Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{-2}\right) -\left(\frac{-6}{-2}\right) -\left(\frac{-5}{10}\right)\\= \frac{3}{2}- \frac{6}{2}+\frac{5}{10}\\=\frac{3}{2}-\frac{3}{1}+\frac{1}{2}\\=\frac{3-3+1}{2}\\=\frac{1}{2}\)
2. \(+\left(\frac{-10}{-3}\right) -\left(\frac{-8}{-3}\right) +\left(\frac{3}{2}\right)\\= \frac{10}{3}- \frac{8}{3}+\frac{3}{2}\\=\frac{20}{6}-\frac{16}{6}+\frac{9}{6}\\=\frac{20-16+9}{6}\\=\frac{13}{6}\)
3. \(-\left(\frac{8}{-7}\right) +\left(\frac{-2}{9}\right) +\left(\frac{-4}{-2}\right)\\= \frac{8}{7}- \frac{2}{9}+\frac{4}{2}\\=\frac{8}{7}-\frac{2}{9}+\frac{2}{1}\\=\frac{72}{63}-\frac{14}{63}+\frac{126}{63}\\=\frac{72-14+126}{63}\\=\frac{184}{63}\)
4. \(+\left(\frac{-9}{-8}\right) -\left(\frac{-4}{-10}\right) -\left(\frac{12}{-10}\right)\\= \frac{9}{8}- \frac{4}{10}+\frac{12}{10}\\=\frac{9}{8}-\frac{2}{5}+\frac{6}{5}\\=\frac{45}{40}-\frac{16}{40}+\frac{48}{40}\\=\frac{45-16+48}{40}\\=\frac{77}{40}\)
5. \(+\left(\frac{-9}{-2}\right) -\left(\frac{2}{6}\right) +\left(\frac{6}{-8}\right)\\= \frac{9}{2}- \frac{2}{6}-\frac{6}{8}\\=\frac{9}{2}-\frac{1}{3}-\frac{3}{4}\\=\frac{54}{12}-\frac{4}{12}-\frac{9}{12}\\=\frac{54-4-9}{12}\\=\frac{41}{12}\)
6. \(-\left(\frac{-9}{2}\right) +\left(\frac{-10}{3}\right) +\left(\frac{-2}{-3}\right)\\= \frac{9}{2}- \frac{10}{3}+\frac{2}{3}\\=\frac{27}{6}-\frac{20}{6}+\frac{4}{6}\\=\frac{27-20+4}{6}\\=\frac{11}{6}\)
7. \(+\left(\frac{-2}{3}\right) +\left(\frac{-8}{5}\right) +\left(\frac{-10}{9}\right)\\= \frac{-2}{3}- \frac{8}{5}-\frac{10}{9}\\=\frac{-30}{45}-\frac{72}{45}-\frac{50}{45}\\=\frac{-30-72-50}{45}\\=\frac{-152}{45}\)
8. \(+\left(\frac{-6}{5}\right) +\left(\frac{-2}{9}\right) +\left(\frac{-4}{-2}\right)\\= \frac{-6}{5}- \frac{2}{9}+\frac{4}{2}\\=\frac{-6}{5}-\frac{2}{9}+\frac{2}{1}\\=\frac{-54}{45}-\frac{10}{45}+\frac{90}{45}\\=\frac{-54-10+90}{45}\\=\frac{26}{45}\)
9. \(+\left(\frac{-10}{-9}\right) -\left(\frac{-7}{3}\right) -\left(\frac{7}{6}\right)\\= \frac{10}{9}+ \frac{7}{3}-\frac{7}{6}\\=\frac{20}{18}+\frac{42}{18}-\frac{21}{18}\\=\frac{20+42-21}{18}\\=\frac{41}{18}\)
10. \(+\left(\frac{3}{-7}\right) +\left(\frac{-4}{-5}\right) -\left(\frac{-3}{-6}\right)\\= \frac{-3}{7}+ \frac{4}{5}-\frac{3}{6}\\=\frac{-3}{7}+\frac{4}{5}-\frac{1}{2}\\=\frac{-30}{70}+\frac{56}{70}-\frac{35}{70}\\=\frac{-30+56-35}{70}\\=\frac{-9}{70}\)
11. \(-\left(\frac{10}{-3}\right) -\left(\frac{5}{-3}\right) -\left(\frac{3}{-12}\right)\\= \frac{10}{3}+ \frac{5}{3}+\frac{3}{12}\\=\frac{10}{3}+\frac{5}{3}+\frac{1}{4}\\=\frac{40}{12}+\frac{20}{12}+\frac{3}{12}\\=\frac{40+20+3}{12}\\=\frac{63}{12}\\=\frac{21}{4}\)
12. \(+\left(\frac{7}{-2}\right) +\left(\frac{10}{-9}\right) -\left(\frac{11}{-7}\right)\\= \frac{-7}{2}- \frac{10}{9}+\frac{11}{7}\\=\frac{-441}{126}-\frac{140}{126}+\frac{198}{126}\\=\frac{-441-140+198}{126}\\=\frac{-383}{126}\)