Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{7}{-6}\right) -\left(\frac{6}{4}\right) +\left(\frac{-8}{11}\right)\\= \frac{-7}{6}- \frac{6}{4}-\frac{8}{11}\\=\frac{-7}{6}-\frac{3}{2}-\frac{8}{11}\\=\frac{-77}{66}-\frac{99}{66}-\frac{48}{66}\\=\frac{-77-99-48}{66}\\=\frac{-224}{66}\\=\frac{-112}{33}\)
2. \(-\left(\frac{3}{-2}\right) +\left(\frac{-2}{-4}\right) +\left(\frac{12}{7}\right)\\= \frac{3}{2}+ \frac{2}{4}+\frac{12}{7}\\=\frac{3}{2}+\frac{1}{2}+\frac{12}{7}\\=\frac{21}{14}+\frac{7}{14}+\frac{24}{14}\\=\frac{21+7+24}{14}\\=\frac{52}{14}\\=\frac{26}{7}\)
3. \(+\left(\frac{-8}{5}\right) -\left(\frac{-2}{5}\right) -\left(\frac{-8}{-10}\right)\\= \frac{-8}{5}+ \frac{2}{5}-\frac{8}{10}\\=\frac{-8}{5}+\frac{2}{5}-\frac{4}{5}\\=\frac{-8+2-4}{5}\\=\frac{-10}{5}\\=\frac{-2}{1}\)
4. \(-\left(\frac{-6}{5}\right) -\left(\frac{-3}{-10}\right) +\left(\frac{4}{-9}\right)\\= \frac{6}{5}- \frac{3}{10}-\frac{4}{9}\\=\frac{108}{90}-\frac{27}{90}-\frac{40}{90}\\=\frac{108-27-40}{90}\\=\frac{41}{90}\)
5. \(-\left(\frac{-3}{7}\right) +\left(\frac{7}{9}\right) +\left(\frac{-10}{8}\right)\\= \frac{3}{7}+ \frac{7}{9}-\frac{10}{8}\\=\frac{3}{7}+\frac{7}{9}-\frac{5}{4}\\=\frac{108}{252}+\frac{196}{252}-\frac{315}{252}\\=\frac{108+196-315}{252}\\=\frac{-11}{252}\)
6. \(+\left(\frac{7}{-8}\right) +\left(\frac{9}{-9}\right) +\left(\frac{7}{9}\right)\\= \frac{-7}{8}- \frac{9}{9}+\frac{7}{9}\\=\frac{-7}{8}-\frac{1}{1}+\frac{7}{9}\\=\frac{-63}{72}-\frac{72}{72}+\frac{56}{72}\\=\frac{-63-72+56}{72}\\=\frac{-79}{72}\)
7. \(-\left(\frac{-6}{-5}\right) -\left(\frac{3}{10}\right) +\left(\frac{-4}{-2}\right)\\= \frac{-6}{5}- \frac{3}{10}+\frac{4}{2}\\=\frac{-6}{5}-\frac{3}{10}+\frac{2}{1}\\=\frac{-12}{10}-\frac{3}{10}+\frac{20}{10}\\=\frac{-12-3+20}{10}\\=\frac{5}{10}\\=\frac{1}{2}\)
8. \(-\left(\frac{8}{-7}\right) +\left(\frac{10}{-6}\right) -\left(\frac{8}{-12}\right)\\= \frac{8}{7}- \frac{10}{6}+\frac{8}{12}\\=\frac{8}{7}-\frac{5}{3}+\frac{2}{3}\\=\frac{24}{21}-\frac{35}{21}+\frac{14}{21}\\=\frac{24-35+14}{21}\\=\frac{3}{21}\\=\frac{1}{7}\)
9. \(-\left(\frac{3}{5}\right) -\left(\frac{8}{5}\right) +\left(\frac{12}{-6}\right)\\= \frac{-3}{5}- \frac{8}{5}-\frac{12}{6}\\=\frac{-3}{5}-\frac{8}{5}-\frac{2}{1}\\=\frac{-3-8-2}{5}\\=\frac{-13}{5}\)
10. \(+\left(\frac{-9}{2}\right) -\left(\frac{-10}{-3}\right) +\left(\frac{-12}{-5}\right)\\= \frac{-9}{2}- \frac{10}{3}+\frac{12}{5}\\=\frac{-135}{30}-\frac{100}{30}+\frac{72}{30}\\=\frac{-135-100+72}{30}\\=\frac{-163}{30}\)
11. \(+\left(\frac{9}{-7}\right) -\left(\frac{-5}{-2}\right) -\left(\frac{10}{-10}\right)\\= \frac{-9}{7}- \frac{5}{2}+\frac{10}{10}\\=\frac{-9}{7}-\frac{5}{2}+\frac{1}{1}\\=\frac{-18}{14}-\frac{35}{14}+\frac{14}{14}\\=\frac{-18-35+14}{14}\\=\frac{-39}{14}\)
12. \(-\left(\frac{3}{-4}\right) -\left(\frac{-10}{5}\right) +\left(\frac{5}{-6}\right)\\= \frac{3}{4}+ \frac{10}{5}-\frac{5}{6}\\=\frac{3}{4}+\frac{2}{1}-\frac{5}{6}\\=\frac{9}{12}+\frac{24}{12}-\frac{10}{12}\\=\frac{9+24-10}{12}\\=\frac{23}{12}\)