Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{-2}\right) +\left(\frac{6}{-9}\right) +\left(\frac{-12}{-8}\right)\\= \frac{-5}{2}- \frac{6}{9}+\frac{12}{8}\\=\frac{-5}{2}-\frac{2}{3}+\frac{3}{2}\\=\frac{-15}{6}-\frac{4}{6}+\frac{9}{6}\\=\frac{-15-4+9}{6}\\=\frac{-10}{6}\\=\frac{-5}{3}\)
2. \(+\left(\frac{-8}{3}\right) +\left(\frac{5}{3}\right) +\left(\frac{-4}{12}\right)\\= \frac{-8}{3}+ \frac{5}{3}-\frac{4}{12}\\=\frac{-8}{3}+\frac{5}{3}-\frac{1}{3}\\=\frac{-8+5-1}{3}\\=\frac{-4}{3}\)
3. \(-\left(\frac{-6}{5}\right) -\left(\frac{-5}{3}\right) +\left(\frac{7}{10}\right)\\= \frac{6}{5}+ \frac{5}{3}+\frac{7}{10}\\=\frac{36}{30}+\frac{50}{30}+\frac{21}{30}\\=\frac{36+50+21}{30}\\=\frac{107}{30}\)
4. \(-\left(\frac{-2}{9}\right) -\left(\frac{-8}{8}\right) +\left(\frac{-11}{-5}\right)\\= \frac{2}{9}+ \frac{8}{8}+\frac{11}{5}\\=\frac{2}{9}+\frac{1}{1}+\frac{11}{5}\\=\frac{10}{45}+\frac{45}{45}+\frac{99}{45}\\=\frac{10+45+99}{45}\\=\frac{154}{45}\)
5. \(-\left(\frac{4}{-9}\right) +\left(\frac{6}{6}\right) +\left(\frac{4}{6}\right)\\= \frac{4}{9}+ \frac{6}{6}+\frac{4}{6}\\=\frac{4}{9}+\frac{1}{1}+\frac{2}{3}\\=\frac{4+1+2}{9}\\=\frac{7}{9}\)
6. \(+\left(\frac{-4}{5}\right) +\left(\frac{7}{-7}\right) -\left(\frac{2}{-11}\right)\\= \frac{-4}{5}- \frac{7}{7}+\frac{2}{11}\\=\frac{-4}{5}-\frac{1}{1}+\frac{2}{11}\\=\frac{-44}{55}-\frac{55}{55}+\frac{10}{55}\\=\frac{-44-55+10}{55}\\=\frac{-89}{55}\)
7. \(+\left(\frac{-10}{-9}\right) -\left(\frac{-2}{-2}\right) +\left(\frac{11}{-5}\right)\\= \frac{10}{9}- \frac{2}{2}-\frac{11}{5}\\=\frac{10}{9}-\frac{1}{1}-\frac{11}{5}\\=\frac{50}{45}-\frac{45}{45}-\frac{99}{45}\\=\frac{50-45-99}{45}\\=\frac{-94}{45}\)
8. \(-\left(\frac{-9}{-5}\right) -\left(\frac{-2}{-7}\right) +\left(\frac{-7}{4}\right)\\= \frac{-9}{5}- \frac{2}{7}-\frac{7}{4}\\=\frac{-252}{140}-\frac{40}{140}-\frac{245}{140}\\=\frac{-252-40-245}{140}\\=\frac{-537}{140}\)
9. \(+\left(\frac{-6}{5}\right) -\left(\frac{10}{-6}\right) +\left(\frac{-2}{11}\right)\\= \frac{-6}{5}+ \frac{10}{6}-\frac{2}{11}\\=\frac{-6}{5}+\frac{5}{3}-\frac{2}{11}\\=\frac{-198}{165}+\frac{275}{165}-\frac{30}{165}\\=\frac{-198+275-30}{165}\\=\frac{47}{165}\)
10. \(+\left(\frac{2}{-3}\right) -\left(\frac{3}{-10}\right) -\left(\frac{7}{-10}\right)\\= \frac{-2}{3}+ \frac{3}{10}+\frac{7}{10}\\=\frac{-20}{30}+\frac{9}{30}+\frac{21}{30}\\=\frac{-20+9+21}{30}\\=\frac{10}{30}\\=\frac{1}{3}\)
11. \(+\left(\frac{10}{-7}\right) -\left(\frac{-9}{6}\right) +\left(\frac{12}{-10}\right)\\= \frac{-10}{7}+ \frac{9}{6}-\frac{12}{10}\\=\frac{-10}{7}+\frac{3}{2}-\frac{6}{5}\\=\frac{-100}{70}+\frac{105}{70}-\frac{84}{70}\\=\frac{-100+105-84}{70}\\=\frac{-79}{70}\)
12. \(-\left(\frac{9}{2}\right) -\left(\frac{2}{8}\right) +\left(\frac{11}{-12}\right)\\= \frac{-9}{2}- \frac{2}{8}-\frac{11}{12}\\=\frac{-9}{2}-\frac{1}{4}-\frac{11}{12}\\=\frac{-54}{12}-\frac{3}{12}-\frac{11}{12}\\=\frac{-54-3-11}{12}\\=\frac{-68}{12}\\=\frac{-17}{3}\)