Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{4}{-9}\right) +\left(\frac{6}{4}\right) +\left(\frac{9}{5}\right)\\= \frac{-4}{9}+ \frac{6}{4}+\frac{9}{5}\\=\frac{-4}{9}+\frac{3}{2}+\frac{9}{5}\\=\frac{-40}{90}+\frac{135}{90}+\frac{162}{90}\\=\frac{-40+135+162}{90}\\=\frac{257}{90}\)
2. \(-\left(\frac{10}{-7}\right) +\left(\frac{7}{4}\right) +\left(\frac{11}{11}\right)\\= \frac{10}{7}+ \frac{7}{4}+\frac{11}{11}\\=\frac{10}{7}+\frac{7}{4}+\frac{1}{1}\\=\frac{40}{28}+\frac{49}{28}+\frac{28}{28}\\=\frac{40+49+28}{28}\\=\frac{117}{28}\)
3. \(-\left(\frac{2}{5}\right) -\left(\frac{-3}{-9}\right) +\left(\frac{8}{-4}\right)\\= \frac{-2}{5}- \frac{3}{9}-\frac{8}{4}\\=\frac{-2}{5}-\frac{1}{3}-\frac{2}{1}\\=\frac{-6}{15}-\frac{5}{15}-\frac{30}{15}\\=\frac{-6-5-30}{15}\\=\frac{-41}{15}\)
4. \(+\left(\frac{-7}{6}\right) -\left(\frac{5}{-4}\right) +\left(\frac{-11}{12}\right)\\= \frac{-7}{6}+ \frac{5}{4}-\frac{11}{12}\\=\frac{-14}{12}+\frac{15}{12}-\frac{11}{12}\\=\frac{-14+15-11}{12}\\=\frac{-10}{12}\\=\frac{-5}{6}\)
5. \(+\left(\frac{2}{9}\right) +\left(\frac{4}{-10}\right) +\left(\frac{-7}{-10}\right)\\= \frac{2}{9}- \frac{4}{10}+\frac{7}{10}\\=\frac{2}{9}-\frac{2}{5}+\frac{7}{10}\\=\frac{20}{90}-\frac{36}{90}+\frac{63}{90}\\=\frac{20-36+63}{90}\\=\frac{47}{90}\)
6. \(-\left(\frac{3}{2}\right) -\left(\frac{3}{6}\right) -\left(\frac{-10}{-7}\right)\\= \frac{-3}{2}- \frac{3}{6}-\frac{10}{7}\\=\frac{-3}{2}-\frac{1}{2}-\frac{10}{7}\\=\frac{-21}{14}-\frac{7}{14}-\frac{20}{14}\\=\frac{-21-7-20}{14}\\=\frac{-48}{14}\\=\frac{-24}{7}\)
7. \(+\left(\frac{-6}{-7}\right) -\left(\frac{-7}{4}\right) -\left(\frac{-4}{7}\right)\\= \frac{6}{7}+ \frac{7}{4}+\frac{4}{7}\\=\frac{24}{28}+\frac{49}{28}+\frac{16}{28}\\=\frac{24+49+16}{28}\\=\frac{89}{28}\)
8. \(-\left(\frac{-4}{-9}\right) -\left(\frac{10}{3}\right) -\left(\frac{-12}{-7}\right)\\= \frac{-4}{9}- \frac{10}{3}-\frac{12}{7}\\=\frac{-28}{63}-\frac{210}{63}-\frac{108}{63}\\=\frac{-28-210-108}{63}\\=\frac{-346}{63}\)
9. \(+\left(\frac{5}{6}\right) -\left(\frac{-7}{-7}\right) +\left(\frac{-2}{4}\right)\\= \frac{5}{6}- \frac{7}{7}-\frac{2}{4}\\=\frac{5}{6}-\frac{1}{1}-\frac{1}{2}\\=\frac{5-1-1}{6}\\=\frac{3}{6}\\=\frac{1}{2}\)
10. \(+\left(\frac{4}{-3}\right) -\left(\frac{-7}{10}\right) +\left(\frac{5}{-6}\right)\\= \frac{-4}{3}+ \frac{7}{10}-\frac{5}{6}\\=\frac{-40}{30}+\frac{21}{30}-\frac{25}{30}\\=\frac{-40+21-25}{30}\\=\frac{-44}{30}\\=\frac{-22}{15}\)
11. \(+\left(\frac{-8}{3}\right) +\left(\frac{5}{2}\right) -\left(\frac{-9}{-7}\right)\\= \frac{-8}{3}+ \frac{5}{2}-\frac{9}{7}\\=\frac{-112}{42}+\frac{105}{42}-\frac{54}{42}\\=\frac{-112+105-54}{42}\\=\frac{-61}{42}\)
12. \(-\left(\frac{-4}{5}\right) -\left(\frac{-8}{10}\right) -\left(\frac{11}{5}\right)\\= \frac{4}{5}+ \frac{8}{10}-\frac{11}{5}\\=\frac{4}{5}+\frac{4}{5}-\frac{11}{5}\\=\frac{4+4-11}{5}\\=\frac{-3}{5}\)