Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{7}\right) -\left(\frac{3}{-10}\right) +\left(\frac{-3}{-10}\right)\\= \frac{9}{7}+ \frac{3}{10}+\frac{3}{10}\\=\frac{90}{70}+\frac{21}{70}+\frac{21}{70}\\=\frac{90+21+21}{70}\\=\frac{132}{70}\\=\frac{66}{35}\)
2. \(-\left(\frac{-9}{4}\right) +\left(\frac{9}{8}\right) -\left(\frac{12}{-4}\right)\\= \frac{9}{4}+ \frac{9}{8}+\frac{12}{4}\\=\frac{9}{4}+\frac{9}{8}+\frac{3}{1}\\=\frac{18}{8}+\frac{9}{8}+\frac{24}{8}\\=\frac{18+9+24}{8}\\=\frac{51}{8}\)
3. \(+\left(\frac{4}{-5}\right) -\left(\frac{-10}{-10}\right) +\left(\frac{-2}{-3}\right)\\= \frac{-4}{5}- \frac{10}{10}+\frac{2}{3}\\=\frac{-4}{5}-\frac{1}{1}+\frac{2}{3}\\=\frac{-12}{15}-\frac{15}{15}+\frac{10}{15}\\=\frac{-12-15+10}{15}\\=\frac{-17}{15}\)
4. \(-\left(\frac{5}{-2}\right) -\left(\frac{-4}{4}\right) +\left(\frac{-7}{6}\right)\\= \frac{5}{2}+ \frac{4}{4}-\frac{7}{6}\\=\frac{5}{2}+\frac{1}{1}-\frac{7}{6}\\=\frac{15}{6}+\frac{6}{6}-\frac{7}{6}\\=\frac{15+6-7}{6}\\=\frac{14}{6}\\=\frac{7}{3}\)
5. \(+\left(\frac{-3}{7}\right) -\left(\frac{-7}{9}\right) -\left(\frac{-10}{-2}\right)\\= \frac{-3}{7}+ \frac{7}{9}-\frac{10}{2}\\=\frac{-3}{7}+\frac{7}{9}-\frac{5}{1}\\=\frac{-27}{63}+\frac{49}{63}-\frac{315}{63}\\=\frac{-27+49-315}{63}\\=\frac{-293}{63}\)
6. \(+\left(\frac{3}{-2}\right) -\left(\frac{-5}{4}\right) -\left(\frac{-6}{-9}\right)\\= \frac{-3}{2}+ \frac{5}{4}-\frac{6}{9}\\=\frac{-3}{2}+\frac{5}{4}-\frac{2}{3}\\=\frac{-18}{12}+\frac{15}{12}-\frac{8}{12}\\=\frac{-18+15-8}{12}\\=\frac{-11}{12}\)
7. \(-\left(\frac{-3}{7}\right) +\left(\frac{6}{-9}\right) -\left(\frac{5}{2}\right)\\= \frac{3}{7}- \frac{6}{9}-\frac{5}{2}\\=\frac{3}{7}-\frac{2}{3}-\frac{5}{2}\\=\frac{18}{42}-\frac{28}{42}-\frac{105}{42}\\=\frac{18-28-105}{42}\\=\frac{-115}{42}\)
8. \(-\left(\frac{-6}{5}\right) -\left(\frac{4}{-9}\right) +\left(\frac{7}{-10}\right)\\= \frac{6}{5}+ \frac{4}{9}-\frac{7}{10}\\=\frac{108}{90}+\frac{40}{90}-\frac{63}{90}\\=\frac{108+40-63}{90}\\=\frac{85}{90}\\=\frac{17}{18}\)
9. \(+\left(\frac{-6}{5}\right) +\left(\frac{8}{-10}\right) -\left(\frac{8}{-12}\right)\\= \frac{-6}{5}- \frac{8}{10}+\frac{8}{12}\\=\frac{-6}{5}-\frac{4}{5}+\frac{2}{3}\\=\frac{-18}{15}-\frac{12}{15}+\frac{10}{15}\\=\frac{-18-12+10}{15}\\=\frac{-20}{15}\\=\frac{-4}{3}\)
10. \(+\left(\frac{-7}{8}\right) -\left(\frac{-8}{-5}\right) -\left(\frac{-2}{-8}\right)\\= \frac{-7}{8}- \frac{8}{5}-\frac{2}{8}\\=\frac{-7}{8}-\frac{8}{5}-\frac{1}{4}\\=\frac{-35}{40}-\frac{64}{40}-\frac{10}{40}\\=\frac{-35-64-10}{40}\\=\frac{-109}{40}\)
11. \(-\left(\frac{-8}{-9}\right) +\left(\frac{-9}{8}\right) +\left(\frac{-2}{-4}\right)\\= \frac{-8}{9}- \frac{9}{8}+\frac{2}{4}\\=\frac{-8}{9}-\frac{9}{8}+\frac{1}{2}\\=\frac{-64}{72}-\frac{81}{72}+\frac{36}{72}\\=\frac{-64-81+36}{72}\\=\frac{-109}{72}\)
12. \(-\left(\frac{-10}{-9}\right) +\left(\frac{-7}{-9}\right) +\left(\frac{12}{-10}\right)\\= \frac{-10}{9}+ \frac{7}{9}-\frac{12}{10}\\=\frac{-10}{9}+\frac{7}{9}-\frac{6}{5}\\=\frac{-50}{45}+\frac{35}{45}-\frac{54}{45}\\=\frac{-50+35-54}{45}\\=\frac{-69}{45}\\=\frac{-23}{15}\)