Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{8}{7}\right) -\left(\frac{6}{10}\right) +\left(\frac{3}{11}\right)\\= \frac{8}{7}- \frac{6}{10}+\frac{3}{11}\\=\frac{8}{7}-\frac{3}{5}+\frac{3}{11}\\=\frac{440}{385}-\frac{231}{385}+\frac{105}{385}\\=\frac{440-231+105}{385}\\=\frac{314}{385}\)
2. \(+\left(\frac{9}{-7}\right) -\left(\frac{-4}{9}\right) +\left(\frac{-9}{5}\right)\\= \frac{-9}{7}+ \frac{4}{9}-\frac{9}{5}\\=\frac{-405}{315}+\frac{140}{315}-\frac{567}{315}\\=\frac{-405+140-567}{315}\\=\frac{-832}{315}\)
3. \(-\left(\frac{-9}{-2}\right) -\left(\frac{2}{4}\right) -\left(\frac{4}{-12}\right)\\= \frac{-9}{2}- \frac{2}{4}+\frac{4}{12}\\=\frac{-9}{2}-\frac{1}{2}+\frac{1}{3}\\=\frac{-27}{6}-\frac{3}{6}+\frac{2}{6}\\=\frac{-27-3+2}{6}\\=\frac{-28}{6}\\=\frac{-14}{3}\)
4. \(-\left(\frac{8}{-5}\right) -\left(\frac{9}{-4}\right) +\left(\frac{8}{-10}\right)\\= \frac{8}{5}+ \frac{9}{4}-\frac{8}{10}\\=\frac{8}{5}+\frac{9}{4}-\frac{4}{5}\\=\frac{32}{20}+\frac{45}{20}-\frac{16}{20}\\=\frac{32+45-16}{20}\\=\frac{61}{20}\)
5. \(-\left(\frac{5}{-2}\right) +\left(\frac{-7}{8}\right) +\left(\frac{-2}{11}\right)\\= \frac{5}{2}- \frac{7}{8}-\frac{2}{11}\\=\frac{220}{88}-\frac{77}{88}-\frac{16}{88}\\=\frac{220-77-16}{88}\\=\frac{127}{88}\)
6. \(+\left(\frac{-3}{2}\right) +\left(\frac{-8}{10}\right) +\left(\frac{-11}{2}\right)\\= \frac{-3}{2}- \frac{8}{10}-\frac{11}{2}\\=\frac{-3}{2}-\frac{4}{5}-\frac{11}{2}\\=\frac{-15}{10}-\frac{8}{10}-\frac{55}{10}\\=\frac{-15-8-55}{10}\\=\frac{-78}{10}\\=\frac{-39}{5}\)
7. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-7}{-2}\right) +\left(\frac{-8}{-10}\right)\\= \frac{-6}{5}- \frac{7}{2}+\frac{8}{10}\\=\frac{-6}{5}-\frac{7}{2}+\frac{4}{5}\\=\frac{-12}{10}-\frac{35}{10}+\frac{8}{10}\\=\frac{-12-35+8}{10}\\=\frac{-39}{10}\)
8. \(-\left(\frac{4}{-5}\right) +\left(\frac{-10}{-10}\right) +\left(\frac{-6}{8}\right)\\= \frac{4}{5}+ \frac{10}{10}-\frac{6}{8}\\=\frac{4}{5}+\frac{1}{1}-\frac{3}{4}\\=\frac{16}{20}+\frac{20}{20}-\frac{15}{20}\\=\frac{16+20-15}{20}\\=\frac{21}{20}\)
9. \(-\left(\frac{-4}{3}\right) +\left(\frac{6}{-8}\right) +\left(\frac{-8}{-9}\right)\\= \frac{4}{3}- \frac{6}{8}+\frac{8}{9}\\=\frac{4}{3}-\frac{3}{4}+\frac{8}{9}\\=\frac{48}{36}-\frac{27}{36}+\frac{32}{36}\\=\frac{48-27+32}{36}\\=\frac{53}{36}\)
10. \(+\left(\frac{-8}{3}\right) +\left(\frac{-10}{-4}\right) -\left(\frac{-2}{-9}\right)\\= \frac{-8}{3}+ \frac{10}{4}-\frac{2}{9}\\=\frac{-8}{3}+\frac{5}{2}-\frac{2}{9}\\=\frac{-48}{18}+\frac{45}{18}-\frac{4}{18}\\=\frac{-48+45-4}{18}\\=\frac{-7}{18}\)
11. \(-\left(\frac{-9}{-2}\right) -\left(\frac{9}{-7}\right) -\left(\frac{6}{-8}\right)\\= \frac{-9}{2}+ \frac{9}{7}+\frac{6}{8}\\=\frac{-9}{2}+\frac{9}{7}+\frac{3}{4}\\=\frac{-126}{28}+\frac{36}{28}+\frac{21}{28}\\=\frac{-126+36+21}{28}\\=\frac{-69}{28}\)
12. \(+\left(\frac{9}{-2}\right) -\left(\frac{3}{7}\right) -\left(\frac{7}{5}\right)\\= \frac{-9}{2}- \frac{3}{7}-\frac{7}{5}\\=\frac{-315}{70}-\frac{30}{70}-\frac{98}{70}\\=\frac{-315-30-98}{70}\\=\frac{-443}{70}\)