Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{-4}\right) -\left(\frac{-6}{5}\right) -\left(\frac{-9}{5}\right)\\= \frac{3}{4}+ \frac{6}{5}+\frac{9}{5}\\=\frac{15}{20}+\frac{24}{20}+\frac{36}{20}\\=\frac{15+24+36}{20}\\=\frac{75}{20}\\=\frac{15}{4}\)
2. \(+\left(\frac{10}{3}\right) -\left(\frac{-3}{-4}\right) +\left(\frac{12}{9}\right)\\= \frac{10}{3}- \frac{3}{4}+\frac{12}{9}\\=\frac{10}{3}-\frac{3}{4}+\frac{4}{3}\\=\frac{40}{12}-\frac{9}{12}+\frac{16}{12}\\=\frac{40-9+16}{12}\\=\frac{47}{12}\)
3. \(-\left(\frac{2}{7}\right) +\left(\frac{-10}{9}\right) -\left(\frac{-10}{10}\right)\\= \frac{-2}{7}- \frac{10}{9}+\frac{10}{10}\\=\frac{-2}{7}-\frac{10}{9}+\frac{1}{1}\\=\frac{-18}{63}-\frac{70}{63}+\frac{63}{63}\\=\frac{-18-70+63}{63}\\=\frac{-25}{63}\)
4. \(+\left(\frac{4}{9}\right) -\left(\frac{-4}{-9}\right) +\left(\frac{4}{-10}\right)\\= \frac{4}{9}- \frac{4}{9}-\frac{4}{10}\\=\frac{4}{9}-\frac{4}{9}-\frac{2}{5}\\=\frac{20}{45}-\frac{20}{45}-\frac{18}{45}\\=\frac{20-20-18}{45}\\=\frac{-18}{45}\\=\frac{-2}{5}\)
5. \(+\left(\frac{-2}{-9}\right) -\left(\frac{-5}{-8}\right) +\left(\frac{-10}{-10}\right)\\= \frac{2}{9}- \frac{5}{8}+\frac{10}{10}\\=\frac{2}{9}-\frac{5}{8}+\frac{1}{1}\\=\frac{16}{72}-\frac{45}{72}+\frac{72}{72}\\=\frac{16-45+72}{72}\\=\frac{43}{72}\)
6. \(+\left(\frac{7}{6}\right) -\left(\frac{-3}{-4}\right) -\left(\frac{-12}{3}\right)\\= \frac{7}{6}- \frac{3}{4}+\frac{12}{3}\\=\frac{7}{6}-\frac{3}{4}+\frac{4}{1}\\=\frac{14}{12}-\frac{9}{12}+\frac{48}{12}\\=\frac{14-9+48}{12}\\=\frac{53}{12}\)
7. \(-\left(\frac{-4}{-5}\right) -\left(\frac{-2}{9}\right) +\left(\frac{-7}{2}\right)\\= \frac{-4}{5}+ \frac{2}{9}-\frac{7}{2}\\=\frac{-72}{90}+\frac{20}{90}-\frac{315}{90}\\=\frac{-72+20-315}{90}\\=\frac{-367}{90}\)
8. \(+\left(\frac{2}{-9}\right) +\left(\frac{-6}{6}\right) -\left(\frac{-11}{-5}\right)\\= \frac{-2}{9}- \frac{6}{6}-\frac{11}{5}\\=\frac{-2}{9}-\frac{1}{1}-\frac{11}{5}\\=\frac{-10}{45}-\frac{45}{45}-\frac{99}{45}\\=\frac{-10-45-99}{45}\\=\frac{-154}{45}\)
9. \(+\left(\frac{5}{-8}\right) +\left(\frac{-8}{-6}\right) +\left(\frac{-7}{-9}\right)\\= \frac{-5}{8}+ \frac{8}{6}+\frac{7}{9}\\=\frac{-5}{8}+\frac{4}{3}+\frac{7}{9}\\=\frac{-45}{72}+\frac{96}{72}+\frac{56}{72}\\=\frac{-45+96+56}{72}\\=\frac{107}{72}\)
10. \(+\left(\frac{-8}{7}\right) +\left(\frac{10}{-9}\right) -\left(\frac{11}{-6}\right)\\= \frac{-8}{7}- \frac{10}{9}+\frac{11}{6}\\=\frac{-144}{126}-\frac{140}{126}+\frac{231}{126}\\=\frac{-144-140+231}{126}\\=\frac{-53}{126}\)
11. \(+\left(\frac{4}{5}\right) +\left(\frac{-9}{-6}\right) +\left(\frac{-6}{11}\right)\\= \frac{4}{5}+ \frac{9}{6}-\frac{6}{11}\\=\frac{4}{5}+\frac{3}{2}-\frac{6}{11}\\=\frac{88}{110}+\frac{165}{110}-\frac{60}{110}\\=\frac{88+165-60}{110}\\=\frac{193}{110}\)
12. \(+\left(\frac{9}{-2}\right) -\left(\frac{6}{-10}\right) +\left(\frac{8}{-2}\right)\\= \frac{-9}{2}+ \frac{6}{10}-\frac{8}{2}\\=\frac{-9}{2}+\frac{3}{5}-\frac{4}{1}\\=\frac{-45}{10}+\frac{6}{10}-\frac{40}{10}\\=\frac{-45+6-40}{10}\\=\frac{-79}{10}\)