Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{-3}\right) +\left(\frac{5}{-7}\right) -\left(\frac{5}{-11}\right)\\= \frac{-10}{3}- \frac{5}{7}+\frac{5}{11}\\=\frac{-770}{231}-\frac{165}{231}+\frac{105}{231}\\=\frac{-770-165+105}{231}\\=\frac{-830}{231}\)
2. \(+\left(\frac{5}{6}\right) +\left(\frac{7}{-9}\right) -\left(\frac{-9}{-9}\right)\\= \frac{5}{6}- \frac{7}{9}-\frac{9}{9}\\=\frac{5}{6}-\frac{7}{9}-\frac{1}{1}\\=\frac{15}{18}-\frac{14}{18}-\frac{18}{18}\\=\frac{15-14-18}{18}\\=\frac{-17}{18}\)
3. \(-\left(\frac{-2}{3}\right) -\left(\frac{7}{4}\right) -\left(\frac{-3}{-11}\right)\\= \frac{2}{3}- \frac{7}{4}-\frac{3}{11}\\=\frac{88}{132}-\frac{231}{132}-\frac{36}{132}\\=\frac{88-231-36}{132}\\=\frac{-179}{132}\)
4. \(+\left(\frac{-4}{5}\right) +\left(\frac{5}{4}\right) +\left(\frac{-5}{11}\right)\\= \frac{-4}{5}+ \frac{5}{4}-\frac{5}{11}\\=\frac{-176}{220}+\frac{275}{220}-\frac{100}{220}\\=\frac{-176+275-100}{220}\\=\frac{-1}{220}\)
5. \(+\left(\frac{-9}{2}\right) -\left(\frac{6}{10}\right) +\left(\frac{5}{-3}\right)\\= \frac{-9}{2}- \frac{6}{10}-\frac{5}{3}\\=\frac{-9}{2}-\frac{3}{5}-\frac{5}{3}\\=\frac{-135}{30}-\frac{18}{30}-\frac{50}{30}\\=\frac{-135-18-50}{30}\\=\frac{-203}{30}\)
6. \(-\left(\frac{-2}{3}\right) -\left(\frac{3}{8}\right) -\left(\frac{8}{3}\right)\\= \frac{2}{3}- \frac{3}{8}-\frac{8}{3}\\=\frac{16}{24}-\frac{9}{24}-\frac{64}{24}\\=\frac{16-9-64}{24}\\=\frac{-57}{24}\\=\frac{-19}{8}\)
7. \(+\left(\frac{9}{-2}\right) +\left(\frac{-6}{4}\right) -\left(\frac{-5}{-3}\right)\\= \frac{-9}{2}- \frac{6}{4}-\frac{5}{3}\\=\frac{-9}{2}-\frac{3}{2}-\frac{5}{3}\\=\frac{-27}{6}-\frac{9}{6}-\frac{10}{6}\\=\frac{-27-9-10}{6}\\=\frac{-46}{6}\\=\frac{-23}{3}\)
8. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-3}{-6}\right) -\left(\frac{-2}{-3}\right)\\= \frac{6}{5}- \frac{3}{6}-\frac{2}{3}\\=\frac{6}{5}-\frac{1}{2}-\frac{2}{3}\\=\frac{36}{30}-\frac{15}{30}-\frac{20}{30}\\=\frac{36-15-20}{30}\\=\frac{1}{30}\)
9. \(+\left(\frac{2}{-3}\right) -\left(\frac{4}{-5}\right) -\left(\frac{-8}{12}\right)\\= \frac{-2}{3}+ \frac{4}{5}+\frac{8}{12}\\=\frac{-2}{3}+\frac{4}{5}+\frac{2}{3}\\=\frac{-10}{15}+\frac{12}{15}+\frac{10}{15}\\=\frac{-10+12+10}{15}\\=\frac{12}{15}\\=\frac{4}{5}\)
10. \(-\left(\frac{-6}{5}\right) -\left(\frac{7}{-3}\right) +\left(\frac{-11}{6}\right)\\= \frac{6}{5}+ \frac{7}{3}-\frac{11}{6}\\=\frac{36}{30}+\frac{70}{30}-\frac{55}{30}\\=\frac{36+70-55}{30}\\=\frac{51}{30}\\=\frac{17}{10}\)
11. \(+\left(\frac{7}{-6}\right) -\left(\frac{-6}{-5}\right) -\left(\frac{-4}{4}\right)\\= \frac{-7}{6}- \frac{6}{5}+\frac{4}{4}\\=\frac{-7}{6}-\frac{6}{5}+\frac{1}{1}\\=\frac{-35}{30}-\frac{36}{30}+\frac{30}{30}\\=\frac{-35-36+30}{30}\\=\frac{-41}{30}\)
12. \(-\left(\frac{7}{-3}\right) +\left(\frac{5}{-6}\right) +\left(\frac{-5}{-6}\right)\\= \frac{7}{3}- \frac{5}{6}+\frac{5}{6}\\=\frac{14}{6}-\frac{5}{6}+\frac{5}{6}\\=\frac{14-5+5}{6}\\=\frac{14}{6}\\=\frac{7}{3}\)