Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{10}{-3}\right) +\left(\frac{-10}{-2}\right) +\left(\frac{-12}{-10}\right)\\= \frac{10}{3}+ \frac{10}{2}+\frac{12}{10}\\=\frac{10}{3}+\frac{5}{1}+\frac{6}{5}\\=\frac{50}{15}+\frac{75}{15}+\frac{18}{15}\\=\frac{50+75+18}{15}\\=\frac{143}{15}\)
2. \(-\left(\frac{2}{9}\right) +\left(\frac{7}{5}\right) -\left(\frac{11}{-12}\right)\\= \frac{-2}{9}+ \frac{7}{5}+\frac{11}{12}\\=\frac{-40}{180}+\frac{252}{180}+\frac{165}{180}\\=\frac{-40+252+165}{180}\\=\frac{377}{180}\)
3. \(+\left(\frac{7}{-9}\right) -\left(\frac{4}{-5}\right) +\left(\frac{3}{-6}\right)\\= \frac{-7}{9}+ \frac{4}{5}-\frac{3}{6}\\=\frac{-7}{9}+\frac{4}{5}-\frac{1}{2}\\=\frac{-70}{90}+\frac{72}{90}-\frac{45}{90}\\=\frac{-70+72-45}{90}\\=\frac{-43}{90}\)
4. \(+\left(\frac{9}{4}\right) -\left(\frac{6}{-7}\right) +\left(\frac{-10}{-5}\right)\\= \frac{9}{4}+ \frac{6}{7}+\frac{10}{5}\\=\frac{9}{4}+\frac{6}{7}+\frac{2}{1}\\=\frac{63}{28}+\frac{24}{28}+\frac{56}{28}\\=\frac{63+24+56}{28}\\=\frac{143}{28}\)
5. \(-\left(\frac{-9}{2}\right) -\left(\frac{5}{-2}\right) -\left(\frac{12}{-9}\right)\\= \frac{9}{2}+ \frac{5}{2}+\frac{12}{9}\\=\frac{9}{2}+\frac{5}{2}+\frac{4}{3}\\=\frac{27}{6}+\frac{15}{6}+\frac{8}{6}\\=\frac{27+15+8}{6}\\=\frac{50}{6}\\=\frac{25}{3}\)
6. \(-\left(\frac{3}{10}\right) -\left(\frac{3}{4}\right) -\left(\frac{12}{2}\right)\\= \frac{-3}{10}- \frac{3}{4}-\frac{12}{2}\\=\frac{-3}{10}-\frac{3}{4}-\frac{6}{1}\\=\frac{-6}{20}-\frac{15}{20}-\frac{120}{20}\\=\frac{-6-15-120}{20}\\=\frac{-141}{20}\)
7. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-10}{10}\right) +\left(\frac{5}{3}\right)\\= \frac{-6}{5}+ \frac{10}{10}+\frac{5}{3}\\=\frac{-6}{5}+\frac{1}{1}+\frac{5}{3}\\=\frac{-18}{15}+\frac{15}{15}+\frac{25}{15}\\=\frac{-18+15+25}{15}\\=\frac{22}{15}\)
8. \(+\left(\frac{4}{-5}\right) +\left(\frac{-7}{3}\right) -\left(\frac{7}{2}\right)\\= \frac{-4}{5}- \frac{7}{3}-\frac{7}{2}\\=\frac{-24}{30}-\frac{70}{30}-\frac{105}{30}\\=\frac{-24-70-105}{30}\\=\frac{-199}{30}\)
9. \(+\left(\frac{-7}{4}\right) +\left(\frac{-4}{8}\right) +\left(\frac{-4}{12}\right)\\= \frac{-7}{4}- \frac{4}{8}-\frac{4}{12}\\=\frac{-7}{4}-\frac{1}{2}-\frac{1}{3}\\=\frac{-21}{12}-\frac{6}{12}-\frac{4}{12}\\=\frac{-21-6-4}{12}\\=\frac{-31}{12}\)
10. \(+\left(\frac{-9}{5}\right) +\left(\frac{5}{7}\right) -\left(\frac{-7}{-9}\right)\\= \frac{-9}{5}+ \frac{5}{7}-\frac{7}{9}\\=\frac{-567}{315}+\frac{225}{315}-\frac{245}{315}\\=\frac{-567+225-245}{315}\\=\frac{-587}{315}\)
11. \(+\left(\frac{4}{7}\right) +\left(\frac{-9}{-9}\right) +\left(\frac{2}{11}\right)\\= \frac{4}{7}+ \frac{9}{9}+\frac{2}{11}\\=\frac{4}{7}+\frac{1}{1}+\frac{2}{11}\\=\frac{44}{77}+\frac{77}{77}+\frac{14}{77}\\=\frac{44+77+14}{77}\\=\frac{135}{77}\)
12. \(+\left(\frac{-2}{3}\right) -\left(\frac{3}{8}\right) -\left(\frac{-7}{8}\right)\\= \frac{-2}{3}- \frac{3}{8}+\frac{7}{8}\\=\frac{-16}{24}-\frac{9}{24}+\frac{21}{24}\\=\frac{-16-9+21}{24}\\=\frac{-4}{24}\\=\frac{-1}{6}\)