Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{5}\right) +\left(\frac{6}{9}\right) -\left(\frac{9}{12}\right)\\= \frac{-3}{5}+ \frac{6}{9}-\frac{9}{12}\\=\frac{-3}{5}+\frac{2}{3}-\frac{3}{4}\\=\frac{-36}{60}+\frac{40}{60}-\frac{45}{60}\\=\frac{-36+40-45}{60}\\=\frac{-41}{60}\)
2. \(-\left(\frac{8}{-7}\right) -\left(\frac{2}{-8}\right) +\left(\frac{-11}{-6}\right)\\= \frac{8}{7}+ \frac{2}{8}+\frac{11}{6}\\=\frac{8}{7}+\frac{1}{4}+\frac{11}{6}\\=\frac{96}{84}+\frac{21}{84}+\frac{154}{84}\\=\frac{96+21+154}{84}\\=\frac{271}{84}\)
3. \(-\left(\frac{10}{-7}\right) -\left(\frac{2}{4}\right) +\left(\frac{11}{2}\right)\\= \frac{10}{7}- \frac{2}{4}+\frac{11}{2}\\=\frac{10}{7}-\frac{1}{2}+\frac{11}{2}\\=\frac{20}{14}-\frac{7}{14}+\frac{77}{14}\\=\frac{20-7+77}{14}\\=\frac{90}{14}\\=\frac{45}{7}\)
4. \(+\left(\frac{-2}{3}\right) +\left(\frac{-9}{-7}\right) -\left(\frac{-7}{-11}\right)\\= \frac{-2}{3}+ \frac{9}{7}-\frac{7}{11}\\=\frac{-154}{231}+\frac{297}{231}-\frac{147}{231}\\=\frac{-154+297-147}{231}\\=\frac{-4}{231}\)
5. \(-\left(\frac{-7}{9}\right) +\left(\frac{6}{-2}\right) -\left(\frac{-10}{7}\right)\\= \frac{7}{9}- \frac{6}{2}+\frac{10}{7}\\=\frac{7}{9}-\frac{3}{1}+\frac{10}{7}\\=\frac{49}{63}-\frac{189}{63}+\frac{90}{63}\\=\frac{49-189+90}{63}\\=\frac{-50}{63}\)
6. \(+\left(\frac{9}{5}\right) -\left(\frac{9}{8}\right) -\left(\frac{-4}{-7}\right)\\= \frac{9}{5}- \frac{9}{8}-\frac{4}{7}\\=\frac{504}{280}-\frac{315}{280}-\frac{160}{280}\\=\frac{504-315-160}{280}\\=\frac{29}{280}\)
7. \(+\left(\frac{-9}{-7}\right) +\left(\frac{5}{-7}\right) -\left(\frac{-3}{12}\right)\\= \frac{9}{7}- \frac{5}{7}+\frac{3}{12}\\=\frac{9}{7}-\frac{5}{7}+\frac{1}{4}\\=\frac{36}{28}-\frac{20}{28}+\frac{7}{28}\\=\frac{36-20+7}{28}\\=\frac{23}{28}\)
8. \(+\left(\frac{6}{-5}\right) -\left(\frac{-9}{3}\right) +\left(\frac{6}{-9}\right)\\= \frac{-6}{5}+ \frac{9}{3}-\frac{6}{9}\\=\frac{-6}{5}+\frac{3}{1}-\frac{2}{3}\\=\frac{-18}{15}+\frac{45}{15}-\frac{10}{15}\\=\frac{-18+45-10}{15}\\=\frac{17}{15}\)
9. \(+\left(\frac{10}{7}\right) -\left(\frac{-9}{7}\right) -\left(\frac{-4}{-10}\right)\\= \frac{10}{7}+ \frac{9}{7}-\frac{4}{10}\\=\frac{10}{7}+\frac{9}{7}-\frac{2}{5}\\=\frac{50}{35}+\frac{45}{35}-\frac{14}{35}\\=\frac{50+45-14}{35}\\=\frac{81}{35}\)
10. \(-\left(\frac{7}{6}\right) +\left(\frac{-4}{5}\right) -\left(\frac{4}{-11}\right)\\= \frac{-7}{6}- \frac{4}{5}+\frac{4}{11}\\=\frac{-385}{330}-\frac{264}{330}+\frac{120}{330}\\=\frac{-385-264+120}{330}\\=\frac{-529}{330}\)
11. \(+\left(\frac{7}{8}\right) +\left(\frac{-7}{9}\right) +\left(\frac{-7}{10}\right)\\= \frac{7}{8}- \frac{7}{9}-\frac{7}{10}\\=\frac{315}{360}-\frac{280}{360}-\frac{252}{360}\\=\frac{315-280-252}{360}\\=\frac{-217}{360}\)
12. \(+\left(\frac{-5}{2}\right) -\left(\frac{9}{2}\right) +\left(\frac{-10}{-4}\right)\\= \frac{-5}{2}- \frac{9}{2}+\frac{10}{4}\\=\frac{-5}{2}-\frac{9}{2}+\frac{5}{2}\\=\frac{-5-9+5}{2}\\=\frac{-9}{2}\)