Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-3}\right) -\left(\frac{7}{8}\right) -\left(\frac{5}{-5}\right)\\= \frac{10}{3}- \frac{7}{8}+\frac{5}{5}\\=\frac{10}{3}-\frac{7}{8}+\frac{1}{1}\\=\frac{80}{24}-\frac{21}{24}+\frac{24}{24}\\=\frac{80-21+24}{24}\\=\frac{83}{24}\)
2. \(+\left(\frac{9}{4}\right) -\left(\frac{-7}{7}\right) +\left(\frac{8}{-4}\right)\\= \frac{9}{4}+ \frac{7}{7}-\frac{8}{4}\\=\frac{9}{4}+\frac{1}{1}-\frac{2}{1}\\=\frac{9+1-2}{4}\\=\frac{8}{4}\\=\frac{2}{1}\)
3. \(+\left(\frac{2}{-9}\right) +\left(\frac{4}{-3}\right) -\left(\frac{-2}{12}\right)\\= \frac{-2}{9}- \frac{4}{3}+\frac{2}{12}\\=\frac{-2}{9}-\frac{4}{3}+\frac{1}{6}\\=\frac{-4}{18}-\frac{24}{18}+\frac{3}{18}\\=\frac{-4-24+3}{18}\\=\frac{-25}{18}\)
4. \(-\left(\frac{6}{-5}\right) +\left(\frac{8}{-8}\right) -\left(\frac{9}{-3}\right)\\= \frac{6}{5}- \frac{8}{8}+\frac{9}{3}\\=\frac{6}{5}-\frac{1}{1}+\frac{3}{1}\\=\frac{6-1+3}{5}\\=\frac{8}{5}\)
5. \(+\left(\frac{9}{-2}\right) -\left(\frac{-3}{-10}\right) +\left(\frac{2}{-3}\right)\\= \frac{-9}{2}- \frac{3}{10}-\frac{2}{3}\\=\frac{-135}{30}-\frac{9}{30}-\frac{20}{30}\\=\frac{-135-9-20}{30}\\=\frac{-164}{30}\\=\frac{-82}{15}\)
6. \(-\left(\frac{10}{7}\right) +\left(\frac{-4}{-2}\right) +\left(\frac{-5}{-9}\right)\\= \frac{-10}{7}+ \frac{4}{2}+\frac{5}{9}\\=\frac{-10}{7}+\frac{2}{1}+\frac{5}{9}\\=\frac{-90}{63}+\frac{126}{63}+\frac{35}{63}\\=\frac{-90+126+35}{63}\\=\frac{71}{63}\)
7. \(-\left(\frac{7}{9}\right) -\left(\frac{-10}{9}\right) +\left(\frac{-8}{6}\right)\\= \frac{-7}{9}+ \frac{10}{9}-\frac{8}{6}\\=\frac{-7}{9}+\frac{10}{9}-\frac{4}{3}\\=\frac{-7+10-4}{9}\\=\frac{-1}{9}\)
8. \(-\left(\frac{5}{6}\right) +\left(\frac{7}{3}\right) -\left(\frac{-12}{6}\right)\\= \frac{-5}{6}+ \frac{7}{3}+\frac{12}{6}\\=\frac{-5}{6}+\frac{7}{3}+\frac{2}{1}\\=\frac{-5+7+2}{6}\\=\frac{4}{6}\\=\frac{2}{3}\)
9. \(+\left(\frac{10}{-7}\right) +\left(\frac{-3}{-5}\right) -\left(\frac{-9}{-5}\right)\\= \frac{-10}{7}+ \frac{3}{5}-\frac{9}{5}\\=\frac{-50}{35}+\frac{21}{35}-\frac{63}{35}\\=\frac{-50+21-63}{35}\\=\frac{-92}{35}\)
10. \(+\left(\frac{5}{-6}\right) -\left(\frac{-6}{-8}\right) +\left(\frac{7}{-10}\right)\\= \frac{-5}{6}- \frac{6}{8}-\frac{7}{10}\\=\frac{-5}{6}-\frac{3}{4}-\frac{7}{10}\\=\frac{-50}{60}-\frac{45}{60}-\frac{42}{60}\\=\frac{-50-45-42}{60}\\=\frac{-137}{60}\)
11. \(+\left(\frac{-3}{2}\right) -\left(\frac{-3}{9}\right) -\left(\frac{-6}{-9}\right)\\= \frac{-3}{2}+ \frac{3}{9}-\frac{6}{9}\\=\frac{-3}{2}+\frac{1}{3}-\frac{2}{3}\\=\frac{-9}{6}+\frac{2}{6}-\frac{4}{6}\\=\frac{-9+2-4}{6}\\=\frac{-11}{6}\)
12. \(+\left(\frac{-3}{-2}\right) -\left(\frac{5}{-9}\right) -\left(\frac{4}{5}\right)\\= \frac{3}{2}+ \frac{5}{9}-\frac{4}{5}\\=\frac{135}{90}+\frac{50}{90}-\frac{72}{90}\\=\frac{135+50-72}{90}\\=\frac{113}{90}\)