Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{9}\right) -\left(\frac{2}{-4}\right) +\left(\frac{2}{-2}\right)\\= \frac{-5}{9}+ \frac{2}{4}-\frac{2}{2}\\=\frac{-5}{9}+\frac{1}{2}-\frac{1}{1}\\=\frac{-10}{18}+\frac{9}{18}-\frac{18}{18}\\=\frac{-10+9-18}{18}\\=\frac{-19}{18}\)
2. \(+\left(\frac{5}{-9}\right) +\left(\frac{-9}{2}\right) -\left(\frac{-11}{11}\right)\\= \frac{-5}{9}- \frac{9}{2}+\frac{11}{11}\\=\frac{-5}{9}-\frac{9}{2}+\frac{1}{1}\\=\frac{-10}{18}-\frac{81}{18}+\frac{18}{18}\\=\frac{-10-81+18}{18}\\=\frac{-73}{18}\)
3. \(+\left(\frac{2}{5}\right) -\left(\frac{6}{2}\right) -\left(\frac{-10}{2}\right)\\= \frac{2}{5}- \frac{6}{2}+\frac{10}{2}\\=\frac{2}{5}-\frac{3}{1}+\frac{5}{1}\\=\frac{2-3+5}{5}\\=\frac{4}{5}\)
4. \(+\left(\frac{7}{-9}\right) +\left(\frac{-5}{8}\right) -\left(\frac{3}{-5}\right)\\= \frac{-7}{9}- \frac{5}{8}+\frac{3}{5}\\=\frac{-280}{360}-\frac{225}{360}+\frac{216}{360}\\=\frac{-280-225+216}{360}\\=\frac{-289}{360}\)
5. \(+\left(\frac{9}{-7}\right) -\left(\frac{2}{4}\right) +\left(\frac{-9}{11}\right)\\= \frac{-9}{7}- \frac{2}{4}-\frac{9}{11}\\=\frac{-9}{7}-\frac{1}{2}-\frac{9}{11}\\=\frac{-198}{154}-\frac{77}{154}-\frac{126}{154}\\=\frac{-198-77-126}{154}\\=\frac{-401}{154}\)
6. \(-\left(\frac{-7}{6}\right) +\left(\frac{6}{9}\right) +\left(\frac{7}{-12}\right)\\= \frac{7}{6}+ \frac{6}{9}-\frac{7}{12}\\=\frac{7}{6}+\frac{2}{3}-\frac{7}{12}\\=\frac{14}{12}+\frac{8}{12}-\frac{7}{12}\\=\frac{14+8-7}{12}\\=\frac{15}{12}\\=\frac{5}{4}\)
7. \(+\left(\frac{6}{-5}\right) -\left(\frac{6}{4}\right) +\left(\frac{-10}{-9}\right)\\= \frac{-6}{5}- \frac{6}{4}+\frac{10}{9}\\=\frac{-6}{5}-\frac{3}{2}+\frac{10}{9}\\=\frac{-108}{90}-\frac{135}{90}+\frac{100}{90}\\=\frac{-108-135+100}{90}\\=\frac{-143}{90}\)
8. \(+\left(\frac{3}{-7}\right) -\left(\frac{2}{10}\right) -\left(\frac{3}{-10}\right)\\= \frac{-3}{7}- \frac{2}{10}+\frac{3}{10}\\=\frac{-3}{7}-\frac{1}{5}+\frac{3}{10}\\=\frac{-30}{70}-\frac{14}{70}+\frac{21}{70}\\=\frac{-30-14+21}{70}\\=\frac{-23}{70}\)
9. \(-\left(\frac{7}{4}\right) +\left(\frac{3}{4}\right) -\left(\frac{-10}{-10}\right)\\= \frac{-7}{4}+ \frac{3}{4}-\frac{10}{10}\\=\frac{-7}{4}+\frac{3}{4}-\frac{1}{1}\\=\frac{-7+3-1}{4}\\=\frac{-5}{4}\)
10. \(+\left(\frac{9}{-5}\right) -\left(\frac{2}{3}\right) +\left(\frac{10}{6}\right)\\= \frac{-9}{5}- \frac{2}{3}+\frac{10}{6}\\=\frac{-9}{5}-\frac{2}{3}+\frac{5}{3}\\=\frac{-27}{15}-\frac{10}{15}+\frac{25}{15}\\=\frac{-27-10+25}{15}\\=\frac{-12}{15}\\=\frac{-4}{5}\)
11. \(+\left(\frac{3}{2}\right) -\left(\frac{4}{6}\right) +\left(\frac{-3}{-6}\right)\\= \frac{3}{2}- \frac{4}{6}+\frac{3}{6}\\=\frac{3}{2}-\frac{2}{3}+\frac{1}{2}\\=\frac{9}{6}-\frac{4}{6}+\frac{3}{6}\\=\frac{9-4+3}{6}\\=\frac{8}{6}\\=\frac{4}{3}\)
12. \(+\left(\frac{4}{-5}\right) +\left(\frac{-10}{10}\right) -\left(\frac{-3}{5}\right)\\= \frac{-4}{5}- \frac{10}{10}+\frac{3}{5}\\=\frac{-4}{5}-\frac{1}{1}+\frac{3}{5}\\=\frac{-4-1+3}{5}\\=\frac{-2}{5}\)