Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{2}\right) +\left(\frac{-4}{5}\right) +\left(\frac{4}{12}\right)\\= \frac{-3}{2}- \frac{4}{5}+\frac{4}{12}\\=\frac{-3}{2}-\frac{4}{5}+\frac{1}{3}\\=\frac{-45}{30}-\frac{24}{30}+\frac{10}{30}\\=\frac{-45-24+10}{30}\\=\frac{-59}{30}\)
2. \(-\left(\frac{10}{7}\right) -\left(\frac{4}{-10}\right) -\left(\frac{8}{5}\right)\\= \frac{-10}{7}+ \frac{4}{10}-\frac{8}{5}\\=\frac{-10}{7}+\frac{2}{5}-\frac{8}{5}\\=\frac{-50}{35}+\frac{14}{35}-\frac{56}{35}\\=\frac{-50+14-56}{35}\\=\frac{-92}{35}\)
3. \(+\left(\frac{9}{7}\right) +\left(\frac{10}{8}\right) -\left(\frac{3}{-5}\right)\\= \frac{9}{7}+ \frac{10}{8}+\frac{3}{5}\\=\frac{9}{7}+\frac{5}{4}+\frac{3}{5}\\=\frac{180}{140}+\frac{175}{140}+\frac{84}{140}\\=\frac{180+175+84}{140}\\=\frac{439}{140}\)
4. \(+\left(\frac{-10}{9}\right) -\left(\frac{-4}{-5}\right) +\left(\frac{-6}{7}\right)\\= \frac{-10}{9}- \frac{4}{5}-\frac{6}{7}\\=\frac{-350}{315}-\frac{252}{315}-\frac{270}{315}\\=\frac{-350-252-270}{315}\\=\frac{-872}{315}\)
5. \(+\left(\frac{4}{3}\right) -\left(\frac{-2}{10}\right) +\left(\frac{12}{-10}\right)\\= \frac{4}{3}+ \frac{2}{10}-\frac{12}{10}\\=\frac{4}{3}+\frac{1}{5}-\frac{6}{5}\\=\frac{20}{15}+\frac{3}{15}-\frac{18}{15}\\=\frac{20+3-18}{15}\\=\frac{5}{15}\\=\frac{1}{3}\)
6. \(+\left(\frac{-3}{-2}\right) +\left(\frac{7}{-7}\right) -\left(\frac{-3}{8}\right)\\= \frac{3}{2}- \frac{7}{7}+\frac{3}{8}\\=\frac{3}{2}-\frac{1}{1}+\frac{3}{8}\\=\frac{12}{8}-\frac{8}{8}+\frac{3}{8}\\=\frac{12-8+3}{8}\\=\frac{7}{8}\)
7. \(+\left(\frac{3}{-2}\right) -\left(\frac{-7}{5}\right) -\left(\frac{-3}{-6}\right)\\= \frac{-3}{2}+ \frac{7}{5}-\frac{3}{6}\\=\frac{-3}{2}+\frac{7}{5}-\frac{1}{2}\\=\frac{-15}{10}+\frac{14}{10}-\frac{5}{10}\\=\frac{-15+14-5}{10}\\=\frac{-6}{10}\\=\frac{-3}{5}\)
8. \(-\left(\frac{-2}{3}\right) -\left(\frac{6}{6}\right) -\left(\frac{8}{11}\right)\\= \frac{2}{3}- \frac{6}{6}-\frac{8}{11}\\=\frac{2}{3}-\frac{1}{1}-\frac{8}{11}\\=\frac{22}{33}-\frac{33}{33}-\frac{24}{33}\\=\frac{22-33-24}{33}\\=\frac{-35}{33}\)
9. \(+\left(\frac{-9}{8}\right) +\left(\frac{-3}{3}\right) +\left(\frac{-8}{6}\right)\\= \frac{-9}{8}- \frac{3}{3}-\frac{8}{6}\\=\frac{-9}{8}-\frac{1}{1}-\frac{4}{3}\\=\frac{-27}{24}-\frac{24}{24}-\frac{32}{24}\\=\frac{-27-24-32}{24}\\=\frac{-83}{24}\)
10. \(+\left(\frac{6}{5}\right) -\left(\frac{-9}{-8}\right) +\left(\frac{2}{-12}\right)\\= \frac{6}{5}- \frac{9}{8}-\frac{2}{12}\\=\frac{6}{5}-\frac{9}{8}-\frac{1}{6}\\=\frac{144}{120}-\frac{135}{120}-\frac{20}{120}\\=\frac{144-135-20}{120}\\=\frac{-11}{120}\)
11. \(+\left(\frac{-9}{4}\right) +\left(\frac{10}{10}\right) -\left(\frac{-12}{2}\right)\\= \frac{-9}{4}+ \frac{10}{10}+\frac{12}{2}\\=\frac{-9}{4}+\frac{1}{1}+\frac{6}{1}\\=\frac{-9+1+6}{4}\\=\frac{-2}{4}\\=\frac{-1}{2}\)
12. \(+\left(\frac{8}{-3}\right) +\left(\frac{-4}{-8}\right) +\left(\frac{2}{8}\right)\\= \frac{-8}{3}+ \frac{4}{8}+\frac{2}{8}\\=\frac{-8}{3}+\frac{1}{2}+\frac{1}{4}\\=\frac{-32}{12}+\frac{6}{12}+\frac{3}{12}\\=\frac{-32+6+3}{12}\\=\frac{-23}{12}\)