Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{5}\right) -\left(\frac{-4}{3}\right) -\left(\frac{-8}{3}\right)\\= \frac{9}{5}+ \frac{4}{3}+\frac{8}{3}\\=\frac{27}{15}+\frac{20}{15}+\frac{40}{15}\\=\frac{27+20+40}{15}\\=\frac{87}{15}\\=\frac{29}{5}\)
2. \(-\left(\frac{-2}{7}\right) -\left(\frac{-6}{7}\right) -\left(\frac{3}{12}\right)\\= \frac{2}{7}+ \frac{6}{7}-\frac{3}{12}\\=\frac{2}{7}+\frac{6}{7}-\frac{1}{4}\\=\frac{8}{28}+\frac{24}{28}-\frac{7}{28}\\=\frac{8+24-7}{28}\\=\frac{25}{28}\)
3. \(-\left(\frac{-3}{4}\right) +\left(\frac{-6}{-7}\right) +\left(\frac{-10}{3}\right)\\= \frac{3}{4}+ \frac{6}{7}-\frac{10}{3}\\=\frac{63}{84}+\frac{72}{84}-\frac{280}{84}\\=\frac{63+72-280}{84}\\=\frac{-145}{84}\)
4. \(-\left(\frac{-2}{5}\right) -\left(\frac{-10}{9}\right) -\left(\frac{-5}{5}\right)\\= \frac{2}{5}+ \frac{10}{9}+\frac{5}{5}\\=\frac{2}{5}+\frac{10}{9}+\frac{1}{1}\\=\frac{18}{45}+\frac{50}{45}+\frac{45}{45}\\=\frac{18+50+45}{45}\\=\frac{113}{45}\)
5. \(-\left(\frac{-2}{7}\right) -\left(\frac{5}{2}\right) +\left(\frac{-8}{-8}\right)\\= \frac{2}{7}- \frac{5}{2}+\frac{8}{8}\\=\frac{2}{7}-\frac{5}{2}+\frac{1}{1}\\=\frac{4}{14}-\frac{35}{14}+\frac{14}{14}\\=\frac{4-35+14}{14}\\=\frac{-17}{14}\)
6. \(+\left(\frac{4}{3}\right) +\left(\frac{7}{3}\right) -\left(\frac{3}{-10}\right)\\= \frac{4}{3}+ \frac{7}{3}+\frac{3}{10}\\=\frac{40}{30}+\frac{70}{30}+\frac{9}{30}\\=\frac{40+70+9}{30}\\=\frac{119}{30}\)
7. \(+\left(\frac{-2}{-3}\right) -\left(\frac{-6}{8}\right) +\left(\frac{8}{-5}\right)\\= \frac{2}{3}+ \frac{6}{8}-\frac{8}{5}\\=\frac{2}{3}+\frac{3}{4}-\frac{8}{5}\\=\frac{40}{60}+\frac{45}{60}-\frac{96}{60}\\=\frac{40+45-96}{60}\\=\frac{-11}{60}\)
8. \(+\left(\frac{-5}{-3}\right) -\left(\frac{3}{-5}\right) +\left(\frac{4}{-7}\right)\\= \frac{5}{3}+ \frac{3}{5}-\frac{4}{7}\\=\frac{175}{105}+\frac{63}{105}-\frac{60}{105}\\=\frac{175+63-60}{105}\\=\frac{178}{105}\)
9. \(+\left(\frac{-5}{-9}\right) +\left(\frac{-5}{-3}\right) +\left(\frac{2}{-6}\right)\\= \frac{5}{9}+ \frac{5}{3}-\frac{2}{6}\\=\frac{5}{9}+\frac{5}{3}-\frac{1}{3}\\=\frac{5+5-1}{9}\\=\frac{9}{9}\\=\frac{1}{1}\)
10. \(+\left(\frac{2}{-9}\right) -\left(\frac{-2}{2}\right) -\left(\frac{11}{-10}\right)\\= \frac{-2}{9}+ \frac{2}{2}+\frac{11}{10}\\=\frac{-2}{9}+\frac{1}{1}+\frac{11}{10}\\=\frac{-20}{90}+\frac{90}{90}+\frac{99}{90}\\=\frac{-20+90+99}{90}\\=\frac{169}{90}\)
11. \(+\left(\frac{3}{-2}\right) +\left(\frac{-5}{-10}\right) +\left(\frac{7}{-10}\right)\\= \frac{-3}{2}+ \frac{5}{10}-\frac{7}{10}\\=\frac{-3}{2}+\frac{1}{2}-\frac{7}{10}\\=\frac{-15}{10}+\frac{5}{10}-\frac{7}{10}\\=\frac{-15+5-7}{10}\\=\frac{-17}{10}\)
12. \(-\left(\frac{10}{-9}\right) -\left(\frac{-6}{3}\right) -\left(\frac{-10}{2}\right)\\= \frac{10}{9}+ \frac{6}{3}+\frac{10}{2}\\=\frac{10}{9}+\frac{2}{1}+\frac{5}{1}\\=\frac{10+2+5}{9}\\=\frac{17}{9}\)