Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{10}{3}\right) -\left(\frac{-3}{-8}\right) -\left(\frac{-10}{11}\right)\\= \frac{10}{3}- \frac{3}{8}+\frac{10}{11}\\=\frac{880}{264}-\frac{99}{264}+\frac{240}{264}\\=\frac{880-99+240}{264}\\=\frac{1021}{264}\)
2. \(+\left(\frac{9}{2}\right) +\left(\frac{2}{6}\right) +\left(\frac{-9}{10}\right)\\= \frac{9}{2}+ \frac{2}{6}-\frac{9}{10}\\=\frac{9}{2}+\frac{1}{3}-\frac{9}{10}\\=\frac{135}{30}+\frac{10}{30}-\frac{27}{30}\\=\frac{135+10-27}{30}\\=\frac{118}{30}\\=\frac{59}{15}\)
3. \(-\left(\frac{-5}{-8}\right) +\left(\frac{-10}{-6}\right) +\left(\frac{6}{11}\right)\\= \frac{-5}{8}+ \frac{10}{6}+\frac{6}{11}\\=\frac{-5}{8}+\frac{5}{3}+\frac{6}{11}\\=\frac{-165}{264}+\frac{440}{264}+\frac{144}{264}\\=\frac{-165+440+144}{264}\\=\frac{419}{264}\)
4. \(-\left(\frac{-3}{7}\right) -\left(\frac{10}{8}\right) +\left(\frac{-3}{-11}\right)\\= \frac{3}{7}- \frac{10}{8}+\frac{3}{11}\\=\frac{3}{7}-\frac{5}{4}+\frac{3}{11}\\=\frac{132}{308}-\frac{385}{308}+\frac{84}{308}\\=\frac{132-385+84}{308}\\=\frac{-169}{308}\)
5. \(+\left(\frac{-2}{-3}\right) +\left(\frac{-7}{-4}\right) +\left(\frac{-3}{8}\right)\\= \frac{2}{3}+ \frac{7}{4}-\frac{3}{8}\\=\frac{16}{24}+\frac{42}{24}-\frac{9}{24}\\=\frac{16+42-9}{24}\\=\frac{49}{24}\)
6. \(+\left(\frac{-2}{-7}\right) +\left(\frac{3}{-2}\right) +\left(\frac{5}{-6}\right)\\= \frac{2}{7}- \frac{3}{2}-\frac{5}{6}\\=\frac{12}{42}-\frac{63}{42}-\frac{35}{42}\\=\frac{12-63-35}{42}\\=\frac{-86}{42}\\=\frac{-43}{21}\)
7. \(+\left(\frac{-6}{5}\right) -\left(\frac{9}{-2}\right) +\left(\frac{-8}{12}\right)\\= \frac{-6}{5}+ \frac{9}{2}-\frac{8}{12}\\=\frac{-6}{5}+\frac{9}{2}-\frac{2}{3}\\=\frac{-36}{30}+\frac{135}{30}-\frac{20}{30}\\=\frac{-36+135-20}{30}\\=\frac{79}{30}\)
8. \(-\left(\frac{-7}{-2}\right) +\left(\frac{-2}{6}\right) -\left(\frac{-4}{-5}\right)\\= \frac{-7}{2}- \frac{2}{6}-\frac{4}{5}\\=\frac{-7}{2}-\frac{1}{3}-\frac{4}{5}\\=\frac{-105}{30}-\frac{10}{30}-\frac{24}{30}\\=\frac{-105-10-24}{30}\\=\frac{-139}{30}\)
9. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-7}{8}\right) -\left(\frac{12}{-12}\right)\\= \frac{-10}{7}- \frac{7}{8}+\frac{12}{12}\\=\frac{-10}{7}-\frac{7}{8}+\frac{1}{1}\\=\frac{-80}{56}-\frac{49}{56}+\frac{56}{56}\\=\frac{-80-49+56}{56}\\=\frac{-73}{56}\)
10. \(-\left(\frac{-4}{-9}\right) +\left(\frac{-7}{-6}\right) +\left(\frac{-9}{-9}\right)\\= \frac{-4}{9}+ \frac{7}{6}+\frac{9}{9}\\=\frac{-4}{9}+\frac{7}{6}+\frac{1}{1}\\=\frac{-8}{18}+\frac{21}{18}+\frac{18}{18}\\=\frac{-8+21+18}{18}\\=\frac{31}{18}\)
11. \(+\left(\frac{5}{7}\right) -\left(\frac{8}{4}\right) -\left(\frac{9}{-3}\right)\\= \frac{5}{7}- \frac{8}{4}+\frac{9}{3}\\=\frac{5}{7}-\frac{2}{1}+\frac{3}{1}\\=\frac{5-2+3}{7}\\=\frac{6}{7}\)
12. \(+\left(\frac{-6}{5}\right) +\left(\frac{-2}{-3}\right) -\left(\frac{11}{8}\right)\\= \frac{-6}{5}+ \frac{2}{3}-\frac{11}{8}\\=\frac{-144}{120}+\frac{80}{120}-\frac{165}{120}\\=\frac{-144+80-165}{120}\\=\frac{-229}{120}\)