Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{3}\right) -\left(\frac{7}{8}\right) -\left(\frac{-9}{-10}\right)\\= \frac{10}{3}- \frac{7}{8}-\frac{9}{10}\\=\frac{400}{120}-\frac{105}{120}-\frac{108}{120}\\=\frac{400-105-108}{120}\\=\frac{187}{120}\)
2. \(+\left(\frac{-8}{-7}\right) -\left(\frac{3}{-3}\right) +\left(\frac{9}{-11}\right)\\= \frac{8}{7}+ \frac{3}{3}-\frac{9}{11}\\=\frac{8}{7}+\frac{1}{1}-\frac{9}{11}\\=\frac{88}{77}+\frac{77}{77}-\frac{63}{77}\\=\frac{88+77-63}{77}\\=\frac{102}{77}\)
3. \(-\left(\frac{5}{-3}\right) +\left(\frac{6}{-10}\right) -\left(\frac{-2}{-11}\right)\\= \frac{5}{3}- \frac{6}{10}-\frac{2}{11}\\=\frac{5}{3}-\frac{3}{5}-\frac{2}{11}\\=\frac{275}{165}-\frac{99}{165}-\frac{30}{165}\\=\frac{275-99-30}{165}\\=\frac{146}{165}\)
4. \(+\left(\frac{7}{2}\right) +\left(\frac{-4}{-10}\right) +\left(\frac{5}{-10}\right)\\= \frac{7}{2}+ \frac{4}{10}-\frac{5}{10}\\=\frac{7}{2}+\frac{2}{5}-\frac{1}{2}\\=\frac{35}{10}+\frac{4}{10}-\frac{5}{10}\\=\frac{35+4-5}{10}\\=\frac{34}{10}\\=\frac{17}{5}\)
5. \(+\left(\frac{6}{7}\right) +\left(\frac{-8}{4}\right) +\left(\frac{-4}{-5}\right)\\= \frac{6}{7}- \frac{8}{4}+\frac{4}{5}\\=\frac{6}{7}-\frac{2}{1}+\frac{4}{5}\\=\frac{30}{35}-\frac{70}{35}+\frac{28}{35}\\=\frac{30-70+28}{35}\\=\frac{-12}{35}\)
6. \(-\left(\frac{7}{8}\right) +\left(\frac{7}{-10}\right) -\left(\frac{-5}{12}\right)\\= \frac{-7}{8}- \frac{7}{10}+\frac{5}{12}\\=\frac{-105}{120}-\frac{84}{120}+\frac{50}{120}\\=\frac{-105-84+50}{120}\\=\frac{-139}{120}\)
7. \(-\left(\frac{-4}{3}\right) +\left(\frac{-3}{-4}\right) +\left(\frac{-8}{7}\right)\\= \frac{4}{3}+ \frac{3}{4}-\frac{8}{7}\\=\frac{112}{84}+\frac{63}{84}-\frac{96}{84}\\=\frac{112+63-96}{84}\\=\frac{79}{84}\)
8. \(+\left(\frac{4}{-9}\right) -\left(\frac{4}{5}\right) -\left(\frac{7}{-9}\right)\\= \frac{-4}{9}- \frac{4}{5}+\frac{7}{9}\\=\frac{-20}{45}-\frac{36}{45}+\frac{35}{45}\\=\frac{-20-36+35}{45}\\=\frac{-21}{45}\\=\frac{-7}{15}\)
9. \(-\left(\frac{6}{-5}\right) -\left(\frac{-9}{10}\right) -\left(\frac{10}{2}\right)\\= \frac{6}{5}+ \frac{9}{10}-\frac{10}{2}\\=\frac{6}{5}+\frac{9}{10}-\frac{5}{1}\\=\frac{12}{10}+\frac{9}{10}-\frac{50}{10}\\=\frac{12+9-50}{10}\\=\frac{-29}{10}\)
10. \(-\left(\frac{-3}{7}\right) -\left(\frac{-9}{-3}\right) -\left(\frac{-5}{10}\right)\\= \frac{3}{7}- \frac{9}{3}+\frac{5}{10}\\=\frac{3}{7}-\frac{3}{1}+\frac{1}{2}\\=\frac{6}{14}-\frac{42}{14}+\frac{7}{14}\\=\frac{6-42+7}{14}\\=\frac{-29}{14}\)
11. \(+\left(\frac{6}{-5}\right) -\left(\frac{3}{-2}\right) -\left(\frac{-11}{-2}\right)\\= \frac{-6}{5}+ \frac{3}{2}-\frac{11}{2}\\=\frac{-12}{10}+\frac{15}{10}-\frac{55}{10}\\=\frac{-12+15-55}{10}\\=\frac{-52}{10}\\=\frac{-26}{5}\)
12. \(+\left(\frac{10}{-7}\right) -\left(\frac{5}{-3}\right) +\left(\frac{-11}{11}\right)\\= \frac{-10}{7}+ \frac{5}{3}-\frac{11}{11}\\=\frac{-10}{7}+\frac{5}{3}-\frac{1}{1}\\=\frac{-30}{21}+\frac{35}{21}-\frac{21}{21}\\=\frac{-30+35-21}{21}\\=\frac{-16}{21}\)