Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{-6}\right) -\left(\frac{-9}{-8}\right) +\left(\frac{5}{-12}\right)\\= \frac{-5}{6}- \frac{9}{8}-\frac{5}{12}\\=\frac{-20}{24}-\frac{27}{24}-\frac{10}{24}\\=\frac{-20-27-10}{24}\\=\frac{-57}{24}\\=\frac{-19}{8}\)
2. \(-\left(\frac{-6}{5}\right) +\left(\frac{-6}{2}\right) -\left(\frac{8}{-8}\right)\\= \frac{6}{5}- \frac{6}{2}+\frac{8}{8}\\=\frac{6}{5}-\frac{3}{1}+\frac{1}{1}\\=\frac{6-3+1}{5}\\=\frac{4}{5}\)
3. \(+\left(\frac{2}{3}\right) -\left(\frac{5}{7}\right) -\left(\frac{6}{7}\right)\\= \frac{2}{3}- \frac{5}{7}-\frac{6}{7}\\=\frac{14}{21}-\frac{15}{21}-\frac{18}{21}\\=\frac{14-15-18}{21}\\=\frac{-19}{21}\)
4. \(+\left(\frac{-7}{2}\right) +\left(\frac{4}{-3}\right) -\left(\frac{5}{-2}\right)\\= \frac{-7}{2}- \frac{4}{3}+\frac{5}{2}\\=\frac{-21}{6}-\frac{8}{6}+\frac{15}{6}\\=\frac{-21-8+15}{6}\\=\frac{-14}{6}\\=\frac{-7}{3}\)
5. \(+\left(\frac{-3}{8}\right) -\left(\frac{-8}{6}\right) -\left(\frac{-10}{5}\right)\\= \frac{-3}{8}+ \frac{8}{6}+\frac{10}{5}\\=\frac{-3}{8}+\frac{4}{3}+\frac{2}{1}\\=\frac{-9}{24}+\frac{32}{24}+\frac{48}{24}\\=\frac{-9+32+48}{24}\\=\frac{71}{24}\)
6. \(+\left(\frac{-6}{5}\right) -\left(\frac{-3}{9}\right) -\left(\frac{2}{-12}\right)\\= \frac{-6}{5}+ \frac{3}{9}+\frac{2}{12}\\=\frac{-6}{5}+\frac{1}{3}+\frac{1}{6}\\=\frac{-36}{30}+\frac{10}{30}+\frac{5}{30}\\=\frac{-36+10+5}{30}\\=\frac{-21}{30}\\=\frac{-7}{10}\)
7. \(+\left(\frac{4}{9}\right) -\left(\frac{2}{3}\right) +\left(\frac{4}{-11}\right)\\= \frac{4}{9}- \frac{2}{3}-\frac{4}{11}\\=\frac{44}{99}-\frac{66}{99}-\frac{36}{99}\\=\frac{44-66-36}{99}\\=\frac{-58}{99}\)
8. \(+\left(\frac{8}{3}\right) -\left(\frac{9}{-8}\right) +\left(\frac{-7}{9}\right)\\= \frac{8}{3}+ \frac{9}{8}-\frac{7}{9}\\=\frac{192}{72}+\frac{81}{72}-\frac{56}{72}\\=\frac{192+81-56}{72}\\=\frac{217}{72}\)
9. \(-\left(\frac{8}{-5}\right) +\left(\frac{7}{2}\right) +\left(\frac{2}{-2}\right)\\= \frac{8}{5}+ \frac{7}{2}-\frac{2}{2}\\=\frac{8}{5}+\frac{7}{2}-\frac{1}{1}\\=\frac{16}{10}+\frac{35}{10}-\frac{10}{10}\\=\frac{16+35-10}{10}\\=\frac{41}{10}\)
10. \(-\left(\frac{-8}{7}\right) +\left(\frac{-3}{4}\right) +\left(\frac{4}{-4}\right)\\= \frac{8}{7}- \frac{3}{4}-\frac{4}{4}\\=\frac{8}{7}-\frac{3}{4}-\frac{1}{1}\\=\frac{32}{28}-\frac{21}{28}-\frac{28}{28}\\=\frac{32-21-28}{28}\\=\frac{-17}{28}\)
11. \(+\left(\frac{8}{7}\right) -\left(\frac{7}{9}\right) -\left(\frac{12}{-12}\right)\\= \frac{8}{7}- \frac{7}{9}+\frac{12}{12}\\=\frac{8}{7}-\frac{7}{9}+\frac{1}{1}\\=\frac{72}{63}-\frac{49}{63}+\frac{63}{63}\\=\frac{72-49+63}{63}\\=\frac{86}{63}\)
12. \(+\left(\frac{-5}{-4}\right) -\left(\frac{-8}{-9}\right) +\left(\frac{-8}{-7}\right)\\= \frac{5}{4}- \frac{8}{9}+\frac{8}{7}\\=\frac{315}{252}-\frac{224}{252}+\frac{288}{252}\\=\frac{315-224+288}{252}\\=\frac{379}{252}\)