Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{3}\right) -\left(\frac{-4}{-6}\right) -\left(\frac{3}{12}\right)\\= \frac{-2}{3}- \frac{4}{6}-\frac{3}{12}\\=\frac{-2}{3}-\frac{2}{3}-\frac{1}{4}\\=\frac{-8}{12}-\frac{8}{12}-\frac{3}{12}\\=\frac{-8-8-3}{12}\\=\frac{-19}{12}\)
2. \(-\left(\frac{10}{-9}\right) +\left(\frac{10}{4}\right) -\left(\frac{-12}{2}\right)\\= \frac{10}{9}+ \frac{10}{4}+\frac{12}{2}\\=\frac{10}{9}+\frac{5}{2}+\frac{6}{1}\\=\frac{20}{18}+\frac{45}{18}+\frac{108}{18}\\=\frac{20+45+108}{18}\\=\frac{173}{18}\)
3. \(-\left(\frac{-2}{-5}\right) -\left(\frac{3}{4}\right) -\left(\frac{-7}{8}\right)\\= \frac{-2}{5}- \frac{3}{4}+\frac{7}{8}\\=\frac{-16}{40}-\frac{30}{40}+\frac{35}{40}\\=\frac{-16-30+35}{40}\\=\frac{-11}{40}\)
4. \(-\left(\frac{4}{-7}\right) +\left(\frac{10}{2}\right) +\left(\frac{-5}{-2}\right)\\= \frac{4}{7}+ \frac{10}{2}+\frac{5}{2}\\=\frac{4}{7}+\frac{5}{1}+\frac{5}{2}\\=\frac{8}{14}+\frac{70}{14}+\frac{35}{14}\\=\frac{8+70+35}{14}\\=\frac{113}{14}\)
5. \(+\left(\frac{-7}{2}\right) +\left(\frac{3}{-6}\right) -\left(\frac{-9}{10}\right)\\= \frac{-7}{2}- \frac{3}{6}+\frac{9}{10}\\=\frac{-7}{2}-\frac{1}{2}+\frac{9}{10}\\=\frac{-35}{10}-\frac{5}{10}+\frac{9}{10}\\=\frac{-35-5+9}{10}\\=\frac{-31}{10}\)
6. \(-\left(\frac{-9}{-8}\right) -\left(\frac{-2}{-4}\right) -\left(\frac{12}{-2}\right)\\= \frac{-9}{8}- \frac{2}{4}+\frac{12}{2}\\=\frac{-9}{8}-\frac{1}{2}+\frac{6}{1}\\=\frac{-9-1+6}{8}\\=\frac{-4}{8}\\=\frac{-1}{2}\)
7. \(-\left(\frac{4}{-3}\right) -\left(\frac{-5}{-7}\right) +\left(\frac{2}{11}\right)\\= \frac{4}{3}- \frac{5}{7}+\frac{2}{11}\\=\frac{308}{231}-\frac{165}{231}+\frac{42}{231}\\=\frac{308-165+42}{231}\\=\frac{185}{231}\)
8. \(-\left(\frac{7}{-3}\right) +\left(\frac{3}{-8}\right) -\left(\frac{10}{2}\right)\\= \frac{7}{3}- \frac{3}{8}-\frac{10}{2}\\=\frac{7}{3}-\frac{3}{8}-\frac{5}{1}\\=\frac{56}{24}-\frac{9}{24}-\frac{120}{24}\\=\frac{56-9-120}{24}\\=\frac{-73}{24}\)
9. \(-\left(\frac{10}{3}\right) +\left(\frac{9}{-7}\right) -\left(\frac{-12}{4}\right)\\= \frac{-10}{3}- \frac{9}{7}+\frac{12}{4}\\=\frac{-10}{3}-\frac{9}{7}+\frac{3}{1}\\=\frac{-70}{21}-\frac{27}{21}+\frac{63}{21}\\=\frac{-70-27+63}{21}\\=\frac{-34}{21}\)
10. \(-\left(\frac{-8}{3}\right) +\left(\frac{5}{-7}\right) -\left(\frac{5}{9}\right)\\= \frac{8}{3}- \frac{5}{7}-\frac{5}{9}\\=\frac{168}{63}-\frac{45}{63}-\frac{35}{63}\\=\frac{168-45-35}{63}\\=\frac{88}{63}\)
11. \(+\left(\frac{2}{3}\right) -\left(\frac{6}{5}\right) -\left(\frac{9}{11}\right)\\= \frac{2}{3}- \frac{6}{5}-\frac{9}{11}\\=\frac{110}{165}-\frac{198}{165}-\frac{135}{165}\\=\frac{110-198-135}{165}\\=\frac{-223}{165}\)
12. \(-\left(\frac{3}{-8}\right) -\left(\frac{-6}{3}\right) -\left(\frac{-2}{8}\right)\\= \frac{3}{8}+ \frac{6}{3}+\frac{2}{8}\\=\frac{3}{8}+\frac{2}{1}+\frac{1}{4}\\=\frac{3+2+1}{8}\\=\frac{6}{8}\\=\frac{3}{4}\)