{2}{8}\\=\frac{-7}{2}-\frac{1}{1}+\frac{1}{4}\\=\frac{-14}{4}-\frac{4}{4}+\frac{1}{4}\\=\frac{-14-4+1}{4}\\=\frac{-17}{4}\)
10. \(-\left(\frac{6}{-5}\right) +\left(\frac{10}{5}\right) -\left(\frac{5}{12}\right)\\= \frac{6}{5}+ \frac{10}{5}-\frac{5}{12}\\=\frac{6}{5}+\frac{2}{1}-\frac{5}{12}\\=\frac{72}{60}+\frac{120}{60}-\frac{25}{60}\\=\frac{72+120-25}{60}\\=\frac{167}{60}\)
11. \(-\left(\frac{8}{-9}\right) -\left(\frac{-9}{-7}\right) +\left(\frac{3}{-5}\right)\\= \frac{8}{9}- \frac{9}{7}-\frac{3}{5}\\=\frac{280}{315}-\frac{405}{315}-\frac{189}{315}\\=\frac{280-405-189}{315}\\=\frac{-314}{315}\)
12. \(-\left(\frac{-9}{-4}\right) -\left(\frac{-7}{-10}\right) +\left(\frac{-8}{12}\right)\\= \frac{-9}{4}- \frac{7}{10}-\frac{8}{12}\\=\frac{-9}{4}-\frac{7}{10}-\frac{2}{3}\\=\frac{-135}{60}-\frac{42}{60}-\frac{40}{60}\\=\frac{-135-42-40}{60}\\=\frac{-217}{60}\)