Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{4}{5}\right) -\left(\frac{-10}{3}\right) +\left(\frac{2}{8}\right)\\= \frac{4}{5}+ \frac{10}{3}+\frac{2}{8}\\=\frac{4}{5}+\frac{10}{3}+\frac{1}{4}\\=\frac{48}{60}+\frac{200}{60}+\frac{15}{60}\\=\frac{48+200+15}{60}\\=\frac{263}{60}\)
2. \(+\left(\frac{-9}{2}\right) -\left(\frac{-3}{-3}\right) -\left(\frac{-10}{-2}\right)\\= \frac{-9}{2}- \frac{3}{3}-\frac{10}{2}\\=\frac{-9}{2}-\frac{1}{1}-\frac{5}{1}\\=\frac{-9-1-5}{2}\\=\frac{-15}{2}\)
3. \(-\left(\frac{-2}{3}\right) +\left(\frac{-3}{3}\right) -\left(\frac{9}{-10}\right)\\= \frac{2}{3}- \frac{3}{3}+\frac{9}{10}\\=\frac{2}{3}-\frac{1}{1}+\frac{9}{10}\\=\frac{20}{30}-\frac{30}{30}+\frac{27}{30}\\=\frac{20-30+27}{30}\\=\frac{17}{30}\)
4. \(+\left(\frac{7}{8}\right) -\left(\frac{-6}{2}\right) +\left(\frac{6}{3}\right)\\= \frac{7}{8}+ \frac{6}{2}+\frac{6}{3}\\=\frac{7}{8}+\frac{3}{1}+\frac{2}{1}\\=\frac{7+3+2}{8}\\=\frac{12}{8}\\=\frac{3}{2}\)
5. \(-\left(\frac{4}{9}\right) +\left(\frac{-4}{6}\right) +\left(\frac{-11}{-5}\right)\\= \frac{-4}{9}- \frac{4}{6}+\frac{11}{5}\\=\frac{-4}{9}-\frac{2}{3}+\frac{11}{5}\\=\frac{-20}{45}-\frac{30}{45}+\frac{99}{45}\\=\frac{-20-30+99}{45}\\=\frac{49}{45}\)
6. \(+\left(\frac{4}{-3}\right) -\left(\frac{4}{-4}\right) -\left(\frac{7}{-2}\right)\\= \frac{-4}{3}+ \frac{4}{4}+\frac{7}{2}\\=\frac{-4}{3}+\frac{1}{1}+\frac{7}{2}\\=\frac{-8}{6}+\frac{6}{6}+\frac{21}{6}\\=\frac{-8+6+21}{6}\\=\frac{19}{6}\)
7. \(-\left(\frac{3}{-2}\right) +\left(\frac{-3}{-6}\right) +\left(\frac{-2}{11}\right)\\= \frac{3}{2}+ \frac{3}{6}-\frac{2}{11}\\=\frac{3}{2}+\frac{1}{2}-\frac{2}{11}\\=\frac{33}{22}+\frac{11}{22}-\frac{4}{22}\\=\frac{33+11-4}{22}\\=\frac{40}{22}\\=\frac{20}{11}\)
8. \(-\left(\frac{-3}{2}\right) -\left(\frac{9}{5}\right) +\left(\frac{-8}{4}\right)\\= \frac{3}{2}- \frac{9}{5}-\frac{8}{4}\\=\frac{3}{2}-\frac{9}{5}-\frac{2}{1}\\=\frac{15}{10}-\frac{18}{10}-\frac{20}{10}\\=\frac{15-18-20}{10}\\=\frac{-23}{10}\)
9. \(+\left(\frac{-5}{-2}\right) -\left(\frac{-5}{6}\right) +\left(\frac{3}{-4}\right)\\= \frac{5}{2}+ \frac{5}{6}-\frac{3}{4}\\=\frac{30}{12}+\frac{10}{12}-\frac{9}{12}\\=\frac{30+10-9}{12}\\=\frac{31}{12}\)
10. \(+\left(\frac{-4}{9}\right) -\left(\frac{9}{-6}\right) +\left(\frac{-6}{-12}\right)\\= \frac{-4}{9}+ \frac{9}{6}+\frac{6}{12}\\=\frac{-4}{9}+\frac{3}{2}+\frac{1}{2}\\=\frac{-8}{18}+\frac{27}{18}+\frac{9}{18}\\=\frac{-8+27+9}{18}\\=\frac{28}{18}\\=\frac{14}{9}\)
11. \(-\left(\frac{-10}{3}\right) -\left(\frac{9}{-4}\right) +\left(\frac{-10}{-7}\right)\\= \frac{10}{3}+ \frac{9}{4}+\frac{10}{7}\\=\frac{280}{84}+\frac{189}{84}+\frac{120}{84}\\=\frac{280+189+120}{84}\\=\frac{589}{84}\)
12. \(+\left(\frac{8}{3}\right) +\left(\frac{2}{7}\right) +\left(\frac{-12}{7}\right)\\= \frac{8}{3}+ \frac{2}{7}-\frac{12}{7}\\=\frac{56}{21}+\frac{6}{21}-\frac{36}{21}\\=\frac{56+6-36}{21}\\=\frac{26}{21}\)