Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{5}\right) +\left(\frac{4}{-4}\right) -\left(\frac{5}{-8}\right)\\= \frac{-6}{5}- \frac{4}{4}+\frac{5}{8}\\=\frac{-6}{5}-\frac{1}{1}+\frac{5}{8}\\=\frac{-48}{40}-\frac{40}{40}+\frac{25}{40}\\=\frac{-48-40+25}{40}\\=\frac{-63}{40}\)
2. \(+\left(\frac{2}{-5}\right) -\left(\frac{-2}{-6}\right) +\left(\frac{5}{7}\right)\\= \frac{-2}{5}- \frac{2}{6}+\frac{5}{7}\\=\frac{-2}{5}-\frac{1}{3}+\frac{5}{7}\\=\frac{-42}{105}-\frac{35}{105}+\frac{75}{105}\\=\frac{-42-35+75}{105}\\=\frac{-2}{105}\)
3. \(-\left(\frac{-2}{7}\right) +\left(\frac{-5}{3}\right) -\left(\frac{3}{5}\right)\\= \frac{2}{7}- \frac{5}{3}-\frac{3}{5}\\=\frac{30}{105}-\frac{175}{105}-\frac{63}{105}\\=\frac{30-175-63}{105}\\=\frac{-208}{105}\)
4. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-6}{2}\right) +\left(\frac{-2}{6}\right)\\= \frac{3}{2}- \frac{6}{2}-\frac{2}{6}\\=\frac{3}{2}-\frac{3}{1}-\frac{1}{3}\\=\frac{9}{6}-\frac{18}{6}-\frac{2}{6}\\=\frac{9-18-2}{6}\\=\frac{-11}{6}\)
5. \(-\left(\frac{-5}{9}\right) -\left(\frac{4}{4}\right) -\left(\frac{-2}{3}\right)\\= \frac{5}{9}- \frac{4}{4}+\frac{2}{3}\\=\frac{5}{9}-\frac{1}{1}+\frac{2}{3}\\=\frac{5-1+2}{9}\\=\frac{6}{9}\\=\frac{2}{3}\)
6. \(-\left(\frac{-3}{-7}\right) +\left(\frac{9}{7}\right) +\left(\frac{-5}{-12}\right)\\= \frac{-3}{7}+ \frac{9}{7}+\frac{5}{12}\\=\frac{-36}{84}+\frac{108}{84}+\frac{35}{84}\\=\frac{-36+108+35}{84}\\=\frac{107}{84}\)
7. \(+\left(\frac{-5}{-6}\right) +\left(\frac{-2}{-8}\right) -\left(\frac{-7}{11}\right)\\= \frac{5}{6}+ \frac{2}{8}+\frac{7}{11}\\=\frac{5}{6}+\frac{1}{4}+\frac{7}{11}\\=\frac{110}{132}+\frac{33}{132}+\frac{84}{132}\\=\frac{110+33+84}{132}\\=\frac{227}{132}\)
8. \(+\left(\frac{6}{5}\right) -\left(\frac{-6}{-7}\right) +\left(\frac{4}{6}\right)\\= \frac{6}{5}- \frac{6}{7}+\frac{4}{6}\\=\frac{6}{5}-\frac{6}{7}+\frac{2}{3}\\=\frac{126}{105}-\frac{90}{105}+\frac{70}{105}\\=\frac{126-90+70}{105}\\=\frac{106}{105}\)
9. \(-\left(\frac{-7}{3}\right) +\left(\frac{-3}{7}\right) -\left(\frac{-6}{-3}\right)\\= \frac{7}{3}- \frac{3}{7}-\frac{6}{3}\\=\frac{7}{3}-\frac{3}{7}-\frac{2}{1}\\=\frac{49}{21}-\frac{9}{21}-\frac{42}{21}\\=\frac{49-9-42}{21}\\=\frac{-2}{21}\)
10. \(-\left(\frac{-3}{4}\right) +\left(\frac{4}{7}\right) -\left(\frac{3}{9}\right)\\= \frac{3}{4}+ \frac{4}{7}-\frac{3}{9}\\=\frac{3}{4}+\frac{4}{7}-\frac{1}{3}\\=\frac{63}{84}+\frac{48}{84}-\frac{28}{84}\\=\frac{63+48-28}{84}\\=\frac{83}{84}\)
11. \(-\left(\frac{2}{3}\right) +\left(\frac{9}{3}\right) +\left(\frac{-5}{-5}\right)\\= \frac{-2}{3}+ \frac{9}{3}+\frac{5}{5}\\=\frac{-2}{3}+\frac{3}{1}+\frac{1}{1}\\=\frac{-2+3+1}{3}\\=\frac{2}{3}\)
12. \(-\left(\frac{-9}{4}\right) +\left(\frac{-6}{-2}\right) -\left(\frac{-11}{8}\right)\\= \frac{9}{4}+ \frac{6}{2}+\frac{11}{8}\\=\frac{9}{4}+\frac{3}{1}+\frac{11}{8}\\=\frac{18}{8}+\frac{24}{8}+\frac{11}{8}\\=\frac{18+24+11}{8}\\=\frac{53}{8}\)