Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{4}{3}\right) +\left(\frac{7}{-5}\right) +\left(\frac{-6}{-2}\right)\\= \frac{4}{3}- \frac{7}{5}+\frac{6}{2}\\=\frac{4}{3}-\frac{7}{5}+\frac{3}{1}\\=\frac{20}{15}-\frac{21}{15}+\frac{45}{15}\\=\frac{20-21+45}{15}\\=\frac{44}{15}\)
2. \(-\left(\frac{3}{-4}\right) +\left(\frac{-2}{9}\right) +\left(\frac{7}{-3}\right)\\= \frac{3}{4}- \frac{2}{9}-\frac{7}{3}\\=\frac{27}{36}-\frac{8}{36}-\frac{84}{36}\\=\frac{27-8-84}{36}\\=\frac{-65}{36}\)
3. \(-\left(\frac{2}{5}\right) -\left(\frac{3}{5}\right) -\left(\frac{7}{-9}\right)\\= \frac{-2}{5}- \frac{3}{5}+\frac{7}{9}\\=\frac{-18}{45}-\frac{27}{45}+\frac{35}{45}\\=\frac{-18-27+35}{45}\\=\frac{-10}{45}\\=\frac{-2}{9}\)
4. \(-\left(\frac{-2}{-5}\right) +\left(\frac{6}{-2}\right) -\left(\frac{-5}{-8}\right)\\= \frac{-2}{5}- \frac{6}{2}-\frac{5}{8}\\=\frac{-2}{5}-\frac{3}{1}-\frac{5}{8}\\=\frac{-16}{40}-\frac{120}{40}-\frac{25}{40}\\=\frac{-16-120-25}{40}\\=\frac{-161}{40}\)
5. \(+\left(\frac{2}{9}\right) +\left(\frac{5}{-3}\right) +\left(\frac{-12}{10}\right)\\= \frac{2}{9}- \frac{5}{3}-\frac{12}{10}\\=\frac{2}{9}-\frac{5}{3}-\frac{6}{5}\\=\frac{10}{45}-\frac{75}{45}-\frac{54}{45}\\=\frac{10-75-54}{45}\\=\frac{-119}{45}\)
6. \(-\left(\frac{-4}{-3}\right) -\left(\frac{6}{-3}\right) -\left(\frac{11}{7}\right)\\= \frac{-4}{3}+ \frac{6}{3}-\frac{11}{7}\\=\frac{-4}{3}+\frac{2}{1}-\frac{11}{7}\\=\frac{-28}{21}+\frac{42}{21}-\frac{33}{21}\\=\frac{-28+42-33}{21}\\=\frac{-19}{21}\)
7. \(-\left(\frac{2}{3}\right) +\left(\frac{-4}{-3}\right) -\left(\frac{3}{10}\right)\\= \frac{-2}{3}+ \frac{4}{3}-\frac{3}{10}\\=\frac{-20}{30}+\frac{40}{30}-\frac{9}{30}\\=\frac{-20+40-9}{30}\\=\frac{11}{30}\)
8. \(+\left(\frac{8}{-5}\right) -\left(\frac{-9}{7}\right) +\left(\frac{-6}{-12}\right)\\= \frac{-8}{5}+ \frac{9}{7}+\frac{6}{12}\\=\frac{-8}{5}+\frac{9}{7}+\frac{1}{2}\\=\frac{-112}{70}+\frac{90}{70}+\frac{35}{70}\\=\frac{-112+90+35}{70}\\=\frac{13}{70}\)
9. \(-\left(\frac{-2}{3}\right) +\left(\frac{-3}{2}\right) +\left(\frac{7}{-10}\right)\\= \frac{2}{3}- \frac{3}{2}-\frac{7}{10}\\=\frac{20}{30}-\frac{45}{30}-\frac{21}{30}\\=\frac{20-45-21}{30}\\=\frac{-46}{30}\\=\frac{-23}{15}\)
10. \(+\left(\frac{-3}{8}\right) +\left(\frac{-7}{9}\right) -\left(\frac{7}{-6}\right)\\= \frac{-3}{8}- \frac{7}{9}+\frac{7}{6}\\=\frac{-27}{72}-\frac{56}{72}+\frac{84}{72}\\=\frac{-27-56+84}{72}\\=\frac{1}{72}\)
11. \(+\left(\frac{6}{-5}\right) -\left(\frac{6}{9}\right) +\left(\frac{6}{-4}\right)\\= \frac{-6}{5}- \frac{6}{9}-\frac{6}{4}\\=\frac{-6}{5}-\frac{2}{3}-\frac{3}{2}\\=\frac{-36}{30}-\frac{20}{30}-\frac{45}{30}\\=\frac{-36-20-45}{30}\\=\frac{-101}{30}\)
12. \(+\left(\frac{-10}{-7}\right) +\left(\frac{7}{7}\right) -\left(\frac{9}{-2}\right)\\= \frac{10}{7}+ \frac{7}{7}+\frac{9}{2}\\=\frac{10}{7}+\frac{1}{1}+\frac{9}{2}\\=\frac{20}{14}+\frac{14}{14}+\frac{63}{14}\\=\frac{20+14+63}{14}\\=\frac{97}{14}\)