Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{-4}\right) +\left(\frac{-9}{7}\right) -\left(\frac{8}{-7}\right)\\= \frac{7}{4}- \frac{9}{7}+\frac{8}{7}\\=\frac{49}{28}-\frac{36}{28}+\frac{32}{28}\\=\frac{49-36+32}{28}\\=\frac{45}{28}\)
2. \(+\left(\frac{-5}{6}\right) +\left(\frac{-2}{-4}\right) -\left(\frac{8}{8}\right)\\= \frac{-5}{6}+ \frac{2}{4}-\frac{8}{8}\\=\frac{-5}{6}+\frac{1}{2}-\frac{1}{1}\\=\frac{-5+1-1}{6}\\=\frac{-5}{6}\)
3. \(+\left(\frac{9}{-8}\right) -\left(\frac{4}{-6}\right) -\left(\frac{5}{3}\right)\\= \frac{-9}{8}+ \frac{4}{6}-\frac{5}{3}\\=\frac{-9}{8}+\frac{2}{3}-\frac{5}{3}\\=\frac{-27}{24}+\frac{16}{24}-\frac{40}{24}\\=\frac{-27+16-40}{24}\\=\frac{-51}{24}\\=\frac{-17}{8}\)
4. \(-\left(\frac{-7}{-8}\right) +\left(\frac{-8}{-4}\right) -\left(\frac{-2}{-2}\right)\\= \frac{-7}{8}+ \frac{8}{4}-\frac{2}{2}\\=\frac{-7}{8}+\frac{2}{1}-\frac{1}{1}\\=\frac{-7+2-1}{8}\\=\frac{-6}{8}\\=\frac{-3}{4}\)
5. \(-\left(\frac{-5}{4}\right) +\left(\frac{-5}{10}\right) +\left(\frac{8}{-4}\right)\\= \frac{5}{4}- \frac{5}{10}-\frac{8}{4}\\=\frac{5}{4}-\frac{1}{2}-\frac{2}{1}\\=\frac{5-1-2}{4}\\=\frac{2}{4}\\=\frac{1}{2}\)
6. \(-\left(\frac{-3}{-2}\right) -\left(\frac{-4}{-9}\right) +\left(\frac{-5}{4}\right)\\= \frac{-3}{2}- \frac{4}{9}-\frac{5}{4}\\=\frac{-54}{36}-\frac{16}{36}-\frac{45}{36}\\=\frac{-54-16-45}{36}\\=\frac{-115}{36}\)
7. \(-\left(\frac{10}{-3}\right) +\left(\frac{-4}{2}\right) -\left(\frac{-9}{-4}\right)\\= \frac{10}{3}- \frac{4}{2}-\frac{9}{4}\\=\frac{10}{3}-\frac{2}{1}-\frac{9}{4}\\=\frac{40}{12}-\frac{24}{12}-\frac{27}{12}\\=\frac{40-24-27}{12}\\=\frac{-11}{12}\)
8. \(-\left(\frac{-2}{-3}\right) -\left(\frac{-10}{8}\right) -\left(\frac{12}{7}\right)\\= \frac{-2}{3}+ \frac{10}{8}-\frac{12}{7}\\=\frac{-2}{3}+\frac{5}{4}-\frac{12}{7}\\=\frac{-56}{84}+\frac{105}{84}-\frac{144}{84}\\=\frac{-56+105-144}{84}\\=\frac{-95}{84}\)
9. \(+\left(\frac{8}{-3}\right) +\left(\frac{-8}{-6}\right) -\left(\frac{8}{6}\right)\\= \frac{-8}{3}+ \frac{8}{6}-\frac{8}{6}\\=\frac{-8}{3}+\frac{4}{3}-\frac{4}{3}\\=\frac{-8+4-4}{3}\\=\frac{-8}{3}\)
10. \(-\left(\frac{4}{9}\right) -\left(\frac{3}{-6}\right) -\left(\frac{-12}{2}\right)\\= \frac{-4}{9}+ \frac{3}{6}+\frac{12}{2}\\=\frac{-4}{9}+\frac{1}{2}+\frac{6}{1}\\=\frac{-8}{18}+\frac{9}{18}+\frac{108}{18}\\=\frac{-8+9+108}{18}\\=\frac{109}{18}\)
11. \(-\left(\frac{8}{-3}\right) -\left(\frac{9}{10}\right) -\left(\frac{7}{-9}\right)\\= \frac{8}{3}- \frac{9}{10}+\frac{7}{9}\\=\frac{240}{90}-\frac{81}{90}+\frac{70}{90}\\=\frac{240-81+70}{90}\\=\frac{229}{90}\)
12. \(-\left(\frac{2}{-7}\right) +\left(\frac{-2}{-9}\right) +\left(\frac{10}{3}\right)\\= \frac{2}{7}+ \frac{2}{9}+\frac{10}{3}\\=\frac{18}{63}+\frac{14}{63}+\frac{210}{63}\\=\frac{18+14+210}{63}\\=\frac{242}{63}\)