Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{3}\right) +\left(\frac{-10}{6}\right) +\left(\frac{10}{2}\right)\\= \frac{10}{3}- \frac{10}{6}+\frac{10}{2}\\=\frac{10}{3}-\frac{5}{3}+\frac{5}{1}\\=\frac{10-5+5}{3}\\=\frac{10}{3}\)
2. \(+\left(\frac{7}{-6}\right) -\left(\frac{2}{-9}\right) -\left(\frac{8}{-2}\right)\\= \frac{-7}{6}+ \frac{2}{9}+\frac{8}{2}\\=\frac{-7}{6}+\frac{2}{9}+\frac{4}{1}\\=\frac{-21}{18}+\frac{4}{18}+\frac{72}{18}\\=\frac{-21+4+72}{18}\\=\frac{55}{18}\)
3. \(-\left(\frac{10}{-9}\right) -\left(\frac{-8}{-7}\right) +\left(\frac{3}{-7}\right)\\= \frac{10}{9}- \frac{8}{7}-\frac{3}{7}\\=\frac{70}{63}-\frac{72}{63}-\frac{27}{63}\\=\frac{70-72-27}{63}\\=\frac{-29}{63}\)
4. \(-\left(\frac{-3}{-2}\right) -\left(\frac{-7}{10}\right) +\left(\frac{8}{10}\right)\\= \frac{-3}{2}+ \frac{7}{10}+\frac{8}{10}\\=\frac{-3}{2}+\frac{7}{10}+\frac{4}{5}\\=\frac{-15}{10}+\frac{7}{10}+\frac{8}{10}\\=\frac{-15+7+8}{10}\\=\frac{0}{10}\\=\frac{0}{1}\)
5. \(-\left(\frac{8}{-9}\right) +\left(\frac{-10}{-4}\right) +\left(\frac{5}{3}\right)\\= \frac{8}{9}+ \frac{10}{4}+\frac{5}{3}\\=\frac{8}{9}+\frac{5}{2}+\frac{5}{3}\\=\frac{16}{18}+\frac{45}{18}+\frac{30}{18}\\=\frac{16+45+30}{18}\\=\frac{91}{18}\)
6. \(+\left(\frac{-9}{-4}\right) +\left(\frac{3}{-7}\right) +\left(\frac{8}{-2}\right)\\= \frac{9}{4}- \frac{3}{7}-\frac{8}{2}\\=\frac{9}{4}-\frac{3}{7}-\frac{4}{1}\\=\frac{63}{28}-\frac{12}{28}-\frac{112}{28}\\=\frac{63-12-112}{28}\\=\frac{-61}{28}\)
7. \(-\left(\frac{-3}{5}\right) +\left(\frac{-10}{-6}\right) +\left(\frac{7}{-11}\right)\\= \frac{3}{5}+ \frac{10}{6}-\frac{7}{11}\\=\frac{3}{5}+\frac{5}{3}-\frac{7}{11}\\=\frac{99}{165}+\frac{275}{165}-\frac{105}{165}\\=\frac{99+275-105}{165}\\=\frac{269}{165}\)
8. \(-\left(\frac{-3}{-5}\right) +\left(\frac{2}{5}\right) +\left(\frac{12}{11}\right)\\= \frac{-3}{5}+ \frac{2}{5}+\frac{12}{11}\\=\frac{-33}{55}+\frac{22}{55}+\frac{60}{55}\\=\frac{-33+22+60}{55}\\=\frac{49}{55}\)
9. \(+\left(\frac{6}{-5}\right) +\left(\frac{3}{2}\right) +\left(\frac{5}{-12}\right)\\= \frac{-6}{5}+ \frac{3}{2}-\frac{5}{12}\\=\frac{-72}{60}+\frac{90}{60}-\frac{25}{60}\\=\frac{-72+90-25}{60}\\=\frac{-7}{60}\)
10. \(+\left(\frac{2}{3}\right) +\left(\frac{8}{5}\right) +\left(\frac{12}{-8}\right)\\= \frac{2}{3}+ \frac{8}{5}-\frac{12}{8}\\=\frac{2}{3}+\frac{8}{5}-\frac{3}{2}\\=\frac{20}{30}+\frac{48}{30}-\frac{45}{30}\\=\frac{20+48-45}{30}\\=\frac{23}{30}\)
11. \(+\left(\frac{-2}{7}\right) -\left(\frac{8}{9}\right) -\left(\frac{-10}{-7}\right)\\= \frac{-2}{7}- \frac{8}{9}-\frac{10}{7}\\=\frac{-18}{63}-\frac{56}{63}-\frac{90}{63}\\=\frac{-18-56-90}{63}\\=\frac{-164}{63}\)
12. \(+\left(\frac{4}{-5}\right) +\left(\frac{2}{2}\right) -\left(\frac{-11}{3}\right)\\= \frac{-4}{5}+ \frac{2}{2}+\frac{11}{3}\\=\frac{-4}{5}+\frac{1}{1}+\frac{11}{3}\\=\frac{-12}{15}+\frac{15}{15}+\frac{55}{15}\\=\frac{-12+15+55}{15}\\=\frac{58}{15}\)