Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{8}{-5}\right) -\left(\frac{-4}{-10}\right) -\left(\frac{7}{-8}\right)\\= \frac{-8}{5}- \frac{4}{10}+\frac{7}{8}\\=\frac{-8}{5}-\frac{2}{5}+\frac{7}{8}\\=\frac{-64}{40}-\frac{16}{40}+\frac{35}{40}\\=\frac{-64-16+35}{40}\\=\frac{-45}{40}\\=\frac{-9}{8}\)
2. \(-\left(\frac{-5}{3}\right) +\left(\frac{7}{7}\right) +\left(\frac{8}{-10}\right)\\= \frac{5}{3}+ \frac{7}{7}-\frac{8}{10}\\=\frac{5}{3}+\frac{1}{1}-\frac{4}{5}\\=\frac{25}{15}+\frac{15}{15}-\frac{12}{15}\\=\frac{25+15-12}{15}\\=\frac{28}{15}\)
3. \(-\left(\frac{6}{-5}\right) +\left(\frac{-9}{2}\right) +\left(\frac{10}{6}\right)\\= \frac{6}{5}- \frac{9}{2}+\frac{10}{6}\\=\frac{6}{5}-\frac{9}{2}+\frac{5}{3}\\=\frac{36}{30}-\frac{135}{30}+\frac{50}{30}\\=\frac{36-135+50}{30}\\=\frac{-49}{30}\)
4. \(+\left(\frac{3}{-2}\right) +\left(\frac{-9}{-9}\right) -\left(\frac{-11}{-11}\right)\\= \frac{-3}{2}+ \frac{9}{9}-\frac{11}{11}\\=\frac{-3}{2}+\frac{1}{1}-\frac{1}{1}\\=\frac{-3+1-1}{2}\\=\frac{-3}{2}\)
5. \(-\left(\frac{9}{-2}\right) +\left(\frac{10}{10}\right) -\left(\frac{-11}{-8}\right)\\= \frac{9}{2}+ \frac{10}{10}-\frac{11}{8}\\=\frac{9}{2}+\frac{1}{1}-\frac{11}{8}\\=\frac{36}{8}+\frac{8}{8}-\frac{11}{8}\\=\frac{36+8-11}{8}\\=\frac{33}{8}\)
6. \(-\left(\frac{-8}{3}\right) -\left(\frac{9}{-6}\right) -\left(\frac{-11}{8}\right)\\= \frac{8}{3}+ \frac{9}{6}+\frac{11}{8}\\=\frac{8}{3}+\frac{3}{2}+\frac{11}{8}\\=\frac{64}{24}+\frac{36}{24}+\frac{33}{24}\\=\frac{64+36+33}{24}\\=\frac{133}{24}\)
7. \(-\left(\frac{-10}{-7}\right) -\left(\frac{6}{7}\right) +\left(\frac{6}{-5}\right)\\= \frac{-10}{7}- \frac{6}{7}-\frac{6}{5}\\=\frac{-50}{35}-\frac{30}{35}-\frac{42}{35}\\=\frac{-50-30-42}{35}\\=\frac{-122}{35}\)
8. \(-\left(\frac{-4}{5}\right) -\left(\frac{-7}{10}\right) +\left(\frac{7}{12}\right)\\= \frac{4}{5}+ \frac{7}{10}+\frac{7}{12}\\=\frac{48}{60}+\frac{42}{60}+\frac{35}{60}\\=\frac{48+42+35}{60}\\=\frac{125}{60}\\=\frac{25}{12}\)
9. \(+\left(\frac{-10}{-3}\right) +\left(\frac{2}{2}\right) +\left(\frac{-6}{-5}\right)\\= \frac{10}{3}+ \frac{2}{2}+\frac{6}{5}\\=\frac{10}{3}+\frac{1}{1}+\frac{6}{5}\\=\frac{50}{15}+\frac{15}{15}+\frac{18}{15}\\=\frac{50+15+18}{15}\\=\frac{83}{15}\)
10. \(-\left(\frac{7}{8}\right) -\left(\frac{9}{-5}\right) -\left(\frac{4}{-6}\right)\\= \frac{-7}{8}+ \frac{9}{5}+\frac{4}{6}\\=\frac{-7}{8}+\frac{9}{5}+\frac{2}{3}\\=\frac{-105}{120}+\frac{216}{120}+\frac{80}{120}\\=\frac{-105+216+80}{120}\\=\frac{191}{120}\)
11. \(-\left(\frac{2}{-3}\right) -\left(\frac{10}{-8}\right) -\left(\frac{-8}{5}\right)\\= \frac{2}{3}+ \frac{10}{8}+\frac{8}{5}\\=\frac{2}{3}+\frac{5}{4}+\frac{8}{5}\\=\frac{40}{60}+\frac{75}{60}+\frac{96}{60}\\=\frac{40+75+96}{60}\\=\frac{211}{60}\)
12. \(+\left(\frac{4}{-3}\right) -\left(\frac{8}{-5}\right) +\left(\frac{-10}{5}\right)\\= \frac{-4}{3}+ \frac{8}{5}-\frac{10}{5}\\=\frac{-4}{3}+\frac{8}{5}-\frac{2}{1}\\=\frac{-20}{15}+\frac{24}{15}-\frac{30}{15}\\=\frac{-20+24-30}{15}\\=\frac{-26}{15}\)