Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{9}\right) +\left(\frac{-9}{7}\right) -\left(\frac{3}{-5}\right)\\= \frac{-2}{9}- \frac{9}{7}+\frac{3}{5}\\=\frac{-70}{315}-\frac{405}{315}+\frac{189}{315}\\=\frac{-70-405+189}{315}\\=\frac{-286}{315}\)
2. \(-\left(\frac{-5}{-2}\right) +\left(\frac{7}{-3}\right) -\left(\frac{-6}{-4}\right)\\= \frac{-5}{2}- \frac{7}{3}-\frac{6}{4}\\=\frac{-5}{2}-\frac{7}{3}-\frac{3}{2}\\=\frac{-15}{6}-\frac{14}{6}-\frac{9}{6}\\=\frac{-15-14-9}{6}\\=\frac{-38}{6}\\=\frac{-19}{3}\)
3. \(+\left(\frac{-4}{-9}\right) +\left(\frac{-2}{4}\right) +\left(\frac{-3}{2}\right)\\= \frac{4}{9}- \frac{2}{4}-\frac{3}{2}\\=\frac{4}{9}-\frac{1}{2}-\frac{3}{2}\\=\frac{8}{18}-\frac{9}{18}-\frac{27}{18}\\=\frac{8-9-27}{18}\\=\frac{-28}{18}\\=\frac{-14}{9}\)
4. \(+\left(\frac{-5}{-2}\right) -\left(\frac{-8}{-9}\right) +\left(\frac{-12}{6}\right)\\= \frac{5}{2}- \frac{8}{9}-\frac{12}{6}\\=\frac{5}{2}-\frac{8}{9}-\frac{2}{1}\\=\frac{45}{18}-\frac{16}{18}-\frac{36}{18}\\=\frac{45-16-36}{18}\\=\frac{-7}{18}\)
5. \(-\left(\frac{-10}{3}\right) -\left(\frac{-5}{6}\right) -\left(\frac{-5}{-11}\right)\\= \frac{10}{3}+ \frac{5}{6}-\frac{5}{11}\\=\frac{220}{66}+\frac{55}{66}-\frac{30}{66}\\=\frac{220+55-30}{66}\\=\frac{245}{66}\)
6. \(+\left(\frac{9}{4}\right) +\left(\frac{4}{-10}\right) +\left(\frac{-6}{4}\right)\\= \frac{9}{4}- \frac{4}{10}-\frac{6}{4}\\=\frac{9}{4}-\frac{2}{5}-\frac{3}{2}\\=\frac{45}{20}-\frac{8}{20}-\frac{30}{20}\\=\frac{45-8-30}{20}\\=\frac{7}{20}\)
7. \(+\left(\frac{4}{-5}\right) +\left(\frac{-10}{-8}\right) -\left(\frac{10}{8}\right)\\= \frac{-4}{5}+ \frac{10}{8}-\frac{10}{8}\\=\frac{-4}{5}+\frac{5}{4}-\frac{5}{4}\\=\frac{-16}{20}+\frac{25}{20}-\frac{25}{20}\\=\frac{-16+25-25}{20}\\=\frac{-16}{20}\\=\frac{-4}{5}\)
8. \(+\left(\frac{7}{9}\right) -\left(\frac{-10}{-7}\right) -\left(\frac{4}{-8}\right)\\= \frac{7}{9}- \frac{10}{7}+\frac{4}{8}\\=\frac{7}{9}-\frac{10}{7}+\frac{1}{2}\\=\frac{98}{126}-\frac{180}{126}+\frac{63}{126}\\=\frac{98-180+63}{126}\\=\frac{-19}{126}\)
9. \(+\left(\frac{-4}{9}\right) -\left(\frac{6}{3}\right) -\left(\frac{-5}{3}\right)\\= \frac{-4}{9}- \frac{6}{3}+\frac{5}{3}\\=\frac{-4}{9}-\frac{2}{1}+\frac{5}{3}\\=\frac{-4-2+5}{9}\\=\frac{-1}{9}\)
10. \(+\left(\frac{8}{9}\right) +\left(\frac{-2}{2}\right) +\left(\frac{9}{-10}\right)\\= \frac{8}{9}- \frac{2}{2}-\frac{9}{10}\\=\frac{8}{9}-\frac{1}{1}-\frac{9}{10}\\=\frac{80}{90}-\frac{90}{90}-\frac{81}{90}\\=\frac{80-90-81}{90}\\=\frac{-91}{90}\)
11. \(-\left(\frac{-2}{-5}\right) -\left(\frac{7}{8}\right) +\left(\frac{11}{-6}\right)\\= \frac{-2}{5}- \frac{7}{8}-\frac{11}{6}\\=\frac{-48}{120}-\frac{105}{120}-\frac{220}{120}\\=\frac{-48-105-220}{120}\\=\frac{-373}{120}\)
12. \(+\left(\frac{8}{-3}\right) -\left(\frac{6}{7}\right) +\left(\frac{10}{11}\right)\\= \frac{-8}{3}- \frac{6}{7}+\frac{10}{11}\\=\frac{-616}{231}-\frac{198}{231}+\frac{210}{231}\\=\frac{-616-198+210}{231}\\=\frac{-604}{231}\)