Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{5}\right) +\left(\frac{-9}{-6}\right) +\left(\frac{-3}{-8}\right)\\= \frac{-3}{5}+ \frac{9}{6}+\frac{3}{8}\\=\frac{-3}{5}+\frac{3}{2}+\frac{3}{8}\\=\frac{-24}{40}+\frac{60}{40}+\frac{15}{40}\\=\frac{-24+60+15}{40}\\=\frac{51}{40}\)
2. \(-\left(\frac{6}{-5}\right) +\left(\frac{8}{5}\right) -\left(\frac{-9}{7}\right)\\= \frac{6}{5}+ \frac{8}{5}+\frac{9}{7}\\=\frac{42}{35}+\frac{56}{35}+\frac{45}{35}\\=\frac{42+56+45}{35}\\=\frac{143}{35}\)
3. \(-\left(\frac{-4}{-9}\right) +\left(\frac{2}{3}\right) +\left(\frac{-3}{8}\right)\\= \frac{-4}{9}+ \frac{2}{3}-\frac{3}{8}\\=\frac{-32}{72}+\frac{48}{72}-\frac{27}{72}\\=\frac{-32+48-27}{72}\\=\frac{-11}{72}\)
4. \(+\left(\frac{-4}{9}\right) -\left(\frac{-7}{9}\right) -\left(\frac{-5}{-9}\right)\\= \frac{-4}{9}+ \frac{7}{9}-\frac{5}{9}\\=\frac{-4+7-5}{9}\\=\frac{-2}{9}\)
5. \(-\left(\frac{10}{-9}\right) +\left(\frac{-6}{-3}\right) +\left(\frac{2}{3}\right)\\= \frac{10}{9}+ \frac{6}{3}+\frac{2}{3}\\=\frac{10}{9}+\frac{2}{1}+\frac{2}{3}\\=\frac{10+2+2}{9}\\=\frac{14}{9}\)
6. \(+\left(\frac{-3}{-5}\right) -\left(\frac{-2}{-9}\right) -\left(\frac{7}{-7}\right)\\= \frac{3}{5}- \frac{2}{9}+\frac{7}{7}\\=\frac{3}{5}-\frac{2}{9}+\frac{1}{1}\\=\frac{27}{45}-\frac{10}{45}+\frac{45}{45}\\=\frac{27-10+45}{45}\\=\frac{62}{45}\)
7. \(-\left(\frac{2}{3}\right) +\left(\frac{2}{10}\right) -\left(\frac{12}{7}\right)\\= \frac{-2}{3}+ \frac{2}{10}-\frac{12}{7}\\=\frac{-2}{3}+\frac{1}{5}-\frac{12}{7}\\=\frac{-70}{105}+\frac{21}{105}-\frac{180}{105}\\=\frac{-70+21-180}{105}\\=\frac{-229}{105}\)
8. \(-\left(\frac{9}{2}\right) -\left(\frac{2}{8}\right) +\left(\frac{-3}{9}\right)\\= \frac{-9}{2}- \frac{2}{8}-\frac{3}{9}\\=\frac{-9}{2}-\frac{1}{4}-\frac{1}{3}\\=\frac{-54}{12}-\frac{3}{12}-\frac{4}{12}\\=\frac{-54-3-4}{12}\\=\frac{-61}{12}\)
9. \(-\left(\frac{-4}{3}\right) +\left(\frac{-10}{9}\right) +\left(\frac{-2}{3}\right)\\= \frac{4}{3}- \frac{10}{9}-\frac{2}{3}\\=\frac{12}{9}-\frac{10}{9}-\frac{6}{9}\\=\frac{12-10-6}{9}\\=\frac{-4}{9}\)
10. \(-\left(\frac{-5}{6}\right) +\left(\frac{-7}{-8}\right) -\left(\frac{5}{9}\right)\\= \frac{5}{6}+ \frac{7}{8}-\frac{5}{9}\\=\frac{60}{72}+\frac{63}{72}-\frac{40}{72}\\=\frac{60+63-40}{72}\\=\frac{83}{72}\)
11. \(+\left(\frac{5}{-3}\right) -\left(\frac{-9}{-10}\right) -\left(\frac{-3}{-12}\right)\\= \frac{-5}{3}- \frac{9}{10}-\frac{3}{12}\\=\frac{-5}{3}-\frac{9}{10}-\frac{1}{4}\\=\frac{-100}{60}-\frac{54}{60}-\frac{15}{60}\\=\frac{-100-54-15}{60}\\=\frac{-169}{60}\)
12. \(-\left(\frac{-8}{-5}\right) +\left(\frac{-6}{-6}\right) +\left(\frac{-4}{-9}\right)\\= \frac{-8}{5}+ \frac{6}{6}+\frac{4}{9}\\=\frac{-8}{5}+\frac{1}{1}+\frac{4}{9}\\=\frac{-72}{45}+\frac{45}{45}+\frac{20}{45}\\=\frac{-72+45+20}{45}\\=\frac{-7}{45}\)