Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{6}{5}\right) -\left(\frac{-3}{-5}\right) -\left(\frac{-7}{2}\right)\\= \frac{-6}{5}- \frac{3}{5}+\frac{7}{2}\\=\frac{-12}{10}-\frac{6}{10}+\frac{35}{10}\\=\frac{-12-6+35}{10}\\=\frac{17}{10}\)
2. \(+\left(\frac{-8}{3}\right) +\left(\frac{-6}{8}\right) +\left(\frac{11}{-8}\right)\\= \frac{-8}{3}- \frac{6}{8}-\frac{11}{8}\\=\frac{-8}{3}-\frac{3}{4}-\frac{11}{8}\\=\frac{-64}{24}-\frac{18}{24}-\frac{33}{24}\\=\frac{-64-18-33}{24}\\=\frac{-115}{24}\)
3. \(-\left(\frac{6}{5}\right) +\left(\frac{-5}{-3}\right) -\left(\frac{-4}{-6}\right)\\= \frac{-6}{5}+ \frac{5}{3}-\frac{4}{6}\\=\frac{-6}{5}+\frac{5}{3}-\frac{2}{3}\\=\frac{-18}{15}+\frac{25}{15}-\frac{10}{15}\\=\frac{-18+25-10}{15}\\=\frac{-3}{15}\\=\frac{-1}{5}\)
4. \(-\left(\frac{-9}{-2}\right) -\left(\frac{6}{-10}\right) -\left(\frac{8}{10}\right)\\= \frac{-9}{2}+ \frac{6}{10}-\frac{8}{10}\\=\frac{-9}{2}+\frac{3}{5}-\frac{4}{5}\\=\frac{-45}{10}+\frac{6}{10}-\frac{8}{10}\\=\frac{-45+6-8}{10}\\=\frac{-47}{10}\)
5. \(-\left(\frac{-9}{2}\right) +\left(\frac{4}{-4}\right) +\left(\frac{3}{2}\right)\\= \frac{9}{2}- \frac{4}{4}+\frac{3}{2}\\=\frac{9}{2}-\frac{1}{1}+\frac{3}{2}\\=\frac{9-1+3}{2}\\=\frac{11}{2}\)
6. \(+\left(\frac{9}{8}\right) +\left(\frac{4}{10}\right) -\left(\frac{-4}{-12}\right)\\= \frac{9}{8}+ \frac{4}{10}-\frac{4}{12}\\=\frac{9}{8}+\frac{2}{5}-\frac{1}{3}\\=\frac{135}{120}+\frac{48}{120}-\frac{40}{120}\\=\frac{135+48-40}{120}\\=\frac{143}{120}\)
7. \(+\left(\frac{-6}{5}\right) +\left(\frac{-3}{9}\right) -\left(\frac{-6}{11}\right)\\= \frac{-6}{5}- \frac{3}{9}+\frac{6}{11}\\=\frac{-6}{5}-\frac{1}{3}+\frac{6}{11}\\=\frac{-198}{165}-\frac{55}{165}+\frac{90}{165}\\=\frac{-198-55+90}{165}\\=\frac{-163}{165}\)
8. \(-\left(\frac{7}{-9}\right) +\left(\frac{3}{-3}\right) +\left(\frac{-2}{10}\right)\\= \frac{7}{9}- \frac{3}{3}-\frac{2}{10}\\=\frac{7}{9}-\frac{1}{1}-\frac{1}{5}\\=\frac{35}{45}-\frac{45}{45}-\frac{9}{45}\\=\frac{35-45-9}{45}\\=\frac{-19}{45}\)
9. \(+\left(\frac{-5}{-2}\right) -\left(\frac{2}{-8}\right) +\left(\frac{-10}{8}\right)\\= \frac{5}{2}+ \frac{2}{8}-\frac{10}{8}\\=\frac{5}{2}+\frac{1}{4}-\frac{5}{4}\\=\frac{10}{4}+\frac{1}{4}-\frac{5}{4}\\=\frac{10+1-5}{4}\\=\frac{6}{4}\\=\frac{3}{2}\)
10. \(+\left(\frac{7}{5}\right) -\left(\frac{-7}{5}\right) -\left(\frac{-11}{8}\right)\\= \frac{7}{5}+ \frac{7}{5}+\frac{11}{8}\\=\frac{56}{40}+\frac{56}{40}+\frac{55}{40}\\=\frac{56+56+55}{40}\\=\frac{167}{40}\)
11. \(+\left(\frac{-7}{-3}\right) -\left(\frac{10}{-3}\right) +\left(\frac{4}{10}\right)\\= \frac{7}{3}+ \frac{10}{3}+\frac{4}{10}\\=\frac{7}{3}+\frac{10}{3}+\frac{2}{5}\\=\frac{35}{15}+\frac{50}{15}+\frac{6}{15}\\=\frac{35+50+6}{15}\\=\frac{91}{15}\)
12. \(+\left(\frac{5}{9}\right) +\left(\frac{5}{6}\right) +\left(\frac{-9}{3}\right)\\= \frac{5}{9}+ \frac{5}{6}-\frac{9}{3}\\=\frac{5}{9}+\frac{5}{6}-\frac{3}{1}\\=\frac{10}{18}+\frac{15}{18}-\frac{54}{18}\\=\frac{10+15-54}{18}\\=\frac{-29}{18}\)