Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{3}\right) +\left(\frac{2}{3}\right) -\left(\frac{9}{-9}\right)\\= \frac{4}{3}+ \frac{2}{3}+\frac{9}{9}\\=\frac{4}{3}+\frac{2}{3}+\frac{1}{1}\\=\frac{4+2+1}{3}\\=\frac{7}{3}\)
2. \(-\left(\frac{3}{8}\right) +\left(\frac{8}{9}\right) +\left(\frac{7}{3}\right)\\= \frac{-3}{8}+ \frac{8}{9}+\frac{7}{3}\\=\frac{-27}{72}+\frac{64}{72}+\frac{168}{72}\\=\frac{-27+64+168}{72}\\=\frac{205}{72}\)
3. \(-\left(\frac{-7}{-3}\right) +\left(\frac{6}{-3}\right) -\left(\frac{3}{6}\right)\\= \frac{-7}{3}- \frac{6}{3}-\frac{3}{6}\\=\frac{-7}{3}-\frac{2}{1}-\frac{1}{2}\\=\frac{-14}{6}-\frac{12}{6}-\frac{3}{6}\\=\frac{-14-12-3}{6}\\=\frac{-29}{6}\)
4. \(+\left(\frac{-9}{2}\right) -\left(\frac{4}{5}\right) +\left(\frac{-3}{2}\right)\\= \frac{-9}{2}- \frac{4}{5}-\frac{3}{2}\\=\frac{-45}{10}-\frac{8}{10}-\frac{15}{10}\\=\frac{-45-8-15}{10}\\=\frac{-68}{10}\\=\frac{-34}{5}\)
5. \(-\left(\frac{-5}{-2}\right) +\left(\frac{-7}{-6}\right) -\left(\frac{5}{8}\right)\\= \frac{-5}{2}+ \frac{7}{6}-\frac{5}{8}\\=\frac{-60}{24}+\frac{28}{24}-\frac{15}{24}\\=\frac{-60+28-15}{24}\\=\frac{-47}{24}\)
6. \(-\left(\frac{8}{-3}\right) -\left(\frac{5}{-4}\right) +\left(\frac{-4}{7}\right)\\= \frac{8}{3}+ \frac{5}{4}-\frac{4}{7}\\=\frac{224}{84}+\frac{105}{84}-\frac{48}{84}\\=\frac{224+105-48}{84}\\=\frac{281}{84}\)
7. \(-\left(\frac{7}{8}\right) +\left(\frac{-8}{-4}\right) -\left(\frac{-2}{-11}\right)\\= \frac{-7}{8}+ \frac{8}{4}-\frac{2}{11}\\=\frac{-7}{8}+\frac{2}{1}-\frac{2}{11}\\=\frac{-77}{88}+\frac{176}{88}-\frac{16}{88}\\=\frac{-77+176-16}{88}\\=\frac{83}{88}\)
8. \(-\left(\frac{-5}{9}\right) +\left(\frac{-10}{5}\right) -\left(\frac{-12}{-10}\right)\\= \frac{5}{9}- \frac{10}{5}-\frac{12}{10}\\=\frac{5}{9}-\frac{2}{1}-\frac{6}{5}\\=\frac{25}{45}-\frac{90}{45}-\frac{54}{45}\\=\frac{25-90-54}{45}\\=\frac{-119}{45}\)
9. \(+\left(\frac{4}{9}\right) +\left(\frac{6}{8}\right) +\left(\frac{3}{-4}\right)\\= \frac{4}{9}+ \frac{6}{8}-\frac{3}{4}\\=\frac{4}{9}+\frac{3}{4}-\frac{3}{4}\\=\frac{16}{36}+\frac{27}{36}-\frac{27}{36}\\=\frac{16+27-27}{36}\\=\frac{16}{36}\\=\frac{4}{9}\)
10. \(-\left(\frac{-6}{5}\right) -\left(\frac{-8}{4}\right) -\left(\frac{-9}{2}\right)\\= \frac{6}{5}+ \frac{8}{4}+\frac{9}{2}\\=\frac{6}{5}+\frac{2}{1}+\frac{9}{2}\\=\frac{12}{10}+\frac{20}{10}+\frac{45}{10}\\=\frac{12+20+45}{10}\\=\frac{77}{10}\)
11. \(+\left(\frac{2}{9}\right) -\left(\frac{4}{8}\right) -\left(\frac{12}{5}\right)\\= \frac{2}{9}- \frac{4}{8}-\frac{12}{5}\\=\frac{2}{9}-\frac{1}{2}-\frac{12}{5}\\=\frac{20}{90}-\frac{45}{90}-\frac{216}{90}\\=\frac{20-45-216}{90}\\=\frac{-241}{90}\)
12. \(-\left(\frac{-6}{-5}\right) -\left(\frac{7}{10}\right) -\left(\frac{-3}{-9}\right)\\= \frac{-6}{5}- \frac{7}{10}-\frac{3}{9}\\=\frac{-6}{5}-\frac{7}{10}-\frac{1}{3}\\=\frac{-36}{30}-\frac{21}{30}-\frac{10}{30}\\=\frac{-36-21-10}{30}\\=\frac{-67}{30}\)