Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{-7}\right) +\left(\frac{-7}{-5}\right) -\left(\frac{-9}{-8}\right)\\= \frac{2}{7}+ \frac{7}{5}-\frac{9}{8}\\=\frac{80}{280}+\frac{392}{280}-\frac{315}{280}\\=\frac{80+392-315}{280}\\=\frac{157}{280}\)
2. \(+\left(\frac{-9}{2}\right) -\left(\frac{9}{5}\right) +\left(\frac{11}{-6}\right)\\= \frac{-9}{2}- \frac{9}{5}-\frac{11}{6}\\=\frac{-135}{30}-\frac{54}{30}-\frac{55}{30}\\=\frac{-135-54-55}{30}\\=\frac{-244}{30}\\=\frac{-122}{15}\)
3. \(+\left(\frac{-9}{5}\right) +\left(\frac{4}{5}\right) -\left(\frac{4}{-11}\right)\\= \frac{-9}{5}+ \frac{4}{5}+\frac{4}{11}\\=\frac{-99}{55}+\frac{44}{55}+\frac{20}{55}\\=\frac{-99+44+20}{55}\\=\frac{-35}{55}\\=\frac{-7}{11}\)
4. \(+\left(\frac{7}{9}\right) -\left(\frac{2}{-3}\right) -\left(\frac{-8}{6}\right)\\= \frac{7}{9}+ \frac{2}{3}+\frac{8}{6}\\=\frac{7}{9}+\frac{2}{3}+\frac{4}{3}\\=\frac{7+2+4}{9}\\=\frac{13}{9}\)
5. \(-\left(\frac{8}{9}\right) -\left(\frac{-9}{7}\right) -\left(\frac{-9}{4}\right)\\= \frac{-8}{9}+ \frac{9}{7}+\frac{9}{4}\\=\frac{-224}{252}+\frac{324}{252}+\frac{567}{252}\\=\frac{-224+324+567}{252}\\=\frac{667}{252}\)
6. \(-\left(\frac{2}{5}\right) -\left(\frac{7}{-7}\right) +\left(\frac{-2}{5}\right)\\= \frac{-2}{5}+ \frac{7}{7}-\frac{2}{5}\\=\frac{-2}{5}+\frac{1}{1}-\frac{2}{5}\\=\frac{-2+1-2}{5}\\=\frac{-3}{5}\)
7. \(-\left(\frac{5}{2}\right) +\left(\frac{-6}{2}\right) -\left(\frac{-10}{2}\right)\\= \frac{-5}{2}- \frac{6}{2}+\frac{10}{2}\\=\frac{-5}{2}-\frac{3}{1}+\frac{5}{1}\\=\frac{-5-3+5}{2}\\=\frac{-3}{2}\)
8. \(-\left(\frac{-9}{4}\right) -\left(\frac{5}{-6}\right) +\left(\frac{2}{-7}\right)\\= \frac{9}{4}+ \frac{5}{6}-\frac{2}{7}\\=\frac{189}{84}+\frac{70}{84}-\frac{24}{84}\\=\frac{189+70-24}{84}\\=\frac{235}{84}\)
9. \(-\left(\frac{9}{2}\right) +\left(\frac{-2}{-7}\right) +\left(\frac{5}{-10}\right)\\= \frac{-9}{2}+ \frac{2}{7}-\frac{5}{10}\\=\frac{-9}{2}+\frac{2}{7}-\frac{1}{2}\\=\frac{-63}{14}+\frac{4}{14}-\frac{7}{14}\\=\frac{-63+4-7}{14}\\=\frac{-66}{14}\\=\frac{-33}{7}\)
10. \(-\left(\frac{-7}{6}\right) +\left(\frac{-8}{4}\right) -\left(\frac{8}{5}\right)\\= \frac{7}{6}- \frac{8}{4}-\frac{8}{5}\\=\frac{7}{6}-\frac{2}{1}-\frac{8}{5}\\=\frac{35}{30}-\frac{60}{30}-\frac{48}{30}\\=\frac{35-60-48}{30}\\=\frac{-73}{30}\)
11. \(+\left(\frac{3}{2}\right) -\left(\frac{-2}{9}\right) +\left(\frac{-10}{2}\right)\\= \frac{3}{2}+ \frac{2}{9}-\frac{10}{2}\\=\frac{3}{2}+\frac{2}{9}-\frac{5}{1}\\=\frac{27}{18}+\frac{4}{18}-\frac{90}{18}\\=\frac{27+4-90}{18}\\=\frac{-59}{18}\)
12. \(+\left(\frac{-4}{-5}\right) +\left(\frac{3}{-8}\right) +\left(\frac{10}{7}\right)\\= \frac{4}{5}- \frac{3}{8}+\frac{10}{7}\\=\frac{224}{280}-\frac{105}{280}+\frac{400}{280}\\=\frac{224-105+400}{280}\\=\frac{519}{280}\)