Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{9}\right) +\left(\frac{9}{-9}\right) +\left(\frac{2}{-10}\right)\\= \frac{-2}{9}- \frac{9}{9}-\frac{2}{10}\\=\frac{-2}{9}-\frac{1}{1}-\frac{1}{5}\\=\frac{-10}{45}-\frac{45}{45}-\frac{9}{45}\\=\frac{-10-45-9}{45}\\=\frac{-64}{45}\)
2. \(+\left(\frac{-3}{-2}\right) -\left(\frac{-9}{-2}\right) +\left(\frac{3}{-9}\right)\\= \frac{3}{2}- \frac{9}{2}-\frac{3}{9}\\=\frac{3}{2}-\frac{9}{2}-\frac{1}{3}\\=\frac{9}{6}-\frac{27}{6}-\frac{2}{6}\\=\frac{9-27-2}{6}\\=\frac{-20}{6}\\=\frac{-10}{3}\)
3. \(+\left(\frac{-7}{-9}\right) +\left(\frac{4}{-3}\right) -\left(\frac{6}{-5}\right)\\= \frac{7}{9}- \frac{4}{3}+\frac{6}{5}\\=\frac{35}{45}-\frac{60}{45}+\frac{54}{45}\\=\frac{35-60+54}{45}\\=\frac{29}{45}\)
4. \(-\left(\frac{-3}{5}\right) +\left(\frac{-9}{-10}\right) -\left(\frac{-11}{8}\right)\\= \frac{3}{5}+ \frac{9}{10}+\frac{11}{8}\\=\frac{24}{40}+\frac{36}{40}+\frac{55}{40}\\=\frac{24+36+55}{40}\\=\frac{115}{40}\\=\frac{23}{8}\)
5. \(+\left(\frac{-7}{-5}\right) -\left(\frac{2}{9}\right) +\left(\frac{9}{-6}\right)\\= \frac{7}{5}- \frac{2}{9}-\frac{9}{6}\\=\frac{7}{5}-\frac{2}{9}-\frac{3}{2}\\=\frac{126}{90}-\frac{20}{90}-\frac{135}{90}\\=\frac{126-20-135}{90}\\=\frac{-29}{90}\)
6. \(-\left(\frac{-3}{4}\right) -\left(\frac{-6}{3}\right) -\left(\frac{-4}{-10}\right)\\= \frac{3}{4}+ \frac{6}{3}-\frac{4}{10}\\=\frac{3}{4}+\frac{2}{1}-\frac{2}{5}\\=\frac{15}{20}+\frac{40}{20}-\frac{8}{20}\\=\frac{15+40-8}{20}\\=\frac{47}{20}\)
7. \(-\left(\frac{-4}{3}\right) -\left(\frac{8}{10}\right) -\left(\frac{-2}{11}\right)\\= \frac{4}{3}- \frac{8}{10}+\frac{2}{11}\\=\frac{4}{3}-\frac{4}{5}+\frac{2}{11}\\=\frac{220}{165}-\frac{132}{165}+\frac{30}{165}\\=\frac{220-132+30}{165}\\=\frac{118}{165}\)
8. \(-\left(\frac{8}{3}\right) +\left(\frac{2}{-7}\right) -\left(\frac{-6}{4}\right)\\= \frac{-8}{3}- \frac{2}{7}+\frac{6}{4}\\=\frac{-8}{3}-\frac{2}{7}+\frac{3}{2}\\=\frac{-112}{42}-\frac{12}{42}+\frac{63}{42}\\=\frac{-112-12+63}{42}\\=\frac{-61}{42}\)
9. \(-\left(\frac{4}{-3}\right) +\left(\frac{8}{-7}\right) -\left(\frac{9}{-10}\right)\\= \frac{4}{3}- \frac{8}{7}+\frac{9}{10}\\=\frac{280}{210}-\frac{240}{210}+\frac{189}{210}\\=\frac{280-240+189}{210}\\=\frac{229}{210}\)
10. \(+\left(\frac{-4}{-5}\right) -\left(\frac{9}{8}\right) -\left(\frac{-12}{-8}\right)\\= \frac{4}{5}- \frac{9}{8}-\frac{12}{8}\\=\frac{4}{5}-\frac{9}{8}-\frac{3}{2}\\=\frac{32}{40}-\frac{45}{40}-\frac{60}{40}\\=\frac{32-45-60}{40}\\=\frac{-73}{40}\)
11. \(-\left(\frac{2}{-3}\right) +\left(\frac{3}{-7}\right) +\left(\frac{3}{8}\right)\\= \frac{2}{3}- \frac{3}{7}+\frac{3}{8}\\=\frac{112}{168}-\frac{72}{168}+\frac{63}{168}\\=\frac{112-72+63}{168}\\=\frac{103}{168}\)
12. \(+\left(\frac{-2}{9}\right) -\left(\frac{-8}{9}\right) +\left(\frac{11}{3}\right)\\= \frac{-2}{9}+ \frac{8}{9}+\frac{11}{3}\\=\frac{-2+8+11}{9}\\=\frac{17}{9}\)