Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{3}{4}\right) +\left(\frac{2}{4}\right) +\left(\frac{10}{-5}\right)\\= \frac{-3}{4}+ \frac{2}{4}-\frac{10}{5}\\=\frac{-3}{4}+\frac{1}{2}-\frac{2}{1}\\=\frac{-3+1-2}{4}\\=\frac{-4}{4}\\=\frac{-1}{1}\)
2. \(+\left(\frac{-6}{-5}\right) +\left(\frac{5}{-8}\right) -\left(\frac{-10}{-4}\right)\\= \frac{6}{5}- \frac{5}{8}-\frac{10}{4}\\=\frac{6}{5}-\frac{5}{8}-\frac{5}{2}\\=\frac{48}{40}-\frac{25}{40}-\frac{100}{40}\\=\frac{48-25-100}{40}\\=\frac{-77}{40}\)
3. \(-\left(\frac{-10}{3}\right) -\left(\frac{-3}{-8}\right) -\left(\frac{-2}{-10}\right)\\= \frac{10}{3}- \frac{3}{8}-\frac{2}{10}\\=\frac{10}{3}-\frac{3}{8}-\frac{1}{5}\\=\frac{400}{120}-\frac{45}{120}-\frac{24}{120}\\=\frac{400-45-24}{120}\\=\frac{331}{120}\)
4. \(-\left(\frac{-2}{-7}\right) +\left(\frac{-6}{-6}\right) +\left(\frac{-6}{-11}\right)\\= \frac{-2}{7}+ \frac{6}{6}+\frac{6}{11}\\=\frac{-2}{7}+\frac{1}{1}+\frac{6}{11}\\=\frac{-22}{77}+\frac{77}{77}+\frac{42}{77}\\=\frac{-22+77+42}{77}\\=\frac{97}{77}\)
5. \(-\left(\frac{4}{-3}\right) -\left(\frac{2}{-5}\right) -\left(\frac{4}{7}\right)\\= \frac{4}{3}+ \frac{2}{5}-\frac{4}{7}\\=\frac{140}{105}+\frac{42}{105}-\frac{60}{105}\\=\frac{140+42-60}{105}\\=\frac{122}{105}\)
6. \(-\left(\frac{10}{-3}\right) -\left(\frac{-8}{-6}\right) -\left(\frac{-4}{4}\right)\\= \frac{10}{3}- \frac{8}{6}+\frac{4}{4}\\=\frac{10}{3}-\frac{4}{3}+\frac{1}{1}\\=\frac{10-4+1}{3}\\=\frac{7}{3}\)
7. \(-\left(\frac{6}{-5}\right) +\left(\frac{6}{9}\right) -\left(\frac{8}{-6}\right)\\= \frac{6}{5}+ \frac{6}{9}+\frac{8}{6}\\=\frac{6}{5}+\frac{2}{3}+\frac{4}{3}\\=\frac{18}{15}+\frac{10}{15}+\frac{20}{15}\\=\frac{18+10+20}{15}\\=\frac{48}{15}\\=\frac{16}{5}\)
8. \(-\left(\frac{-4}{3}\right) -\left(\frac{-9}{5}\right) +\left(\frac{12}{-11}\right)\\= \frac{4}{3}+ \frac{9}{5}-\frac{12}{11}\\=\frac{220}{165}+\frac{297}{165}-\frac{180}{165}\\=\frac{220+297-180}{165}\\=\frac{337}{165}\)
9. \(+\left(\frac{-7}{9}\right) +\left(\frac{-7}{-4}\right) +\left(\frac{-12}{4}\right)\\= \frac{-7}{9}+ \frac{7}{4}-\frac{12}{4}\\=\frac{-7}{9}+\frac{7}{4}-\frac{3}{1}\\=\frac{-28}{36}+\frac{63}{36}-\frac{108}{36}\\=\frac{-28+63-108}{36}\\=\frac{-73}{36}\)
10. \(+\left(\frac{-9}{-2}\right) +\left(\frac{-4}{-9}\right) -\left(\frac{-11}{-8}\right)\\= \frac{9}{2}+ \frac{4}{9}-\frac{11}{8}\\=\frac{324}{72}+\frac{32}{72}-\frac{99}{72}\\=\frac{324+32-99}{72}\\=\frac{257}{72}\)
11. \(-\left(\frac{10}{-3}\right) +\left(\frac{-6}{-10}\right) -\left(\frac{-12}{12}\right)\\= \frac{10}{3}+ \frac{6}{10}+\frac{12}{12}\\=\frac{10}{3}+\frac{3}{5}+\frac{1}{1}\\=\frac{50}{15}+\frac{9}{15}+\frac{15}{15}\\=\frac{50+9+15}{15}\\=\frac{74}{15}\)
12. \(-\left(\frac{-7}{-6}\right) +\left(\frac{7}{-2}\right) +\left(\frac{-8}{11}\right)\\= \frac{-7}{6}- \frac{7}{2}-\frac{8}{11}\\=\frac{-77}{66}-\frac{231}{66}-\frac{48}{66}\\=\frac{-77-231-48}{66}\\=\frac{-356}{66}\\=\frac{-178}{33}\)