Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{-7}\right) -\left(\frac{4}{-2}\right) -\left(\frac{6}{-9}\right)\\= \frac{4}{7}+ \frac{4}{2}+\frac{6}{9}\\=\frac{4}{7}+\frac{2}{1}+\frac{2}{3}\\=\frac{12}{21}+\frac{42}{21}+\frac{14}{21}\\=\frac{12+42+14}{21}\\=\frac{68}{21}\)
2. \(+\left(\frac{-2}{-5}\right) +\left(\frac{-3}{4}\right) -\left(\frac{4}{2}\right)\\= \frac{2}{5}- \frac{3}{4}-\frac{4}{2}\\=\frac{2}{5}-\frac{3}{4}-\frac{2}{1}\\=\frac{8}{20}-\frac{15}{20}-\frac{40}{20}\\=\frac{8-15-40}{20}\\=\frac{-47}{20}\)
3. \(-\left(\frac{2}{3}\right) +\left(\frac{7}{7}\right) +\left(\frac{-2}{-11}\right)\\= \frac{-2}{3}+ \frac{7}{7}+\frac{2}{11}\\=\frac{-2}{3}+\frac{1}{1}+\frac{2}{11}\\=\frac{-22}{33}+\frac{33}{33}+\frac{6}{33}\\=\frac{-22+33+6}{33}\\=\frac{17}{33}\)
4. \(-\left(\frac{-5}{2}\right) +\left(\frac{-10}{-9}\right) -\left(\frac{3}{-2}\right)\\= \frac{5}{2}+ \frac{10}{9}+\frac{3}{2}\\=\frac{45}{18}+\frac{20}{18}+\frac{27}{18}\\=\frac{45+20+27}{18}\\=\frac{92}{18}\\=\frac{46}{9}\)
5. \(-\left(\frac{8}{9}\right) +\left(\frac{-7}{4}\right) -\left(\frac{5}{-4}\right)\\= \frac{-8}{9}- \frac{7}{4}+\frac{5}{4}\\=\frac{-32}{36}-\frac{63}{36}+\frac{45}{36}\\=\frac{-32-63+45}{36}\\=\frac{-50}{36}\\=\frac{-25}{18}\)
6. \(-\left(\frac{-2}{-3}\right) -\left(\frac{-6}{5}\right) +\left(\frac{6}{-3}\right)\\= \frac{-2}{3}+ \frac{6}{5}-\frac{6}{3}\\=\frac{-2}{3}+\frac{6}{5}-\frac{2}{1}\\=\frac{-10}{15}+\frac{18}{15}-\frac{30}{15}\\=\frac{-10+18-30}{15}\\=\frac{-22}{15}\)
7. \(+\left(\frac{-2}{5}\right) +\left(\frac{2}{-8}\right) -\left(\frac{-11}{-9}\right)\\= \frac{-2}{5}- \frac{2}{8}-\frac{11}{9}\\=\frac{-2}{5}-\frac{1}{4}-\frac{11}{9}\\=\frac{-72}{180}-\frac{45}{180}-\frac{220}{180}\\=\frac{-72-45-220}{180}\\=\frac{-337}{180}\)
8. \(+\left(\frac{4}{3}\right) -\left(\frac{7}{2}\right) +\left(\frac{-6}{11}\right)\\= \frac{4}{3}- \frac{7}{2}-\frac{6}{11}\\=\frac{88}{66}-\frac{231}{66}-\frac{36}{66}\\=\frac{88-231-36}{66}\\=\frac{-179}{66}\)
9. \(-\left(\frac{2}{3}\right) -\left(\frac{-10}{-4}\right) -\left(\frac{-3}{6}\right)\\= \frac{-2}{3}- \frac{10}{4}+\frac{3}{6}\\=\frac{-2}{3}-\frac{5}{2}+\frac{1}{2}\\=\frac{-4}{6}-\frac{15}{6}+\frac{3}{6}\\=\frac{-4-15+3}{6}\\=\frac{-16}{6}\\=\frac{-8}{3}\)
10. \(+\left(\frac{-2}{9}\right) -\left(\frac{-4}{7}\right) -\left(\frac{3}{-9}\right)\\= \frac{-2}{9}+ \frac{4}{7}+\frac{3}{9}\\=\frac{-2}{9}+\frac{4}{7}+\frac{1}{3}\\=\frac{-14}{63}+\frac{36}{63}+\frac{21}{63}\\=\frac{-14+36+21}{63}\\=\frac{43}{63}\)
11. \(+\left(\frac{6}{5}\right) +\left(\frac{3}{8}\right) -\left(\frac{-5}{-2}\right)\\= \frac{6}{5}+ \frac{3}{8}-\frac{5}{2}\\=\frac{48}{40}+\frac{15}{40}-\frac{100}{40}\\=\frac{48+15-100}{40}\\=\frac{-37}{40}\)
12. \(-\left(\frac{-8}{-9}\right) -\left(\frac{9}{-7}\right) -\left(\frac{6}{-10}\right)\\= \frac{-8}{9}+ \frac{9}{7}+\frac{6}{10}\\=\frac{-8}{9}+\frac{9}{7}+\frac{3}{5}\\=\frac{-280}{315}+\frac{405}{315}+\frac{189}{315}\\=\frac{-280+405+189}{315}\\=\frac{314}{315}\)