Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{-5}\right) -\left(\frac{-6}{2}\right) +\left(\frac{5}{6}\right)\\= \frac{8}{5}+ \frac{6}{2}-\frac{5}{6}\\=\frac{8}{5}+\frac{3}{1}-\frac{5}{6}\\=\frac{48}{30}+\frac{90}{30}-\frac{25}{30}\\=\frac{48+90-25}{30}\\=\frac{113}{30}\)
2. \(+\left(\frac{-7}{-2}\right) +\left(\frac{6}{-10}\right) -\left(\frac{-6}{2}\right)\\= \frac{7}{2}- \frac{6}{10}-\frac{6}{2}\\=\frac{7}{2}-\frac{3}{5}-\frac{3}{1}\\=\frac{35}{10}-\frac{6}{10}-\frac{30}{10}\\=\frac{35-6-30}{10}\\=\frac{-1}{10}\)
3. \(-\left(\frac{10}{-7}\right) +\left(\frac{8}{-8}\right) -\left(\frac{3}{-10}\right)\\= \frac{10}{7}- \frac{8}{8}+\frac{3}{10}\\=\frac{10}{7}-\frac{1}{1}+\frac{3}{10}\\=\frac{100}{70}-\frac{70}{70}+\frac{21}{70}\\=\frac{100-70+21}{70}\\=\frac{51}{70}\)
4. \(+\left(\frac{9}{-2}\right) +\left(\frac{-4}{9}\right) -\left(\frac{-6}{-6}\right)\\= \frac{-9}{2}- \frac{4}{9}-\frac{6}{6}\\=\frac{-9}{2}-\frac{4}{9}-\frac{1}{1}\\=\frac{-81}{18}-\frac{8}{18}-\frac{18}{18}\\=\frac{-81-8-18}{18}\\=\frac{-107}{18}\)
5. \(-\left(\frac{-7}{4}\right) +\left(\frac{3}{-10}\right) +\left(\frac{6}{10}\right)\\= \frac{7}{4}- \frac{3}{10}+\frac{6}{10}\\=\frac{7}{4}-\frac{3}{10}+\frac{3}{5}\\=\frac{35}{20}-\frac{6}{20}+\frac{12}{20}\\=\frac{35-6+12}{20}\\=\frac{41}{20}\)
6. \(+\left(\frac{9}{7}\right) -\left(\frac{-9}{5}\right) +\left(\frac{11}{4}\right)\\= \frac{9}{7}+ \frac{9}{5}-\frac{11}{4}\\=\frac{180}{140}+\frac{252}{140}-\frac{385}{140}\\=\frac{180+252-385}{140}\\=\frac{47}{140}\)
7. \(+\left(\frac{-8}{-5}\right) +\left(\frac{-3}{-8}\right) +\left(\frac{4}{-12}\right)\\= \frac{8}{5}+ \frac{3}{8}+\frac{4}{12}\\=\frac{8}{5}+\frac{3}{8}+\frac{1}{3}\\=\frac{192}{120}+\frac{45}{120}+\frac{40}{120}\\=\frac{192+45+40}{120}\\=\frac{277}{120}\)
8. \(-\left(\frac{2}{-5}\right) -\left(\frac{-6}{-3}\right) +\left(\frac{4}{4}\right)\\= \frac{2}{5}- \frac{6}{3}-\frac{4}{4}\\=\frac{2}{5}-\frac{2}{1}-\frac{1}{1}\\=\frac{2-2-1}{5}\\=\frac{-1}{5}\)
9. \(+\left(\frac{5}{-8}\right) -\left(\frac{10}{-10}\right) -\left(\frac{4}{7}\right)\\= \frac{-5}{8}+ \frac{10}{10}-\frac{4}{7}\\=\frac{-5}{8}+\frac{1}{1}-\frac{4}{7}\\=\frac{-35}{56}+\frac{56}{56}-\frac{32}{56}\\=\frac{-35+56-32}{56}\\=\frac{-11}{56}\)
10. \(-\left(\frac{10}{3}\right) -\left(\frac{4}{-8}\right) +\left(\frac{-2}{-10}\right)\\= \frac{-10}{3}+ \frac{4}{8}-\frac{2}{10}\\=\frac{-10}{3}+\frac{1}{2}-\frac{1}{5}\\=\frac{-100}{30}+\frac{15}{30}-\frac{6}{30}\\=\frac{-100+15-6}{30}\\=\frac{-91}{30}\)
11. \(-\left(\frac{-10}{9}\right) +\left(\frac{8}{-9}\right) +\left(\frac{12}{7}\right)\\= \frac{10}{9}- \frac{8}{9}+\frac{12}{7}\\=\frac{70}{63}-\frac{56}{63}+\frac{108}{63}\\=\frac{70-56+108}{63}\\=\frac{122}{63}\)
12. \(-\left(\frac{-7}{-2}\right) -\left(\frac{-10}{5}\right) +\left(\frac{12}{12}\right)\\= \frac{-7}{2}+ \frac{10}{5}-\frac{12}{12}\\=\frac{-7}{2}+\frac{2}{1}-\frac{1}{1}\\=\frac{-7+2-1}{2}\\=\frac{-6}{2}\\=\frac{-3}{1}\)