Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{-9}\right) +\left(\frac{-3}{7}\right) +\left(\frac{-2}{8}\right)\\= \frac{-4}{9}- \frac{3}{7}-\frac{2}{8}\\=\frac{-4}{9}-\frac{3}{7}-\frac{1}{4}\\=\frac{-112}{252}-\frac{108}{252}-\frac{63}{252}\\=\frac{-112-108-63}{252}\\=\frac{-283}{252}\)
2. \(+\left(\frac{3}{-4}\right) +\left(\frac{-5}{-6}\right) +\left(\frac{10}{12}\right)\\= \frac{-3}{4}+ \frac{5}{6}+\frac{10}{12}\\=\frac{-3}{4}+\frac{5}{6}+\frac{5}{6}\\=\frac{-9}{12}+\frac{10}{12}+\frac{10}{12}\\=\frac{-9+10+10}{12}\\=\frac{11}{12}\)
3. \(-\left(\frac{7}{8}\right) -\left(\frac{4}{9}\right) +\left(\frac{2}{3}\right)\\= \frac{-7}{8}- \frac{4}{9}+\frac{2}{3}\\=\frac{-63}{72}-\frac{32}{72}+\frac{48}{72}\\=\frac{-63-32+48}{72}\\=\frac{-47}{72}\)
4. \(-\left(\frac{-8}{3}\right) -\left(\frac{10}{4}\right) +\left(\frac{-6}{3}\right)\\= \frac{8}{3}- \frac{10}{4}-\frac{6}{3}\\=\frac{8}{3}-\frac{5}{2}-\frac{2}{1}\\=\frac{16}{6}-\frac{15}{6}-\frac{12}{6}\\=\frac{16-15-12}{6}\\=\frac{-11}{6}\)
5. \(+\left(\frac{4}{3}\right) -\left(\frac{10}{7}\right) +\left(\frac{-11}{-2}\right)\\= \frac{4}{3}- \frac{10}{7}+\frac{11}{2}\\=\frac{56}{42}-\frac{60}{42}+\frac{231}{42}\\=\frac{56-60+231}{42}\\=\frac{227}{42}\)
6. \(+\left(\frac{-7}{-8}\right) -\left(\frac{5}{-4}\right) +\left(\frac{-10}{-7}\right)\\= \frac{7}{8}+ \frac{5}{4}+\frac{10}{7}\\=\frac{49}{56}+\frac{70}{56}+\frac{80}{56}\\=\frac{49+70+80}{56}\\=\frac{199}{56}\)
7. \(-\left(\frac{-6}{-5}\right) +\left(\frac{8}{-3}\right) -\left(\frac{4}{-8}\right)\\= \frac{-6}{5}- \frac{8}{3}+\frac{4}{8}\\=\frac{-6}{5}-\frac{8}{3}+\frac{1}{2}\\=\frac{-36}{30}-\frac{80}{30}+\frac{15}{30}\\=\frac{-36-80+15}{30}\\=\frac{-101}{30}\)
8. \(+\left(\frac{-6}{-5}\right) -\left(\frac{8}{-2}\right) -\left(\frac{-10}{-3}\right)\\= \frac{6}{5}+ \frac{8}{2}-\frac{10}{3}\\=\frac{6}{5}+\frac{4}{1}-\frac{10}{3}\\=\frac{18}{15}+\frac{60}{15}-\frac{50}{15}\\=\frac{18+60-50}{15}\\=\frac{28}{15}\)
9. \(-\left(\frac{3}{-2}\right) +\left(\frac{-6}{2}\right) +\left(\frac{6}{3}\right)\\= \frac{3}{2}- \frac{6}{2}+\frac{6}{3}\\=\frac{3}{2}-\frac{3}{1}+\frac{2}{1}\\=\frac{3-3+2}{2}\\=\frac{2}{2}\\=\frac{1}{1}\)
10. \(-\left(\frac{4}{3}\right) -\left(\frac{-5}{-3}\right) -\left(\frac{-3}{3}\right)\\= \frac{-4}{3}- \frac{5}{3}+\frac{3}{3}\\=\frac{-4}{3}-\frac{5}{3}+\frac{1}{1}\\=\frac{-4-5+1}{3}\\=\frac{-8}{3}\)
11. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-9}{4}\right) +\left(\frac{-7}{-7}\right)\\= \frac{-6}{5}+ \frac{9}{4}+\frac{7}{7}\\=\frac{-6}{5}+\frac{9}{4}+\frac{1}{1}\\=\frac{-24}{20}+\frac{45}{20}+\frac{20}{20}\\=\frac{-24+45+20}{20}\\=\frac{41}{20}\)
12. \(+\left(\frac{-2}{-3}\right) -\left(\frac{-5}{-8}\right) -\left(\frac{-3}{8}\right)\\= \frac{2}{3}- \frac{5}{8}+\frac{3}{8}\\=\frac{16}{24}-\frac{15}{24}+\frac{9}{24}\\=\frac{16-15+9}{24}\\=\frac{10}{24}\\=\frac{5}{12}\)