Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{-3}\right) -\left(\frac{-3}{-8}\right) -\left(\frac{-6}{-2}\right)\\= \frac{-5}{3}- \frac{3}{8}-\frac{6}{2}\\=\frac{-5}{3}-\frac{3}{8}-\frac{3}{1}\\=\frac{-40}{24}-\frac{9}{24}-\frac{72}{24}\\=\frac{-40-9-72}{24}\\=\frac{-121}{24}\)
2. \(+\left(\frac{-10}{-9}\right) +\left(\frac{6}{9}\right) +\left(\frac{-4}{-5}\right)\\= \frac{10}{9}+ \frac{6}{9}+\frac{4}{5}\\=\frac{10}{9}+\frac{2}{3}+\frac{4}{5}\\=\frac{50}{45}+\frac{30}{45}+\frac{36}{45}\\=\frac{50+30+36}{45}\\=\frac{116}{45}\)
3. \(-\left(\frac{-5}{-4}\right) +\left(\frac{4}{9}\right) +\left(\frac{-12}{4}\right)\\= \frac{-5}{4}+ \frac{4}{9}-\frac{12}{4}\\=\frac{-5}{4}+\frac{4}{9}-\frac{3}{1}\\=\frac{-45}{36}+\frac{16}{36}-\frac{108}{36}\\=\frac{-45+16-108}{36}\\=\frac{-137}{36}\)
4. \(+\left(\frac{-8}{3}\right) -\left(\frac{3}{9}\right) -\left(\frac{5}{6}\right)\\= \frac{-8}{3}- \frac{3}{9}-\frac{5}{6}\\=\frac{-8}{3}-\frac{1}{3}-\frac{5}{6}\\=\frac{-16}{6}-\frac{2}{6}-\frac{5}{6}\\=\frac{-16-2-5}{6}\\=\frac{-23}{6}\)
5. \(-\left(\frac{-3}{-2}\right) +\left(\frac{-8}{4}\right) +\left(\frac{-10}{-4}\right)\\= \frac{-3}{2}- \frac{8}{4}+\frac{10}{4}\\=\frac{-3}{2}-\frac{2}{1}+\frac{5}{2}\\=\frac{-3-2+5}{2}\\=\frac{0}{2}\\=\frac{0}{1}\)
6. \(-\left(\frac{8}{7}\right) -\left(\frac{7}{-3}\right) +\left(\frac{3}{-4}\right)\\= \frac{-8}{7}+ \frac{7}{3}-\frac{3}{4}\\=\frac{-96}{84}+\frac{196}{84}-\frac{63}{84}\\=\frac{-96+196-63}{84}\\=\frac{37}{84}\)
7. \(-\left(\frac{-8}{3}\right) -\left(\frac{-5}{-2}\right) -\left(\frac{-8}{2}\right)\\= \frac{8}{3}- \frac{5}{2}+\frac{8}{2}\\=\frac{8}{3}-\frac{5}{2}+\frac{4}{1}\\=\frac{16}{6}-\frac{15}{6}+\frac{24}{6}\\=\frac{16-15+24}{6}\\=\frac{25}{6}\)
8. \(-\left(\frac{-6}{5}\right) +\left(\frac{-6}{-2}\right) -\left(\frac{12}{-5}\right)\\= \frac{6}{5}+ \frac{6}{2}+\frac{12}{5}\\=\frac{6}{5}+\frac{3}{1}+\frac{12}{5}\\=\frac{6+3+12}{5}\\=\frac{21}{5}\)
9. \(+\left(\frac{8}{-3}\right) -\left(\frac{-10}{-10}\right) -\left(\frac{-8}{-11}\right)\\= \frac{-8}{3}- \frac{10}{10}-\frac{8}{11}\\=\frac{-8}{3}-\frac{1}{1}-\frac{8}{11}\\=\frac{-88}{33}-\frac{33}{33}-\frac{24}{33}\\=\frac{-88-33-24}{33}\\=\frac{-145}{33}\)
10. \(-\left(\frac{7}{5}\right) -\left(\frac{9}{8}\right) -\left(\frac{5}{9}\right)\\= \frac{-7}{5}- \frac{9}{8}-\frac{5}{9}\\=\frac{-504}{360}-\frac{405}{360}-\frac{200}{360}\\=\frac{-504-405-200}{360}\\=\frac{-1109}{360}\)
11. \(-\left(\frac{4}{3}\right) +\left(\frac{5}{-6}\right) +\left(\frac{7}{7}\right)\\= \frac{-4}{3}- \frac{5}{6}+\frac{7}{7}\\=\frac{-4}{3}-\frac{5}{6}+\frac{1}{1}\\=\frac{-8}{6}-\frac{5}{6}+\frac{6}{6}\\=\frac{-8-5+6}{6}\\=\frac{-7}{6}\)
12. \(+\left(\frac{2}{5}\right) -\left(\frac{4}{9}\right) -\left(\frac{6}{2}\right)\\= \frac{2}{5}- \frac{4}{9}-\frac{6}{2}\\=\frac{2}{5}-\frac{4}{9}-\frac{3}{1}\\=\frac{18}{45}-\frac{20}{45}-\frac{135}{45}\\=\frac{18-20-135}{45}\\=\frac{-137}{45}\)