Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{4}{3}\right) -\left(\frac{8}{-4}\right) +\left(\frac{7}{-2}\right)\\= \frac{4}{3}+ \frac{8}{4}-\frac{7}{2}\\=\frac{4}{3}+\frac{2}{1}-\frac{7}{2}\\=\frac{8}{6}+\frac{12}{6}-\frac{21}{6}\\=\frac{8+12-21}{6}\\=\frac{-1}{6}\)
2. \(+\left(\frac{-8}{-7}\right) +\left(\frac{-5}{-9}\right) +\left(\frac{4}{-8}\right)\\= \frac{8}{7}+ \frac{5}{9}-\frac{4}{8}\\=\frac{8}{7}+\frac{5}{9}-\frac{1}{2}\\=\frac{144}{126}+\frac{70}{126}-\frac{63}{126}\\=\frac{144+70-63}{126}\\=\frac{151}{126}\)
3. \(-\left(\frac{-3}{7}\right) -\left(\frac{4}{10}\right) -\left(\frac{-12}{11}\right)\\= \frac{3}{7}- \frac{4}{10}+\frac{12}{11}\\=\frac{3}{7}-\frac{2}{5}+\frac{12}{11}\\=\frac{165}{385}-\frac{154}{385}+\frac{420}{385}\\=\frac{165-154+420}{385}\\=\frac{431}{385}\)
4. \(-\left(\frac{2}{-3}\right) -\left(\frac{-3}{6}\right) -\left(\frac{-2}{-4}\right)\\= \frac{2}{3}+ \frac{3}{6}-\frac{2}{4}\\=\frac{2}{3}+\frac{1}{2}-\frac{1}{2}\\=\frac{4}{6}+\frac{3}{6}-\frac{3}{6}\\=\frac{4+3-3}{6}\\=\frac{4}{6}\\=\frac{2}{3}\)
5. \(-\left(\frac{8}{-3}\right) +\left(\frac{-6}{-9}\right) -\left(\frac{2}{11}\right)\\= \frac{8}{3}+ \frac{6}{9}-\frac{2}{11}\\=\frac{8}{3}+\frac{2}{3}-\frac{2}{11}\\=\frac{88}{33}+\frac{22}{33}-\frac{6}{33}\\=\frac{88+22-6}{33}\\=\frac{104}{33}\)
6. \(-\left(\frac{2}{-9}\right) +\left(\frac{-3}{3}\right) -\left(\frac{-5}{-6}\right)\\= \frac{2}{9}- \frac{3}{3}-\frac{5}{6}\\=\frac{2}{9}-\frac{1}{1}-\frac{5}{6}\\=\frac{4}{18}-\frac{18}{18}-\frac{15}{18}\\=\frac{4-18-15}{18}\\=\frac{-29}{18}\)
7. \(-\left(\frac{5}{-6}\right) +\left(\frac{-7}{-4}\right) +\left(\frac{11}{11}\right)\\= \frac{5}{6}+ \frac{7}{4}+\frac{11}{11}\\=\frac{5}{6}+\frac{7}{4}+\frac{1}{1}\\=\frac{10}{12}+\frac{21}{12}+\frac{12}{12}\\=\frac{10+21+12}{12}\\=\frac{43}{12}\)
8. \(+\left(\frac{6}{5}\right) +\left(\frac{2}{-8}\right) +\left(\frac{5}{-8}\right)\\= \frac{6}{5}- \frac{2}{8}-\frac{5}{8}\\=\frac{6}{5}-\frac{1}{4}-\frac{5}{8}\\=\frac{48}{40}-\frac{10}{40}-\frac{25}{40}\\=\frac{48-10-25}{40}\\=\frac{13}{40}\)
9. \(-\left(\frac{-3}{8}\right) -\left(\frac{-7}{-8}\right) +\left(\frac{12}{-11}\right)\\= \frac{3}{8}- \frac{7}{8}-\frac{12}{11}\\=\frac{33}{88}-\frac{77}{88}-\frac{96}{88}\\=\frac{33-77-96}{88}\\=\frac{-140}{88}\\=\frac{-35}{22}\)
10. \(+\left(\frac{-4}{9}\right) -\left(\frac{-6}{-7}\right) +\left(\frac{6}{3}\right)\\= \frac{-4}{9}- \frac{6}{7}+\frac{6}{3}\\=\frac{-4}{9}-\frac{6}{7}+\frac{2}{1}\\=\frac{-28}{63}-\frac{54}{63}+\frac{126}{63}\\=\frac{-28-54+126}{63}\\=\frac{44}{63}\)
11. \(-\left(\frac{5}{-7}\right) -\left(\frac{4}{-8}\right) -\left(\frac{-8}{-7}\right)\\= \frac{5}{7}+ \frac{4}{8}-\frac{8}{7}\\=\frac{5}{7}+\frac{1}{2}-\frac{8}{7}\\=\frac{10}{14}+\frac{7}{14}-\frac{16}{14}\\=\frac{10+7-16}{14}\\=\frac{1}{14}\)
12. \(-\left(\frac{4}{-3}\right) -\left(\frac{3}{7}\right) +\left(\frac{6}{3}\right)\\= \frac{4}{3}- \frac{3}{7}+\frac{6}{3}\\=\frac{4}{3}-\frac{3}{7}+\frac{2}{1}\\=\frac{28}{21}-\frac{9}{21}+\frac{42}{21}\\=\frac{28-9+42}{21}\\=\frac{61}{21}\)