Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{-5}\right) +\left(\frac{2}{10}\right) +\left(\frac{-4}{4}\right)\\= \frac{6}{5}+ \frac{2}{10}-\frac{4}{4}\\=\frac{6}{5}+\frac{1}{5}-\frac{1}{1}\\=\frac{6+1-1}{5}\\=\frac{6}{5}\)
2. \(+\left(\frac{3}{7}\right) +\left(\frac{-3}{10}\right) -\left(\frac{-11}{-5}\right)\\= \frac{3}{7}- \frac{3}{10}-\frac{11}{5}\\=\frac{30}{70}-\frac{21}{70}-\frac{154}{70}\\=\frac{30-21-154}{70}\\=\frac{-145}{70}\\=\frac{-29}{14}\)
3. \(-\left(\frac{-9}{5}\right) -\left(\frac{9}{9}\right) +\left(\frac{6}{7}\right)\\= \frac{9}{5}- \frac{9}{9}+\frac{6}{7}\\=\frac{9}{5}-\frac{1}{1}+\frac{6}{7}\\=\frac{63}{35}-\frac{35}{35}+\frac{30}{35}\\=\frac{63-35+30}{35}\\=\frac{58}{35}\)
4. \(-\left(\frac{-4}{-3}\right) +\left(\frac{3}{3}\right) -\left(\frac{-12}{2}\right)\\= \frac{-4}{3}+ \frac{3}{3}+\frac{12}{2}\\=\frac{-4}{3}+\frac{1}{1}+\frac{6}{1}\\=\frac{-4+1+6}{3}\\=\frac{3}{3}\\=\frac{1}{1}\)
5. \(+\left(\frac{10}{7}\right) +\left(\frac{-3}{9}\right) -\left(\frac{11}{12}\right)\\= \frac{10}{7}- \frac{3}{9}-\frac{11}{12}\\=\frac{10}{7}-\frac{1}{3}-\frac{11}{12}\\=\frac{120}{84}-\frac{28}{84}-\frac{77}{84}\\=\frac{120-28-77}{84}\\=\frac{15}{84}\\=\frac{5}{28}\)
6. \(+\left(\frac{-9}{5}\right) +\left(\frac{-10}{10}\right) +\left(\frac{10}{11}\right)\\= \frac{-9}{5}- \frac{10}{10}+\frac{10}{11}\\=\frac{-9}{5}-\frac{1}{1}+\frac{10}{11}\\=\frac{-99}{55}-\frac{55}{55}+\frac{50}{55}\\=\frac{-99-55+50}{55}\\=\frac{-104}{55}\)
7. \(+\left(\frac{6}{7}\right) -\left(\frac{9}{-2}\right) -\left(\frac{-2}{-3}\right)\\= \frac{6}{7}+ \frac{9}{2}-\frac{2}{3}\\=\frac{36}{42}+\frac{189}{42}-\frac{28}{42}\\=\frac{36+189-28}{42}\\=\frac{197}{42}\)
8. \(-\left(\frac{-10}{7}\right) +\left(\frac{10}{-8}\right) -\left(\frac{2}{10}\right)\\= \frac{10}{7}- \frac{10}{8}-\frac{2}{10}\\=\frac{10}{7}-\frac{5}{4}-\frac{1}{5}\\=\frac{200}{140}-\frac{175}{140}-\frac{28}{140}\\=\frac{200-175-28}{140}\\=\frac{-3}{140}\)
9. \(+\left(\frac{-5}{2}\right) +\left(\frac{-7}{-2}\right) +\left(\frac{3}{-7}\right)\\= \frac{-5}{2}+ \frac{7}{2}-\frac{3}{7}\\=\frac{-35}{14}+\frac{49}{14}-\frac{6}{14}\\=\frac{-35+49-6}{14}\\=\frac{8}{14}\\=\frac{4}{7}\)
10. \(+\left(\frac{7}{-2}\right) -\left(\frac{8}{-8}\right) -\left(\frac{-7}{12}\right)\\= \frac{-7}{2}+ \frac{8}{8}+\frac{7}{12}\\=\frac{-7}{2}+\frac{1}{1}+\frac{7}{12}\\=\frac{-42}{12}+\frac{12}{12}+\frac{7}{12}\\=\frac{-42+12+7}{12}\\=\frac{-23}{12}\)
11. \(-\left(\frac{-3}{-5}\right) +\left(\frac{-2}{4}\right) +\left(\frac{4}{4}\right)\\= \frac{-3}{5}- \frac{2}{4}+\frac{4}{4}\\=\frac{-3}{5}-\frac{1}{2}+\frac{1}{1}\\=\frac{-6}{10}-\frac{5}{10}+\frac{10}{10}\\=\frac{-6-5+10}{10}\\=\frac{-1}{10}\)
12. \(-\left(\frac{7}{-9}\right) +\left(\frac{-5}{7}\right) +\left(\frac{6}{3}\right)\\= \frac{7}{9}- \frac{5}{7}+\frac{6}{3}\\=\frac{7}{9}-\frac{5}{7}+\frac{2}{1}\\=\frac{49}{63}-\frac{45}{63}+\frac{126}{63}\\=\frac{49-45+126}{63}\\=\frac{130}{63}\)