Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{9}\right) +\left(\frac{-9}{-4}\right) -\left(\frac{2}{3}\right)\\= \frac{4}{9}+ \frac{9}{4}-\frac{2}{3}\\=\frac{16}{36}+\frac{81}{36}-\frac{24}{36}\\=\frac{16+81-24}{36}\\=\frac{73}{36}\)
2. \(-\left(\frac{10}{3}\right) -\left(\frac{4}{7}\right) +\left(\frac{-2}{-9}\right)\\= \frac{-10}{3}- \frac{4}{7}+\frac{2}{9}\\=\frac{-210}{63}-\frac{36}{63}+\frac{14}{63}\\=\frac{-210-36+14}{63}\\=\frac{-232}{63}\)
3. \(-\left(\frac{-4}{-9}\right) +\left(\frac{4}{-8}\right) -\left(\frac{-5}{-12}\right)\\= \frac{-4}{9}- \frac{4}{8}-\frac{5}{12}\\=\frac{-4}{9}-\frac{1}{2}-\frac{5}{12}\\=\frac{-16}{36}-\frac{18}{36}-\frac{15}{36}\\=\frac{-16-18-15}{36}\\=\frac{-49}{36}\)
4. \(-\left(\frac{5}{-7}\right) +\left(\frac{5}{-8}\right) -\left(\frac{-5}{-9}\right)\\= \frac{5}{7}- \frac{5}{8}-\frac{5}{9}\\=\frac{360}{504}-\frac{315}{504}-\frac{280}{504}\\=\frac{360-315-280}{504}\\=\frac{-235}{504}\)
5. \(-\left(\frac{10}{-7}\right) -\left(\frac{-10}{5}\right) +\left(\frac{12}{-5}\right)\\= \frac{10}{7}+ \frac{10}{5}-\frac{12}{5}\\=\frac{10}{7}+\frac{2}{1}-\frac{12}{5}\\=\frac{50}{35}+\frac{70}{35}-\frac{84}{35}\\=\frac{50+70-84}{35}\\=\frac{36}{35}\)
6. \(+\left(\frac{4}{7}\right) +\left(\frac{5}{7}\right) -\left(\frac{12}{10}\right)\\= \frac{4}{7}+ \frac{5}{7}-\frac{12}{10}\\=\frac{4}{7}+\frac{5}{7}-\frac{6}{5}\\=\frac{20}{35}+\frac{25}{35}-\frac{42}{35}\\=\frac{20+25-42}{35}\\=\frac{3}{35}\)
7. \(+\left(\frac{-8}{5}\right) +\left(\frac{10}{2}\right) +\left(\frac{-11}{7}\right)\\= \frac{-8}{5}+ \frac{10}{2}-\frac{11}{7}\\=\frac{-8}{5}+\frac{5}{1}-\frac{11}{7}\\=\frac{-56}{35}+\frac{175}{35}-\frac{55}{35}\\=\frac{-56+175-55}{35}\\=\frac{64}{35}\)
8. \(-\left(\frac{8}{-5}\right) +\left(\frac{-7}{-9}\right) +\left(\frac{-12}{-8}\right)\\= \frac{8}{5}+ \frac{7}{9}+\frac{12}{8}\\=\frac{8}{5}+\frac{7}{9}+\frac{3}{2}\\=\frac{144}{90}+\frac{70}{90}+\frac{135}{90}\\=\frac{144+70+135}{90}\\=\frac{349}{90}\)
9. \(+\left(\frac{-7}{-2}\right) +\left(\frac{-6}{4}\right) -\left(\frac{8}{-2}\right)\\= \frac{7}{2}- \frac{6}{4}+\frac{8}{2}\\=\frac{7}{2}-\frac{3}{2}+\frac{4}{1}\\=\frac{7-3+4}{2}\\=\frac{8}{2}\\=\frac{4}{1}\)
10. \(-\left(\frac{6}{-7}\right) +\left(\frac{-3}{8}\right) -\left(\frac{-3}{6}\right)\\= \frac{6}{7}- \frac{3}{8}+\frac{3}{6}\\=\frac{6}{7}-\frac{3}{8}+\frac{1}{2}\\=\frac{48}{56}-\frac{21}{56}+\frac{28}{56}\\=\frac{48-21+28}{56}\\=\frac{55}{56}\)
11. \(+\left(\frac{2}{-9}\right) +\left(\frac{-9}{-6}\right) +\left(\frac{8}{-8}\right)\\= \frac{-2}{9}+ \frac{9}{6}-\frac{8}{8}\\=\frac{-2}{9}+\frac{3}{2}-\frac{1}{1}\\=\frac{-4}{18}+\frac{27}{18}-\frac{18}{18}\\=\frac{-4+27-18}{18}\\=\frac{5}{18}\)
12. \(+\left(\frac{7}{9}\right) +\left(\frac{-4}{10}\right) -\left(\frac{3}{-12}\right)\\= \frac{7}{9}- \frac{4}{10}+\frac{3}{12}\\=\frac{7}{9}-\frac{2}{5}+\frac{1}{4}\\=\frac{140}{180}-\frac{72}{180}+\frac{45}{180}\\=\frac{140-72+45}{180}\\=\frac{113}{180}\)