Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{6}{-5}\right) +\left(\frac{8}{-5}\right) -\left(\frac{8}{11}\right)\\= \frac{-6}{5}- \frac{8}{5}-\frac{8}{11}\\=\frac{-66}{55}-\frac{88}{55}-\frac{40}{55}\\=\frac{-66-88-40}{55}\\=\frac{-194}{55}\)
2. \(+\left(\frac{-9}{-4}\right) -\left(\frac{-4}{-8}\right) +\left(\frac{12}{-11}\right)\\= \frac{9}{4}- \frac{4}{8}-\frac{12}{11}\\=\frac{9}{4}-\frac{1}{2}-\frac{12}{11}\\=\frac{99}{44}-\frac{22}{44}-\frac{48}{44}\\=\frac{99-22-48}{44}\\=\frac{29}{44}\)
3. \(-\left(\frac{10}{-3}\right) -\left(\frac{10}{9}\right) -\left(\frac{10}{-5}\right)\\= \frac{10}{3}- \frac{10}{9}+\frac{10}{5}\\=\frac{10}{3}-\frac{10}{9}+\frac{2}{1}\\=\frac{30}{9}-\frac{10}{9}+\frac{18}{9}\\=\frac{30-10+18}{9}\\=\frac{38}{9}\)
4. \(-\left(\frac{-2}{-7}\right) -\left(\frac{-3}{-4}\right) -\left(\frac{-12}{-5}\right)\\= \frac{-2}{7}- \frac{3}{4}-\frac{12}{5}\\=\frac{-40}{140}-\frac{105}{140}-\frac{336}{140}\\=\frac{-40-105-336}{140}\\=\frac{-481}{140}\)
5. \(-\left(\frac{8}{-9}\right) +\left(\frac{7}{8}\right) +\left(\frac{9}{-3}\right)\\= \frac{8}{9}+ \frac{7}{8}-\frac{9}{3}\\=\frac{8}{9}+\frac{7}{8}-\frac{3}{1}\\=\frac{64}{72}+\frac{63}{72}-\frac{216}{72}\\=\frac{64+63-216}{72}\\=\frac{-89}{72}\)
6. \(+\left(\frac{6}{5}\right) -\left(\frac{-9}{-2}\right) +\left(\frac{3}{12}\right)\\= \frac{6}{5}- \frac{9}{2}+\frac{3}{12}\\=\frac{6}{5}-\frac{9}{2}+\frac{1}{4}\\=\frac{24}{20}-\frac{90}{20}+\frac{5}{20}\\=\frac{24-90+5}{20}\\=\frac{-61}{20}\)
7. \(-\left(\frac{4}{7}\right) +\left(\frac{10}{-7}\right) -\left(\frac{11}{11}\right)\\= \frac{-4}{7}- \frac{10}{7}-\frac{11}{11}\\=\frac{-4}{7}-\frac{10}{7}-\frac{1}{1}\\=\frac{-4-10-1}{7}\\=\frac{-15}{7}\)
8. \(-\left(\frac{-10}{-7}\right) -\left(\frac{3}{3}\right) +\left(\frac{10}{5}\right)\\= \frac{-10}{7}- \frac{3}{3}+\frac{10}{5}\\=\frac{-10}{7}-\frac{1}{1}+\frac{2}{1}\\=\frac{-10-1+2}{7}\\=\frac{-9}{7}\)
9. \(+\left(\frac{-5}{-6}\right) +\left(\frac{5}{-8}\right) -\left(\frac{7}{-2}\right)\\= \frac{5}{6}- \frac{5}{8}+\frac{7}{2}\\=\frac{20}{24}-\frac{15}{24}+\frac{84}{24}\\=\frac{20-15+84}{24}\\=\frac{89}{24}\)
10. \(-\left(\frac{-3}{8}\right) -\left(\frac{-7}{2}\right) +\left(\frac{-7}{-10}\right)\\= \frac{3}{8}+ \frac{7}{2}+\frac{7}{10}\\=\frac{15}{40}+\frac{140}{40}+\frac{28}{40}\\=\frac{15+140+28}{40}\\=\frac{183}{40}\)
11. \(+\left(\frac{-6}{-5}\right) -\left(\frac{6}{9}\right) +\left(\frac{2}{12}\right)\\= \frac{6}{5}- \frac{6}{9}+\frac{2}{12}\\=\frac{6}{5}-\frac{2}{3}+\frac{1}{6}\\=\frac{36}{30}-\frac{20}{30}+\frac{5}{30}\\=\frac{36-20+5}{30}\\=\frac{21}{30}\\=\frac{7}{10}\)
12. \(-\left(\frac{-5}{2}\right) +\left(\frac{10}{-5}\right) +\left(\frac{4}{-3}\right)\\= \frac{5}{2}- \frac{10}{5}-\frac{4}{3}\\=\frac{5}{2}-\frac{2}{1}-\frac{4}{3}\\=\frac{15}{6}-\frac{12}{6}-\frac{8}{6}\\=\frac{15-12-8}{6}\\=\frac{-5}{6}\)