Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{-4}\right) +\left(\frac{3}{-9}\right) +\left(\frac{10}{7}\right)\\= \frac{7}{4}- \frac{3}{9}+\frac{10}{7}\\=\frac{7}{4}-\frac{1}{3}+\frac{10}{7}\\=\frac{147}{84}-\frac{28}{84}+\frac{120}{84}\\=\frac{147-28+120}{84}\\=\frac{239}{84}\)
2. \(-\left(\frac{10}{-7}\right) -\left(\frac{-6}{-8}\right) -\left(\frac{-10}{9}\right)\\= \frac{10}{7}- \frac{6}{8}+\frac{10}{9}\\=\frac{10}{7}-\frac{3}{4}+\frac{10}{9}\\=\frac{360}{252}-\frac{189}{252}+\frac{280}{252}\\=\frac{360-189+280}{252}\\=\frac{451}{252}\)
3. \(-\left(\frac{-10}{7}\right) +\left(\frac{8}{-9}\right) -\left(\frac{2}{5}\right)\\= \frac{10}{7}- \frac{8}{9}-\frac{2}{5}\\=\frac{450}{315}-\frac{280}{315}-\frac{126}{315}\\=\frac{450-280-126}{315}\\=\frac{44}{315}\)
4. \(-\left(\frac{4}{-5}\right) -\left(\frac{-10}{-7}\right) -\left(\frac{-6}{2}\right)\\= \frac{4}{5}- \frac{10}{7}+\frac{6}{2}\\=\frac{4}{5}-\frac{10}{7}+\frac{3}{1}\\=\frac{28}{35}-\frac{50}{35}+\frac{105}{35}\\=\frac{28-50+105}{35}\\=\frac{83}{35}\)
5. \(+\left(\frac{-9}{-2}\right) -\left(\frac{2}{-2}\right) +\left(\frac{-3}{12}\right)\\= \frac{9}{2}+ \frac{2}{2}-\frac{3}{12}\\=\frac{9}{2}+\frac{1}{1}-\frac{1}{4}\\=\frac{18}{4}+\frac{4}{4}-\frac{1}{4}\\=\frac{18+4-1}{4}\\=\frac{21}{4}\)
6. \(+\left(\frac{-7}{-6}\right) +\left(\frac{-9}{-4}\right) -\left(\frac{-2}{-6}\right)\\= \frac{7}{6}+ \frac{9}{4}-\frac{2}{6}\\=\frac{7}{6}+\frac{9}{4}-\frac{1}{3}\\=\frac{14}{12}+\frac{27}{12}-\frac{4}{12}\\=\frac{14+27-4}{12}\\=\frac{37}{12}\)
7. \(+\left(\frac{8}{-7}\right) -\left(\frac{10}{-7}\right) -\left(\frac{-2}{-9}\right)\\= \frac{-8}{7}+ \frac{10}{7}-\frac{2}{9}\\=\frac{-72}{63}+\frac{90}{63}-\frac{14}{63}\\=\frac{-72+90-14}{63}\\=\frac{4}{63}\)
8. \(+\left(\frac{-4}{3}\right) -\left(\frac{-7}{2}\right) +\left(\frac{8}{4}\right)\\= \frac{-4}{3}+ \frac{7}{2}+\frac{8}{4}\\=\frac{-4}{3}+\frac{7}{2}+\frac{2}{1}\\=\frac{-8}{6}+\frac{21}{6}+\frac{12}{6}\\=\frac{-8+21+12}{6}\\=\frac{25}{6}\)
9. \(+\left(\frac{-3}{-8}\right) +\left(\frac{-3}{3}\right) -\left(\frac{3}{8}\right)\\= \frac{3}{8}- \frac{3}{3}-\frac{3}{8}\\=\frac{3}{8}-\frac{1}{1}-\frac{3}{8}\\=\frac{3-1-3}{8}\\=\frac{-1}{8}\)
10. \(-\left(\frac{-7}{8}\right) -\left(\frac{7}{-10}\right) -\left(\frac{6}{8}\right)\\= \frac{7}{8}+ \frac{7}{10}-\frac{6}{8}\\=\frac{7}{8}+\frac{7}{10}-\frac{3}{4}\\=\frac{35}{40}+\frac{28}{40}-\frac{30}{40}\\=\frac{35+28-30}{40}\\=\frac{33}{40}\)
11. \(+\left(\frac{2}{-7}\right) +\left(\frac{-9}{-6}\right) +\left(\frac{-11}{-4}\right)\\= \frac{-2}{7}+ \frac{9}{6}+\frac{11}{4}\\=\frac{-2}{7}+\frac{3}{2}+\frac{11}{4}\\=\frac{-8}{28}+\frac{42}{28}+\frac{77}{28}\\=\frac{-8+42+77}{28}\\=\frac{111}{28}\)
12. \(-\left(\frac{-10}{7}\right) -\left(\frac{-5}{-4}\right) +\left(\frac{-8}{8}\right)\\= \frac{10}{7}- \frac{5}{4}-\frac{8}{8}\\=\frac{10}{7}-\frac{5}{4}-\frac{1}{1}\\=\frac{40}{28}-\frac{35}{28}-\frac{28}{28}\\=\frac{40-35-28}{28}\\=\frac{-23}{28}\)