Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{2}\right) -\left(\frac{-2}{4}\right) +\left(\frac{5}{-4}\right)\\= \frac{3}{2}+ \frac{2}{4}-\frac{5}{4}\\=\frac{3}{2}+\frac{1}{2}-\frac{5}{4}\\=\frac{6}{4}+\frac{2}{4}-\frac{5}{4}\\=\frac{6+2-5}{4}\\=\frac{3}{4}\)
2. \(-\left(\frac{-7}{8}\right) -\left(\frac{3}{4}\right) +\left(\frac{4}{-10}\right)\\= \frac{7}{8}- \frac{3}{4}-\frac{4}{10}\\=\frac{7}{8}-\frac{3}{4}-\frac{2}{5}\\=\frac{35}{40}-\frac{30}{40}-\frac{16}{40}\\=\frac{35-30-16}{40}\\=\frac{-11}{40}\)
3. \(-\left(\frac{7}{-9}\right) -\left(\frac{-4}{7}\right) -\left(\frac{8}{4}\right)\\= \frac{7}{9}+ \frac{4}{7}-\frac{8}{4}\\=\frac{7}{9}+\frac{4}{7}-\frac{2}{1}\\=\frac{49}{63}+\frac{36}{63}-\frac{126}{63}\\=\frac{49+36-126}{63}\\=\frac{-41}{63}\)
4. \(-\left(\frac{7}{5}\right) -\left(\frac{4}{5}\right) -\left(\frac{-3}{2}\right)\\= \frac{-7}{5}- \frac{4}{5}+\frac{3}{2}\\=\frac{-14}{10}-\frac{8}{10}+\frac{15}{10}\\=\frac{-14-8+15}{10}\\=\frac{-7}{10}\)
5. \(-\left(\frac{-7}{2}\right) +\left(\frac{10}{2}\right) +\left(\frac{-10}{3}\right)\\= \frac{7}{2}+ \frac{10}{2}-\frac{10}{3}\\=\frac{7}{2}+\frac{5}{1}-\frac{10}{3}\\=\frac{21}{6}+\frac{30}{6}-\frac{20}{6}\\=\frac{21+30-20}{6}\\=\frac{31}{6}\)
6. \(-\left(\frac{7}{3}\right) +\left(\frac{4}{4}\right) +\left(\frac{-8}{-9}\right)\\= \frac{-7}{3}+ \frac{4}{4}+\frac{8}{9}\\=\frac{-7}{3}+\frac{1}{1}+\frac{8}{9}\\=\frac{-21}{9}+\frac{9}{9}+\frac{8}{9}\\=\frac{-21+9+8}{9}\\=\frac{-4}{9}\)
7. \(+\left(\frac{-8}{-3}\right) +\left(\frac{-7}{2}\right) +\left(\frac{10}{-2}\right)\\= \frac{8}{3}- \frac{7}{2}-\frac{10}{2}\\=\frac{8}{3}-\frac{7}{2}-\frac{5}{1}\\=\frac{16}{6}-\frac{21}{6}-\frac{30}{6}\\=\frac{16-21-30}{6}\\=\frac{-35}{6}\)
8. \(+\left(\frac{-6}{5}\right) +\left(\frac{-6}{-3}\right) -\left(\frac{-4}{5}\right)\\= \frac{-6}{5}+ \frac{6}{3}+\frac{4}{5}\\=\frac{-6}{5}+\frac{2}{1}+\frac{4}{5}\\=\frac{-6+2+4}{5}\\=\frac{0}{5}\\=\frac{0}{1}\)
9. \(+\left(\frac{6}{5}\right) -\left(\frac{-5}{-5}\right) -\left(\frac{11}{-12}\right)\\= \frac{6}{5}- \frac{5}{5}+\frac{11}{12}\\=\frac{6}{5}-\frac{1}{1}+\frac{11}{12}\\=\frac{72}{60}-\frac{60}{60}+\frac{55}{60}\\=\frac{72-60+55}{60}\\=\frac{67}{60}\)
10. \(-\left(\frac{-10}{-7}\right) -\left(\frac{7}{5}\right) +\left(\frac{7}{5}\right)\\= \frac{-10}{7}- \frac{7}{5}+\frac{7}{5}\\=\frac{-50}{35}-\frac{49}{35}+\frac{49}{35}\\=\frac{-50-49+49}{35}\\=\frac{-50}{35}\\=\frac{-10}{7}\)
11. \(-\left(\frac{8}{-3}\right) -\left(\frac{-3}{5}\right) -\left(\frac{-12}{7}\right)\\= \frac{8}{3}+ \frac{3}{5}+\frac{12}{7}\\=\frac{280}{105}+\frac{63}{105}+\frac{180}{105}\\=\frac{280+63+180}{105}\\=\frac{523}{105}\)
12. \(+\left(\frac{-9}{5}\right) +\left(\frac{3}{6}\right) -\left(\frac{-7}{-12}\right)\\= \frac{-9}{5}+ \frac{3}{6}-\frac{7}{12}\\=\frac{-9}{5}+\frac{1}{2}-\frac{7}{12}\\=\frac{-108}{60}+\frac{30}{60}-\frac{35}{60}\\=\frac{-108+30-35}{60}\\=\frac{-113}{60}\)