Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{3}\right) +\left(\frac{-10}{2}\right) -\left(\frac{4}{-2}\right)\\= \frac{-4}{3}- \frac{10}{2}+\frac{4}{2}\\=\frac{-4}{3}-\frac{5}{1}+\frac{2}{1}\\=\frac{-4-5+2}{3}\\=\frac{-7}{3}\)
2. \(+\left(\frac{-4}{5}\right) -\left(\frac{-10}{-4}\right) -\left(\frac{2}{6}\right)\\= \frac{-4}{5}- \frac{10}{4}-\frac{2}{6}\\=\frac{-4}{5}-\frac{5}{2}-\frac{1}{3}\\=\frac{-24}{30}-\frac{75}{30}-\frac{10}{30}\\=\frac{-24-75-10}{30}\\=\frac{-109}{30}\)
3. \(-\left(\frac{-4}{-3}\right) -\left(\frac{-7}{-3}\right) +\left(\frac{-11}{8}\right)\\= \frac{-4}{3}- \frac{7}{3}-\frac{11}{8}\\=\frac{-32}{24}-\frac{56}{24}-\frac{33}{24}\\=\frac{-32-56-33}{24}\\=\frac{-121}{24}\)
4. \(-\left(\frac{-2}{3}\right) -\left(\frac{10}{-4}\right) -\left(\frac{-10}{-11}\right)\\= \frac{2}{3}+ \frac{10}{4}-\frac{10}{11}\\=\frac{2}{3}+\frac{5}{2}-\frac{10}{11}\\=\frac{44}{66}+\frac{165}{66}-\frac{60}{66}\\=\frac{44+165-60}{66}\\=\frac{149}{66}\)
5. \(-\left(\frac{3}{5}\right) +\left(\frac{-10}{-7}\right) -\left(\frac{12}{2}\right)\\= \frac{-3}{5}+ \frac{10}{7}-\frac{12}{2}\\=\frac{-3}{5}+\frac{10}{7}-\frac{6}{1}\\=\frac{-21}{35}+\frac{50}{35}-\frac{210}{35}\\=\frac{-21+50-210}{35}\\=\frac{-181}{35}\)
6. \(-\left(\frac{-5}{3}\right) -\left(\frac{-7}{2}\right) +\left(\frac{11}{-8}\right)\\= \frac{5}{3}+ \frac{7}{2}-\frac{11}{8}\\=\frac{40}{24}+\frac{84}{24}-\frac{33}{24}\\=\frac{40+84-33}{24}\\=\frac{91}{24}\)
7. \(+\left(\frac{10}{-3}\right) +\left(\frac{-7}{-9}\right) +\left(\frac{4}{-9}\right)\\= \frac{-10}{3}+ \frac{7}{9}-\frac{4}{9}\\=\frac{-30}{9}+\frac{7}{9}-\frac{4}{9}\\=\frac{-30+7-4}{9}\\=\frac{-27}{9}\\=\frac{-3}{1}\)
8. \(+\left(\frac{-8}{3}\right) +\left(\frac{7}{3}\right) -\left(\frac{8}{3}\right)\\= \frac{-8}{3}+ \frac{7}{3}-\frac{8}{3}\\=\frac{-8+7-8}{3}\\=\frac{-9}{3}\\=\frac{-3}{1}\)
9. \(-\left(\frac{-2}{3}\right) +\left(\frac{-2}{-9}\right) +\left(\frac{7}{-7}\right)\\= \frac{2}{3}+ \frac{2}{9}-\frac{7}{7}\\=\frac{2}{3}+\frac{2}{9}-\frac{1}{1}\\=\frac{6}{9}+\frac{2}{9}-\frac{9}{9}\\=\frac{6+2-9}{9}\\=\frac{-1}{9}\)
10. \(-\left(\frac{2}{-3}\right) +\left(\frac{-5}{-3}\right) +\left(\frac{6}{-10}\right)\\= \frac{2}{3}+ \frac{5}{3}-\frac{6}{10}\\=\frac{2}{3}+\frac{5}{3}-\frac{3}{5}\\=\frac{10}{15}+\frac{25}{15}-\frac{9}{15}\\=\frac{10+25-9}{15}\\=\frac{26}{15}\)
11. \(+\left(\frac{-5}{6}\right) -\left(\frac{4}{8}\right) -\left(\frac{-10}{8}\right)\\= \frac{-5}{6}- \frac{4}{8}+\frac{10}{8}\\=\frac{-5}{6}-\frac{1}{2}+\frac{5}{4}\\=\frac{-10}{12}-\frac{6}{12}+\frac{15}{12}\\=\frac{-10-6+15}{12}\\=\frac{-1}{12}\)
12. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-8}{-5}\right) +\left(\frac{-5}{-10}\right)\\= \frac{6}{5}+ \frac{8}{5}+\frac{5}{10}\\=\frac{6}{5}+\frac{8}{5}+\frac{1}{2}\\=\frac{12}{10}+\frac{16}{10}+\frac{5}{10}\\=\frac{12+16+5}{10}\\=\frac{33}{10}\)