Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{-2}\right) -\left(\frac{-2}{-3}\right) +\left(\frac{-8}{8}\right)\\= \frac{3}{2}- \frac{2}{3}-\frac{8}{8}\\=\frac{3}{2}-\frac{2}{3}-\frac{1}{1}\\=\frac{9}{6}-\frac{4}{6}-\frac{6}{6}\\=\frac{9-4-6}{6}\\=\frac{-1}{6}\)
2. \(+\left(\frac{-2}{-7}\right) +\left(\frac{5}{3}\right) +\left(\frac{-9}{9}\right)\\= \frac{2}{7}+ \frac{5}{3}-\frac{9}{9}\\=\frac{2}{7}+\frac{5}{3}-\frac{1}{1}\\=\frac{6}{21}+\frac{35}{21}-\frac{21}{21}\\=\frac{6+35-21}{21}\\=\frac{20}{21}\)
3. \(+\left(\frac{-7}{9}\right) +\left(\frac{-10}{7}\right) -\left(\frac{9}{-9}\right)\\= \frac{-7}{9}- \frac{10}{7}+\frac{9}{9}\\=\frac{-7}{9}-\frac{10}{7}+\frac{1}{1}\\=\frac{-49}{63}-\frac{90}{63}+\frac{63}{63}\\=\frac{-49-90+63}{63}\\=\frac{-76}{63}\)
4. \(-\left(\frac{6}{-5}\right) +\left(\frac{8}{10}\right) +\left(\frac{6}{12}\right)\\= \frac{6}{5}+ \frac{8}{10}+\frac{6}{12}\\=\frac{6}{5}+\frac{4}{5}+\frac{1}{2}\\=\frac{12}{10}+\frac{8}{10}+\frac{5}{10}\\=\frac{12+8+5}{10}\\=\frac{25}{10}\\=\frac{5}{2}\)
5. \(-\left(\frac{10}{9}\right) -\left(\frac{-8}{4}\right) +\left(\frac{-3}{-6}\right)\\= \frac{-10}{9}+ \frac{8}{4}+\frac{3}{6}\\=\frac{-10}{9}+\frac{2}{1}+\frac{1}{2}\\=\frac{-20}{18}+\frac{36}{18}+\frac{9}{18}\\=\frac{-20+36+9}{18}\\=\frac{25}{18}\)
6. \(-\left(\frac{2}{-5}\right) +\left(\frac{-3}{7}\right) -\left(\frac{5}{-4}\right)\\= \frac{2}{5}- \frac{3}{7}+\frac{5}{4}\\=\frac{56}{140}-\frac{60}{140}+\frac{175}{140}\\=\frac{56-60+175}{140}\\=\frac{171}{140}\)
7. \(+\left(\frac{-10}{-7}\right) +\left(\frac{3}{-5}\right) +\left(\frac{-10}{-9}\right)\\= \frac{10}{7}- \frac{3}{5}+\frac{10}{9}\\=\frac{450}{315}-\frac{189}{315}+\frac{350}{315}\\=\frac{450-189+350}{315}\\=\frac{611}{315}\)
8. \(+\left(\frac{6}{-5}\right) +\left(\frac{10}{6}\right) -\left(\frac{-8}{12}\right)\\= \frac{-6}{5}+ \frac{10}{6}+\frac{8}{12}\\=\frac{-6}{5}+\frac{5}{3}+\frac{2}{3}\\=\frac{-18}{15}+\frac{25}{15}+\frac{10}{15}\\=\frac{-18+25+10}{15}\\=\frac{17}{15}\)
9. \(+\left(\frac{-7}{6}\right) -\left(\frac{-4}{-3}\right) +\left(\frac{-10}{6}\right)\\= \frac{-7}{6}- \frac{4}{3}-\frac{10}{6}\\=\frac{-7}{6}-\frac{4}{3}-\frac{5}{3}\\=\frac{-7-4-5}{6}\\=\frac{-16}{6}\\=\frac{-8}{3}\)
10. \(-\left(\frac{-4}{-3}\right) +\left(\frac{9}{-3}\right) +\left(\frac{-4}{-11}\right)\\= \frac{-4}{3}- \frac{9}{3}+\frac{4}{11}\\=\frac{-4}{3}-\frac{3}{1}+\frac{4}{11}\\=\frac{-44}{33}-\frac{99}{33}+\frac{12}{33}\\=\frac{-44-99+12}{33}\\=\frac{-131}{33}\)
11. \(-\left(\frac{8}{-3}\right) -\left(\frac{6}{-5}\right) +\left(\frac{12}{6}\right)\\= \frac{8}{3}+ \frac{6}{5}+\frac{12}{6}\\=\frac{8}{3}+\frac{6}{5}+\frac{2}{1}\\=\frac{40}{15}+\frac{18}{15}+\frac{30}{15}\\=\frac{40+18+30}{15}\\=\frac{88}{15}\)
12. \(-\left(\frac{4}{-3}\right) -\left(\frac{8}{-2}\right) +\left(\frac{11}{2}\right)\\= \frac{4}{3}+ \frac{8}{2}+\frac{11}{2}\\=\frac{4}{3}+\frac{4}{1}+\frac{11}{2}\\=\frac{8}{6}+\frac{24}{6}+\frac{33}{6}\\=\frac{8+24+33}{6}\\=\frac{65}{6}\)