Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{-5}\right) +\left(\frac{-2}{6}\right) -\left(\frac{11}{11}\right)\\= \frac{8}{5}- \frac{2}{6}-\frac{11}{11}\\=\frac{8}{5}-\frac{1}{3}-\frac{1}{1}\\=\frac{24}{15}-\frac{5}{15}-\frac{15}{15}\\=\frac{24-5-15}{15}\\=\frac{4}{15}\)
2. \(-\left(\frac{3}{-7}\right) -\left(\frac{5}{10}\right) +\left(\frac{2}{-7}\right)\\= \frac{3}{7}- \frac{5}{10}-\frac{2}{7}\\=\frac{3}{7}-\frac{1}{2}-\frac{2}{7}\\=\frac{6}{14}-\frac{7}{14}-\frac{4}{14}\\=\frac{6-7-4}{14}\\=\frac{-5}{14}\)
3. \(+\left(\frac{4}{-5}\right) +\left(\frac{-3}{-9}\right) +\left(\frac{-3}{-8}\right)\\= \frac{-4}{5}+ \frac{3}{9}+\frac{3}{8}\\=\frac{-4}{5}+\frac{1}{3}+\frac{3}{8}\\=\frac{-96}{120}+\frac{40}{120}+\frac{45}{120}\\=\frac{-96+40+45}{120}\\=\frac{-11}{120}\)
4. \(+\left(\frac{3}{5}\right) -\left(\frac{8}{-7}\right) +\left(\frac{3}{4}\right)\\= \frac{3}{5}+ \frac{8}{7}+\frac{3}{4}\\=\frac{84}{140}+\frac{160}{140}+\frac{105}{140}\\=\frac{84+160+105}{140}\\=\frac{349}{140}\)
5. \(+\left(\frac{-6}{5}\right) -\left(\frac{-4}{-6}\right) +\left(\frac{-7}{-6}\right)\\= \frac{-6}{5}- \frac{4}{6}+\frac{7}{6}\\=\frac{-6}{5}-\frac{2}{3}+\frac{7}{6}\\=\frac{-36}{30}-\frac{20}{30}+\frac{35}{30}\\=\frac{-36-20+35}{30}\\=\frac{-21}{30}\\=\frac{-7}{10}\)
6. \(-\left(\frac{8}{-9}\right) +\left(\frac{-5}{-5}\right) +\left(\frac{8}{11}\right)\\= \frac{8}{9}+ \frac{5}{5}+\frac{8}{11}\\=\frac{8}{9}+\frac{1}{1}+\frac{8}{11}\\=\frac{88}{99}+\frac{99}{99}+\frac{72}{99}\\=\frac{88+99+72}{99}\\=\frac{259}{99}\)
7. \(-\left(\frac{10}{-3}\right) +\left(\frac{-7}{-4}\right) -\left(\frac{-11}{-7}\right)\\= \frac{10}{3}+ \frac{7}{4}-\frac{11}{7}\\=\frac{280}{84}+\frac{147}{84}-\frac{132}{84}\\=\frac{280+147-132}{84}\\=\frac{295}{84}\)
8. \(-\left(\frac{-8}{5}\right) +\left(\frac{8}{-8}\right) +\left(\frac{-10}{4}\right)\\= \frac{8}{5}- \frac{8}{8}-\frac{10}{4}\\=\frac{8}{5}-\frac{1}{1}-\frac{5}{2}\\=\frac{16}{10}-\frac{10}{10}-\frac{25}{10}\\=\frac{16-10-25}{10}\\=\frac{-19}{10}\)
9. \(-\left(\frac{5}{-9}\right) -\left(\frac{-6}{8}\right) -\left(\frac{-5}{9}\right)\\= \frac{5}{9}+ \frac{6}{8}+\frac{5}{9}\\=\frac{5}{9}+\frac{3}{4}+\frac{5}{9}\\=\frac{20}{36}+\frac{27}{36}+\frac{20}{36}\\=\frac{20+27+20}{36}\\=\frac{67}{36}\)
10. \(-\left(\frac{9}{-4}\right) -\left(\frac{-9}{-3}\right) -\left(\frac{-9}{-11}\right)\\= \frac{9}{4}- \frac{9}{3}-\frac{9}{11}\\=\frac{9}{4}-\frac{3}{1}-\frac{9}{11}\\=\frac{99}{44}-\frac{132}{44}-\frac{36}{44}\\=\frac{99-132-36}{44}\\=\frac{-69}{44}\)
11. \(-\left(\frac{-9}{-2}\right) -\left(\frac{6}{-2}\right) +\left(\frac{-2}{10}\right)\\= \frac{-9}{2}+ \frac{6}{2}-\frac{2}{10}\\=\frac{-9}{2}+\frac{3}{1}-\frac{1}{5}\\=\frac{-45}{10}+\frac{30}{10}-\frac{2}{10}\\=\frac{-45+30-2}{10}\\=\frac{-17}{10}\)
12. \(+\left(\frac{-8}{-9}\right) -\left(\frac{4}{2}\right) -\left(\frac{-4}{9}\right)\\= \frac{8}{9}- \frac{4}{2}+\frac{4}{9}\\=\frac{8}{9}-\frac{2}{1}+\frac{4}{9}\\=\frac{8-2+4}{9}\\=\frac{10}{9}\)