Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{-7}\right) +\left(\frac{2}{10}\right) +\left(\frac{-9}{-6}\right)\\= \frac{-4}{7}+ \frac{2}{10}+\frac{9}{6}\\=\frac{-4}{7}+\frac{1}{5}+\frac{3}{2}\\=\frac{-40}{70}+\frac{14}{70}+\frac{105}{70}\\=\frac{-40+14+105}{70}\\=\frac{79}{70}\)
2. \(+\left(\frac{2}{9}\right) -\left(\frac{-8}{-8}\right) +\left(\frac{4}{-7}\right)\\= \frac{2}{9}- \frac{8}{8}-\frac{4}{7}\\=\frac{2}{9}-\frac{1}{1}-\frac{4}{7}\\=\frac{14}{63}-\frac{63}{63}-\frac{36}{63}\\=\frac{14-63-36}{63}\\=\frac{-85}{63}\)
3. \(+\left(\frac{2}{-9}\right) +\left(\frac{10}{-4}\right) +\left(\frac{-8}{7}\right)\\= \frac{-2}{9}- \frac{10}{4}-\frac{8}{7}\\=\frac{-2}{9}-\frac{5}{2}-\frac{8}{7}\\=\frac{-28}{126}-\frac{315}{126}-\frac{144}{126}\\=\frac{-28-315-144}{126}\\=\frac{-487}{126}\)
4. \(-\left(\frac{-3}{5}\right) +\left(\frac{-9}{6}\right) +\left(\frac{4}{-4}\right)\\= \frac{3}{5}- \frac{9}{6}-\frac{4}{4}\\=\frac{3}{5}-\frac{3}{2}-\frac{1}{1}\\=\frac{6}{10}-\frac{15}{10}-\frac{10}{10}\\=\frac{6-15-10}{10}\\=\frac{-19}{10}\)
5. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-2}{-7}\right) +\left(\frac{-3}{-3}\right)\\= \frac{-10}{7}+ \frac{2}{7}+\frac{3}{3}\\=\frac{-10}{7}+\frac{2}{7}+\frac{1}{1}\\=\frac{-10+2+1}{7}\\=\frac{-7}{7}\\=\frac{-1}{1}\)
6. \(-\left(\frac{8}{7}\right) +\left(\frac{6}{8}\right) +\left(\frac{8}{-6}\right)\\= \frac{-8}{7}+ \frac{6}{8}-\frac{8}{6}\\=\frac{-8}{7}+\frac{3}{4}-\frac{4}{3}\\=\frac{-96}{84}+\frac{63}{84}-\frac{112}{84}\\=\frac{-96+63-112}{84}\\=\frac{-145}{84}\)
7. \(-\left(\frac{2}{3}\right) +\left(\frac{-6}{2}\right) -\left(\frac{-4}{-3}\right)\\= \frac{-2}{3}- \frac{6}{2}-\frac{4}{3}\\=\frac{-2}{3}-\frac{3}{1}-\frac{4}{3}\\=\frac{-2-3-4}{3}\\=\frac{-9}{3}\\=\frac{-3}{1}\)
8. \(+\left(\frac{8}{9}\right) +\left(\frac{6}{-10}\right) -\left(\frac{-4}{11}\right)\\= \frac{8}{9}- \frac{6}{10}+\frac{4}{11}\\=\frac{8}{9}-\frac{3}{5}+\frac{4}{11}\\=\frac{440}{495}-\frac{297}{495}+\frac{180}{495}\\=\frac{440-297+180}{495}\\=\frac{323}{495}\)
9. \(+\left(\frac{8}{3}\right) +\left(\frac{9}{-7}\right) +\left(\frac{2}{3}\right)\\= \frac{8}{3}- \frac{9}{7}+\frac{2}{3}\\=\frac{56}{21}-\frac{27}{21}+\frac{14}{21}\\=\frac{56-27+14}{21}\\=\frac{43}{21}\)
10. \(+\left(\frac{10}{-7}\right) -\left(\frac{-4}{4}\right) -\left(\frac{-5}{2}\right)\\= \frac{-10}{7}+ \frac{4}{4}+\frac{5}{2}\\=\frac{-10}{7}+\frac{1}{1}+\frac{5}{2}\\=\frac{-20}{14}+\frac{14}{14}+\frac{35}{14}\\=\frac{-20+14+35}{14}\\=\frac{29}{14}\)
11. \(-\left(\frac{7}{3}\right) +\left(\frac{2}{-3}\right) -\left(\frac{-6}{4}\right)\\= \frac{-7}{3}- \frac{2}{3}+\frac{6}{4}\\=\frac{-7}{3}-\frac{2}{3}+\frac{3}{2}\\=\frac{-14}{6}-\frac{4}{6}+\frac{9}{6}\\=\frac{-14-4+9}{6}\\=\frac{-9}{6}\\=\frac{-3}{2}\)
12. \(-\left(\frac{4}{-3}\right) +\left(\frac{8}{10}\right) +\left(\frac{-7}{2}\right)\\= \frac{4}{3}+ \frac{8}{10}-\frac{7}{2}\\=\frac{4}{3}+\frac{4}{5}-\frac{7}{2}\\=\frac{40}{30}+\frac{24}{30}-\frac{105}{30}\\=\frac{40+24-105}{30}\\=\frac{-41}{30}\)