Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{5}\right) -\left(\frac{-7}{-5}\right) -\left(\frac{12}{-8}\right)\\= \frac{4}{5}- \frac{7}{5}+\frac{12}{8}\\=\frac{4}{5}-\frac{7}{5}+\frac{3}{2}\\=\frac{8}{10}-\frac{14}{10}+\frac{15}{10}\\=\frac{8-14+15}{10}\\=\frac{9}{10}\)
2. \(-\left(\frac{-7}{8}\right) -\left(\frac{-7}{-10}\right) -\left(\frac{7}{-6}\right)\\= \frac{7}{8}- \frac{7}{10}+\frac{7}{6}\\=\frac{105}{120}-\frac{84}{120}+\frac{140}{120}\\=\frac{105-84+140}{120}\\=\frac{161}{120}\)
3. \(-\left(\frac{-4}{7}\right) +\left(\frac{-3}{9}\right) +\left(\frac{8}{-6}\right)\\= \frac{4}{7}- \frac{3}{9}-\frac{8}{6}\\=\frac{4}{7}-\frac{1}{3}-\frac{4}{3}\\=\frac{12}{21}-\frac{7}{21}-\frac{28}{21}\\=\frac{12-7-28}{21}\\=\frac{-23}{21}\)
4. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-2}{4}\right) -\left(\frac{-5}{4}\right)\\= \frac{3}{2}- \frac{2}{4}+\frac{5}{4}\\=\frac{3}{2}-\frac{1}{2}+\frac{5}{4}\\=\frac{6}{4}-\frac{2}{4}+\frac{5}{4}\\=\frac{6-2+5}{4}\\=\frac{9}{4}\)
5. \(-\left(\frac{-5}{4}\right) +\left(\frac{5}{-9}\right) -\left(\frac{3}{2}\right)\\= \frac{5}{4}- \frac{5}{9}-\frac{3}{2}\\=\frac{45}{36}-\frac{20}{36}-\frac{54}{36}\\=\frac{45-20-54}{36}\\=\frac{-29}{36}\)
6. \(+\left(\frac{7}{3}\right) -\left(\frac{-4}{-3}\right) -\left(\frac{9}{-10}\right)\\= \frac{7}{3}- \frac{4}{3}+\frac{9}{10}\\=\frac{70}{30}-\frac{40}{30}+\frac{27}{30}\\=\frac{70-40+27}{30}\\=\frac{57}{30}\\=\frac{19}{10}\)
7. \(+\left(\frac{-9}{-7}\right) +\left(\frac{-6}{4}\right) +\left(\frac{-9}{7}\right)\\= \frac{9}{7}- \frac{6}{4}-\frac{9}{7}\\=\frac{9}{7}-\frac{3}{2}-\frac{9}{7}\\=\frac{18}{14}-\frac{21}{14}-\frac{18}{14}\\=\frac{18-21-18}{14}\\=\frac{-21}{14}\\=\frac{-3}{2}\)
8. \(-\left(\frac{-6}{5}\right) -\left(\frac{4}{-4}\right) -\left(\frac{-6}{4}\right)\\= \frac{6}{5}+ \frac{4}{4}+\frac{6}{4}\\=\frac{6}{5}+\frac{1}{1}+\frac{3}{2}\\=\frac{12}{10}+\frac{10}{10}+\frac{15}{10}\\=\frac{12+10+15}{10}\\=\frac{37}{10}\)
9. \(+\left(\frac{4}{-7}\right) +\left(\frac{6}{4}\right) +\left(\frac{2}{-7}\right)\\= \frac{-4}{7}+ \frac{6}{4}-\frac{2}{7}\\=\frac{-4}{7}+\frac{3}{2}-\frac{2}{7}\\=\frac{-8}{14}+\frac{21}{14}-\frac{4}{14}\\=\frac{-8+21-4}{14}\\=\frac{9}{14}\)
10. \(+\left(\frac{3}{-7}\right) +\left(\frac{10}{-2}\right) -\left(\frac{12}{5}\right)\\= \frac{-3}{7}- \frac{10}{2}-\frac{12}{5}\\=\frac{-3}{7}-\frac{5}{1}-\frac{12}{5}\\=\frac{-15}{35}-\frac{175}{35}-\frac{84}{35}\\=\frac{-15-175-84}{35}\\=\frac{-274}{35}\)
11. \(-\left(\frac{-2}{7}\right) +\left(\frac{-7}{-4}\right) +\left(\frac{-5}{9}\right)\\= \frac{2}{7}+ \frac{7}{4}-\frac{5}{9}\\=\frac{72}{252}+\frac{441}{252}-\frac{140}{252}\\=\frac{72+441-140}{252}\\=\frac{373}{252}\)
12. \(+\left(\frac{9}{2}\right) +\left(\frac{-9}{3}\right) -\left(\frac{-6}{-5}\right)\\= \frac{9}{2}- \frac{9}{3}-\frac{6}{5}\\=\frac{9}{2}-\frac{3}{1}-\frac{6}{5}\\=\frac{45}{10}-\frac{30}{10}-\frac{12}{10}\\=\frac{45-30-12}{10}\\=\frac{3}{10}\)