Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{-9}\right) +\left(\frac{-5}{-6}\right) +\left(\frac{5}{5}\right)\\= \frac{2}{9}+ \frac{5}{6}+\frac{5}{5}\\=\frac{2}{9}+\frac{5}{6}+\frac{1}{1}\\=\frac{4}{18}+\frac{15}{18}+\frac{18}{18}\\=\frac{4+15+18}{18}\\=\frac{37}{18}\)
2. \(-\left(\frac{-8}{-5}\right) -\left(\frac{-7}{9}\right) +\left(\frac{6}{-8}\right)\\= \frac{-8}{5}+ \frac{7}{9}-\frac{6}{8}\\=\frac{-8}{5}+\frac{7}{9}-\frac{3}{4}\\=\frac{-288}{180}+\frac{140}{180}-\frac{135}{180}\\=\frac{-288+140-135}{180}\\=\frac{-283}{180}\)
3. \(-\left(\frac{-10}{-7}\right) +\left(\frac{10}{9}\right) +\left(\frac{-7}{10}\right)\\= \frac{-10}{7}+ \frac{10}{9}-\frac{7}{10}\\=\frac{-900}{630}+\frac{700}{630}-\frac{441}{630}\\=\frac{-900+700-441}{630}\\=\frac{-641}{630}\)
4. \(+\left(\frac{-5}{7}\right) -\left(\frac{-9}{10}\right) -\left(\frac{4}{-11}\right)\\= \frac{-5}{7}+ \frac{9}{10}+\frac{4}{11}\\=\frac{-550}{770}+\frac{693}{770}+\frac{280}{770}\\=\frac{-550+693+280}{770}\\=\frac{423}{770}\)
5. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-3}{6}\right) +\left(\frac{8}{9}\right)\\= \frac{-6}{5}- \frac{3}{6}+\frac{8}{9}\\=\frac{-6}{5}-\frac{1}{2}+\frac{8}{9}\\=\frac{-108}{90}-\frac{45}{90}+\frac{80}{90}\\=\frac{-108-45+80}{90}\\=\frac{-73}{90}\)
6. \(-\left(\frac{5}{6}\right) +\left(\frac{-2}{5}\right) +\left(\frac{7}{2}\right)\\= \frac{-5}{6}- \frac{2}{5}+\frac{7}{2}\\=\frac{-25}{30}-\frac{12}{30}+\frac{105}{30}\\=\frac{-25-12+105}{30}\\=\frac{68}{30}\\=\frac{34}{15}\)
7. \(+\left(\frac{-6}{5}\right) -\left(\frac{-3}{7}\right) +\left(\frac{-6}{11}\right)\\= \frac{-6}{5}+ \frac{3}{7}-\frac{6}{11}\\=\frac{-462}{385}+\frac{165}{385}-\frac{210}{385}\\=\frac{-462+165-210}{385}\\=\frac{-507}{385}\)
8. \(+\left(\frac{-5}{2}\right) -\left(\frac{6}{-9}\right) -\left(\frac{-7}{-4}\right)\\= \frac{-5}{2}+ \frac{6}{9}-\frac{7}{4}\\=\frac{-5}{2}+\frac{2}{3}-\frac{7}{4}\\=\frac{-30}{12}+\frac{8}{12}-\frac{21}{12}\\=\frac{-30+8-21}{12}\\=\frac{-43}{12}\)
9. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-5}{5}\right) +\left(\frac{6}{10}\right)\\= \frac{-6}{5}- \frac{5}{5}+\frac{6}{10}\\=\frac{-6}{5}-\frac{1}{1}+\frac{3}{5}\\=\frac{-6-1+3}{5}\\=\frac{-4}{5}\)
10. \(+\left(\frac{-7}{8}\right) -\left(\frac{-8}{2}\right) +\left(\frac{-2}{7}\right)\\= \frac{-7}{8}+ \frac{8}{2}-\frac{2}{7}\\=\frac{-7}{8}+\frac{4}{1}-\frac{2}{7}\\=\frac{-49}{56}+\frac{224}{56}-\frac{16}{56}\\=\frac{-49+224-16}{56}\\=\frac{159}{56}\)
11. \(+\left(\frac{10}{3}\right) +\left(\frac{7}{-3}\right) +\left(\frac{10}{5}\right)\\= \frac{10}{3}- \frac{7}{3}+\frac{10}{5}\\=\frac{10}{3}-\frac{7}{3}+\frac{2}{1}\\=\frac{10-7+2}{3}\\=\frac{5}{3}\)
12. \(+\left(\frac{7}{5}\right) -\left(\frac{-10}{10}\right) -\left(\frac{6}{12}\right)\\= \frac{7}{5}+ \frac{10}{10}-\frac{6}{12}\\=\frac{7}{5}+\frac{1}{1}-\frac{1}{2}\\=\frac{14}{10}+\frac{10}{10}-\frac{5}{10}\\=\frac{14+10-5}{10}\\=\frac{19}{10}\)