Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{10}{7}\right) -\left(\frac{7}{-3}\right) +\left(\frac{11}{-2}\right)\\= \frac{10}{7}+ \frac{7}{3}-\frac{11}{2}\\=\frac{60}{42}+\frac{98}{42}-\frac{231}{42}\\=\frac{60+98-231}{42}\\=\frac{-73}{42}\)
2. \(+\left(\frac{2}{-3}\right) -\left(\frac{-2}{-10}\right) +\left(\frac{-2}{-6}\right)\\= \frac{-2}{3}- \frac{2}{10}+\frac{2}{6}\\=\frac{-2}{3}-\frac{1}{5}+\frac{1}{3}\\=\frac{-10}{15}-\frac{3}{15}+\frac{5}{15}\\=\frac{-10-3+5}{15}\\=\frac{-8}{15}\)
3. \(-\left(\frac{5}{-2}\right) +\left(\frac{7}{4}\right) -\left(\frac{-11}{7}\right)\\= \frac{5}{2}+ \frac{7}{4}+\frac{11}{7}\\=\frac{70}{28}+\frac{49}{28}+\frac{44}{28}\\=\frac{70+49+44}{28}\\=\frac{163}{28}\)
4. \(-\left(\frac{-2}{5}\right) +\left(\frac{-10}{5}\right) -\left(\frac{-8}{8}\right)\\= \frac{2}{5}- \frac{10}{5}+\frac{8}{8}\\=\frac{2}{5}-\frac{2}{1}+\frac{1}{1}\\=\frac{2-2+1}{5}\\=\frac{1}{5}\)
5. \(-\left(\frac{3}{-4}\right) -\left(\frac{10}{-4}\right) +\left(\frac{9}{-2}\right)\\= \frac{3}{4}+ \frac{10}{4}-\frac{9}{2}\\=\frac{3}{4}+\frac{5}{2}-\frac{9}{2}\\=\frac{3+5-9}{4}\\=\frac{-1}{4}\)
6. \(+\left(\frac{-2}{-3}\right) -\left(\frac{-5}{6}\right) -\left(\frac{3}{7}\right)\\= \frac{2}{3}+ \frac{5}{6}-\frac{3}{7}\\=\frac{28}{42}+\frac{35}{42}-\frac{18}{42}\\=\frac{28+35-18}{42}\\=\frac{45}{42}\\=\frac{15}{14}\)
7. \(-\left(\frac{-2}{3}\right) +\left(\frac{6}{8}\right) -\left(\frac{2}{-4}\right)\\= \frac{2}{3}+ \frac{6}{8}+\frac{2}{4}\\=\frac{2}{3}+\frac{3}{4}+\frac{1}{2}\\=\frac{8}{12}+\frac{9}{12}+\frac{6}{12}\\=\frac{8+9+6}{12}\\=\frac{23}{12}\)
8. \(-\left(\frac{-8}{3}\right) +\left(\frac{4}{-7}\right) +\left(\frac{3}{4}\right)\\= \frac{8}{3}- \frac{4}{7}+\frac{3}{4}\\=\frac{224}{84}-\frac{48}{84}+\frac{63}{84}\\=\frac{224-48+63}{84}\\=\frac{239}{84}\)
9. \(-\left(\frac{9}{-5}\right) -\left(\frac{-7}{7}\right) +\left(\frac{11}{-3}\right)\\= \frac{9}{5}+ \frac{7}{7}-\frac{11}{3}\\=\frac{9}{5}+\frac{1}{1}-\frac{11}{3}\\=\frac{27}{15}+\frac{15}{15}-\frac{55}{15}\\=\frac{27+15-55}{15}\\=\frac{-13}{15}\)
10. \(+\left(\frac{10}{-9}\right) -\left(\frac{4}{5}\right) +\left(\frac{-5}{-3}\right)\\= \frac{-10}{9}- \frac{4}{5}+\frac{5}{3}\\=\frac{-50}{45}-\frac{36}{45}+\frac{75}{45}\\=\frac{-50-36+75}{45}\\=\frac{-11}{45}\)
11. \(-\left(\frac{4}{-3}\right) -\left(\frac{-3}{5}\right) +\left(\frac{10}{-3}\right)\\= \frac{4}{3}+ \frac{3}{5}-\frac{10}{3}\\=\frac{20}{15}+\frac{9}{15}-\frac{50}{15}\\=\frac{20+9-50}{15}\\=\frac{-21}{15}\\=\frac{-7}{5}\)
12. \(+\left(\frac{5}{-9}\right) +\left(\frac{-8}{7}\right) +\left(\frac{-9}{12}\right)\\= \frac{-5}{9}- \frac{8}{7}-\frac{9}{12}\\=\frac{-5}{9}-\frac{8}{7}-\frac{3}{4}\\=\frac{-140}{252}-\frac{288}{252}-\frac{189}{252}\\=\frac{-140-288-189}{252}\\=\frac{-617}{252}\)