Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{-3}\right) +\left(\frac{4}{3}\right) -\left(\frac{4}{-8}\right)\\= \frac{8}{3}+ \frac{4}{3}+\frac{4}{8}\\=\frac{8}{3}+\frac{4}{3}+\frac{1}{2}\\=\frac{16}{6}+\frac{8}{6}+\frac{3}{6}\\=\frac{16+8+3}{6}\\=\frac{27}{6}\\=\frac{9}{2}\)
2. \(+\left(\frac{-7}{3}\right) +\left(\frac{-5}{7}\right) +\left(\frac{9}{10}\right)\\= \frac{-7}{3}- \frac{5}{7}+\frac{9}{10}\\=\frac{-490}{210}-\frac{150}{210}+\frac{189}{210}\\=\frac{-490-150+189}{210}\\=\frac{-451}{210}\)
3. \(-\left(\frac{10}{3}\right) +\left(\frac{-4}{-4}\right) +\left(\frac{-12}{11}\right)\\= \frac{-10}{3}+ \frac{4}{4}-\frac{12}{11}\\=\frac{-10}{3}+\frac{1}{1}-\frac{12}{11}\\=\frac{-110}{33}+\frac{33}{33}-\frac{36}{33}\\=\frac{-110+33-36}{33}\\=\frac{-113}{33}\)
4. \(+\left(\frac{-9}{8}\right) +\left(\frac{8}{4}\right) -\left(\frac{7}{-9}\right)\\= \frac{-9}{8}+ \frac{8}{4}+\frac{7}{9}\\=\frac{-9}{8}+\frac{2}{1}+\frac{7}{9}\\=\frac{-81}{72}+\frac{144}{72}+\frac{56}{72}\\=\frac{-81+144+56}{72}\\=\frac{119}{72}\)
5. \(+\left(\frac{-6}{5}\right) -\left(\frac{-4}{9}\right) +\left(\frac{-8}{-2}\right)\\= \frac{-6}{5}+ \frac{4}{9}+\frac{8}{2}\\=\frac{-6}{5}+\frac{4}{9}+\frac{4}{1}\\=\frac{-54}{45}+\frac{20}{45}+\frac{180}{45}\\=\frac{-54+20+180}{45}\\=\frac{146}{45}\)
6. \(-\left(\frac{-4}{-7}\right) -\left(\frac{-6}{6}\right) -\left(\frac{-5}{5}\right)\\= \frac{-4}{7}+ \frac{6}{6}+\frac{5}{5}\\=\frac{-4}{7}+\frac{1}{1}+\frac{1}{1}\\=\frac{-4+1+1}{7}\\=\frac{-2}{7}\)
7. \(-\left(\frac{-4}{5}\right) +\left(\frac{-4}{-4}\right) -\left(\frac{7}{-3}\right)\\= \frac{4}{5}+ \frac{4}{4}+\frac{7}{3}\\=\frac{4}{5}+\frac{1}{1}+\frac{7}{3}\\=\frac{12}{15}+\frac{15}{15}+\frac{35}{15}\\=\frac{12+15+35}{15}\\=\frac{62}{15}\)
8. \(+\left(\frac{-8}{-9}\right) -\left(\frac{5}{-5}\right) -\left(\frac{11}{-2}\right)\\= \frac{8}{9}+ \frac{5}{5}+\frac{11}{2}\\=\frac{8}{9}+\frac{1}{1}+\frac{11}{2}\\=\frac{16}{18}+\frac{18}{18}+\frac{99}{18}\\=\frac{16+18+99}{18}\\=\frac{133}{18}\)
9. \(-\left(\frac{7}{-3}\right) -\left(\frac{2}{3}\right) -\left(\frac{5}{-12}\right)\\= \frac{7}{3}- \frac{2}{3}+\frac{5}{12}\\=\frac{28}{12}-\frac{8}{12}+\frac{5}{12}\\=\frac{28-8+5}{12}\\=\frac{25}{12}\)
10. \(+\left(\frac{-9}{2}\right) +\left(\frac{8}{3}\right) -\left(\frac{-11}{12}\right)\\= \frac{-9}{2}+ \frac{8}{3}+\frac{11}{12}\\=\frac{-54}{12}+\frac{32}{12}+\frac{11}{12}\\=\frac{-54+32+11}{12}\\=\frac{-11}{12}\)
11. \(+\left(\frac{-8}{-3}\right) +\left(\frac{8}{10}\right) +\left(\frac{-8}{-10}\right)\\= \frac{8}{3}+ \frac{8}{10}+\frac{8}{10}\\=\frac{8}{3}+\frac{4}{5}+\frac{4}{5}\\=\frac{40}{15}+\frac{12}{15}+\frac{12}{15}\\=\frac{40+12+12}{15}\\=\frac{64}{15}\)
12. \(+\left(\frac{-3}{5}\right) +\left(\frac{-7}{-9}\right) -\left(\frac{6}{7}\right)\\= \frac{-3}{5}+ \frac{7}{9}-\frac{6}{7}\\=\frac{-189}{315}+\frac{245}{315}-\frac{270}{315}\\=\frac{-189+245-270}{315}\\=\frac{-214}{315}\)