Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-7}\right) +\left(\frac{8}{4}\right) +\left(\frac{5}{-5}\right)\\= \frac{10}{7}+ \frac{8}{4}-\frac{5}{5}\\=\frac{10}{7}+\frac{2}{1}-\frac{1}{1}\\=\frac{10+2-1}{7}\\=\frac{11}{7}\)
2. \(+\left(\frac{6}{5}\right) -\left(\frac{4}{3}\right) -\left(\frac{-4}{5}\right)\\= \frac{6}{5}- \frac{4}{3}+\frac{4}{5}\\=\frac{18}{15}-\frac{20}{15}+\frac{12}{15}\\=\frac{18-20+12}{15}\\=\frac{10}{15}\\=\frac{2}{3}\)
3. \(+\left(\frac{-5}{-8}\right) +\left(\frac{-4}{5}\right) -\left(\frac{-11}{9}\right)\\= \frac{5}{8}- \frac{4}{5}+\frac{11}{9}\\=\frac{225}{360}-\frac{288}{360}+\frac{440}{360}\\=\frac{225-288+440}{360}\\=\frac{377}{360}\)
4. \(-\left(\frac{-2}{9}\right) +\left(\frac{-6}{-2}\right) +\left(\frac{11}{-4}\right)\\= \frac{2}{9}+ \frac{6}{2}-\frac{11}{4}\\=\frac{2}{9}+\frac{3}{1}-\frac{11}{4}\\=\frac{8}{36}+\frac{108}{36}-\frac{99}{36}\\=\frac{8+108-99}{36}\\=\frac{17}{36}\)
5. \(-\left(\frac{-2}{9}\right) -\left(\frac{-2}{5}\right) -\left(\frac{-4}{3}\right)\\= \frac{2}{9}+ \frac{2}{5}+\frac{4}{3}\\=\frac{10}{45}+\frac{18}{45}+\frac{60}{45}\\=\frac{10+18+60}{45}\\=\frac{88}{45}\)
6. \(+\left(\frac{2}{7}\right) -\left(\frac{5}{-5}\right) +\left(\frac{-6}{-7}\right)\\= \frac{2}{7}+ \frac{5}{5}+\frac{6}{7}\\=\frac{2}{7}+\frac{1}{1}+\frac{6}{7}\\=\frac{2+1+6}{7}\\=\frac{9}{7}\)
7. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-5}{-7}\right) -\left(\frac{-9}{-8}\right)\\= \frac{6}{5}- \frac{5}{7}-\frac{9}{8}\\=\frac{336}{280}-\frac{200}{280}-\frac{315}{280}\\=\frac{336-200-315}{280}\\=\frac{-179}{280}\)
8. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-8}{3}\right) +\left(\frac{-9}{-8}\right)\\= \frac{-6}{5}- \frac{8}{3}+\frac{9}{8}\\=\frac{-144}{120}-\frac{320}{120}+\frac{135}{120}\\=\frac{-144-320+135}{120}\\=\frac{-329}{120}\)
9. \(+\left(\frac{-4}{5}\right) +\left(\frac{6}{-8}\right) +\left(\frac{-9}{4}\right)\\= \frac{-4}{5}- \frac{6}{8}-\frac{9}{4}\\=\frac{-4}{5}-\frac{3}{4}-\frac{9}{4}\\=\frac{-16}{20}-\frac{15}{20}-\frac{45}{20}\\=\frac{-16-15-45}{20}\\=\frac{-76}{20}\\=\frac{-19}{5}\)
10. \(+\left(\frac{-2}{9}\right) +\left(\frac{-5}{-8}\right) +\left(\frac{-7}{10}\right)\\= \frac{-2}{9}+ \frac{5}{8}-\frac{7}{10}\\=\frac{-80}{360}+\frac{225}{360}-\frac{252}{360}\\=\frac{-80+225-252}{360}\\=\frac{-107}{360}\)
11. \(-\left(\frac{-3}{5}\right) +\left(\frac{10}{-9}\right) +\left(\frac{-2}{-3}\right)\\= \frac{3}{5}- \frac{10}{9}+\frac{2}{3}\\=\frac{27}{45}-\frac{50}{45}+\frac{30}{45}\\=\frac{27-50+30}{45}\\=\frac{7}{45}\)
12. \(+\left(\frac{7}{-8}\right) +\left(\frac{-2}{-8}\right) +\left(\frac{12}{-10}\right)\\= \frac{-7}{8}+ \frac{2}{8}-\frac{12}{10}\\=\frac{-7}{8}+\frac{1}{4}-\frac{6}{5}\\=\frac{-35}{40}+\frac{10}{40}-\frac{48}{40}\\=\frac{-35+10-48}{40}\\=\frac{-73}{40}\)