Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{9}\right) -\left(\frac{-7}{5}\right) -\left(\frac{6}{-11}\right)\\= \frac{-10}{9}+ \frac{7}{5}+\frac{6}{11}\\=\frac{-550}{495}+\frac{693}{495}+\frac{270}{495}\\=\frac{-550+693+270}{495}\\=\frac{413}{495}\)
2. \(+\left(\frac{3}{2}\right) +\left(\frac{-9}{7}\right) +\left(\frac{12}{8}\right)\\= \frac{3}{2}- \frac{9}{7}+\frac{12}{8}\\=\frac{3}{2}-\frac{9}{7}+\frac{3}{2}\\=\frac{21}{14}-\frac{18}{14}+\frac{21}{14}\\=\frac{21-18+21}{14}\\=\frac{24}{14}\\=\frac{12}{7}\)
3. \(-\left(\frac{3}{-4}\right) +\left(\frac{-7}{-2}\right) -\left(\frac{-6}{4}\right)\\= \frac{3}{4}+ \frac{7}{2}+\frac{6}{4}\\=\frac{3}{4}+\frac{7}{2}+\frac{3}{2}\\=\frac{3+7+3}{4}\\=\frac{13}{4}\)
4. \(-\left(\frac{-5}{7}\right) -\left(\frac{2}{-9}\right) +\left(\frac{3}{-3}\right)\\= \frac{5}{7}+ \frac{2}{9}-\frac{3}{3}\\=\frac{5}{7}+\frac{2}{9}-\frac{1}{1}\\=\frac{45}{63}+\frac{14}{63}-\frac{63}{63}\\=\frac{45+14-63}{63}\\=\frac{-4}{63}\)
5. \(-\left(\frac{8}{5}\right) +\left(\frac{10}{3}\right) -\left(\frac{-7}{-10}\right)\\= \frac{-8}{5}+ \frac{10}{3}-\frac{7}{10}\\=\frac{-48}{30}+\frac{100}{30}-\frac{21}{30}\\=\frac{-48+100-21}{30}\\=\frac{31}{30}\)
6. \(+\left(\frac{2}{-5}\right) +\left(\frac{-5}{-2}\right) +\left(\frac{-5}{-4}\right)\\= \frac{-2}{5}+ \frac{5}{2}+\frac{5}{4}\\=\frac{-8}{20}+\frac{50}{20}+\frac{25}{20}\\=\frac{-8+50+25}{20}\\=\frac{67}{20}\)
7. \(-\left(\frac{9}{2}\right) +\left(\frac{-6}{-10}\right) +\left(\frac{-11}{-3}\right)\\= \frac{-9}{2}+ \frac{6}{10}+\frac{11}{3}\\=\frac{-9}{2}+\frac{3}{5}+\frac{11}{3}\\=\frac{-135}{30}+\frac{18}{30}+\frac{110}{30}\\=\frac{-135+18+110}{30}\\=\frac{-7}{30}\)
8. \(-\left(\frac{-8}{3}\right) +\left(\frac{3}{2}\right) -\left(\frac{3}{4}\right)\\= \frac{8}{3}+ \frac{3}{2}-\frac{3}{4}\\=\frac{32}{12}+\frac{18}{12}-\frac{9}{12}\\=\frac{32+18-9}{12}\\=\frac{41}{12}\)
9. \(+\left(\frac{10}{3}\right) +\left(\frac{5}{8}\right) -\left(\frac{-9}{-3}\right)\\= \frac{10}{3}+ \frac{5}{8}-\frac{9}{3}\\=\frac{10}{3}+\frac{5}{8}-\frac{3}{1}\\=\frac{80}{24}+\frac{15}{24}-\frac{72}{24}\\=\frac{80+15-72}{24}\\=\frac{23}{24}\)
10. \(-\left(\frac{-10}{7}\right) +\left(\frac{7}{-10}\right) -\left(\frac{-4}{-10}\right)\\= \frac{10}{7}- \frac{7}{10}-\frac{4}{10}\\=\frac{10}{7}-\frac{7}{10}-\frac{2}{5}\\=\frac{100}{70}-\frac{49}{70}-\frac{28}{70}\\=\frac{100-49-28}{70}\\=\frac{23}{70}\)
11. \(-\left(\frac{7}{9}\right) -\left(\frac{8}{-5}\right) +\left(\frac{-2}{-12}\right)\\= \frac{-7}{9}+ \frac{8}{5}+\frac{2}{12}\\=\frac{-7}{9}+\frac{8}{5}+\frac{1}{6}\\=\frac{-70}{90}+\frac{144}{90}+\frac{15}{90}\\=\frac{-70+144+15}{90}\\=\frac{89}{90}\)
12. \(+\left(\frac{9}{2}\right) +\left(\frac{3}{-10}\right) +\left(\frac{-8}{-7}\right)\\= \frac{9}{2}- \frac{3}{10}+\frac{8}{7}\\=\frac{315}{70}-\frac{21}{70}+\frac{80}{70}\\=\frac{315-21+80}{70}\\=\frac{374}{70}\\=\frac{187}{35}\)