Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{-5}\right) -\left(\frac{-9}{7}\right) +\left(\frac{-10}{-11}\right)\\= \frac{9}{5}+ \frac{9}{7}+\frac{10}{11}\\=\frac{693}{385}+\frac{495}{385}+\frac{350}{385}\\=\frac{693+495+350}{385}\\=\frac{1538}{385}\)
2. \(-\left(\frac{-3}{8}\right) -\left(\frac{3}{-2}\right) -\left(\frac{-6}{-10}\right)\\= \frac{3}{8}+ \frac{3}{2}-\frac{6}{10}\\=\frac{3}{8}+\frac{3}{2}-\frac{3}{5}\\=\frac{15}{40}+\frac{60}{40}-\frac{24}{40}\\=\frac{15+60-24}{40}\\=\frac{51}{40}\)
3. \(+\left(\frac{-2}{3}\right) +\left(\frac{-10}{-4}\right) -\left(\frac{3}{2}\right)\\= \frac{-2}{3}+ \frac{10}{4}-\frac{3}{2}\\=\frac{-2}{3}+\frac{5}{2}-\frac{3}{2}\\=\frac{-4}{6}+\frac{15}{6}-\frac{9}{6}\\=\frac{-4+15-9}{6}\\=\frac{2}{6}\\=\frac{1}{3}\)
4. \(+\left(\frac{-2}{-9}\right) +\left(\frac{-10}{6}\right) +\left(\frac{-3}{-4}\right)\\= \frac{2}{9}- \frac{10}{6}+\frac{3}{4}\\=\frac{2}{9}-\frac{5}{3}+\frac{3}{4}\\=\frac{8}{36}-\frac{60}{36}+\frac{27}{36}\\=\frac{8-60+27}{36}\\=\frac{-25}{36}\)
5. \(+\left(\frac{5}{2}\right) -\left(\frac{6}{-8}\right) +\left(\frac{9}{8}\right)\\= \frac{5}{2}+ \frac{6}{8}+\frac{9}{8}\\=\frac{5}{2}+\frac{3}{4}+\frac{9}{8}\\=\frac{20}{8}+\frac{6}{8}+\frac{9}{8}\\=\frac{20+6+9}{8}\\=\frac{35}{8}\)
6. \(+\left(\frac{-8}{-9}\right) -\left(\frac{-6}{-2}\right) -\left(\frac{5}{-6}\right)\\= \frac{8}{9}- \frac{6}{2}+\frac{5}{6}\\=\frac{8}{9}-\frac{3}{1}+\frac{5}{6}\\=\frac{16}{18}-\frac{54}{18}+\frac{15}{18}\\=\frac{16-54+15}{18}\\=\frac{-23}{18}\)
7. \(+\left(\frac{4}{3}\right) -\left(\frac{-4}{5}\right) +\left(\frac{9}{-7}\right)\\= \frac{4}{3}+ \frac{4}{5}-\frac{9}{7}\\=\frac{140}{105}+\frac{84}{105}-\frac{135}{105}\\=\frac{140+84-135}{105}\\=\frac{89}{105}\)
8. \(-\left(\frac{7}{-4}\right) +\left(\frac{10}{10}\right) -\left(\frac{7}{6}\right)\\= \frac{7}{4}+ \frac{10}{10}-\frac{7}{6}\\=\frac{7}{4}+\frac{1}{1}-\frac{7}{6}\\=\frac{21}{12}+\frac{12}{12}-\frac{14}{12}\\=\frac{21+12-14}{12}\\=\frac{19}{12}\)
9. \(+\left(\frac{3}{-4}\right) +\left(\frac{6}{7}\right) +\left(\frac{10}{-12}\right)\\= \frac{-3}{4}+ \frac{6}{7}-\frac{10}{12}\\=\frac{-3}{4}+\frac{6}{7}-\frac{5}{6}\\=\frac{-63}{84}+\frac{72}{84}-\frac{70}{84}\\=\frac{-63+72-70}{84}\\=\frac{-61}{84}\)
10. \(-\left(\frac{9}{7}\right) -\left(\frac{-6}{6}\right) -\left(\frac{3}{3}\right)\\= \frac{-9}{7}+ \frac{6}{6}-\frac{3}{3}\\=\frac{-9}{7}+\frac{1}{1}-\frac{1}{1}\\=\frac{-9+1-1}{7}\\=\frac{-9}{7}\)
11. \(-\left(\frac{3}{-5}\right) -\left(\frac{8}{6}\right) +\left(\frac{-5}{-3}\right)\\= \frac{3}{5}- \frac{8}{6}+\frac{5}{3}\\=\frac{3}{5}-\frac{4}{3}+\frac{5}{3}\\=\frac{9}{15}-\frac{20}{15}+\frac{25}{15}\\=\frac{9-20+25}{15}\\=\frac{14}{15}\)
12. \(-\left(\frac{3}{2}\right) +\left(\frac{-4}{9}\right) -\left(\frac{9}{6}\right)\\= \frac{-3}{2}- \frac{4}{9}-\frac{9}{6}\\=\frac{-3}{2}-\frac{4}{9}-\frac{3}{2}\\=\frac{-27}{18}-\frac{8}{18}-\frac{27}{18}\\=\frac{-27-8-27}{18}\\=\frac{-62}{18}\\=\frac{-31}{9}\)