Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{6}{7}\right) +\left(\frac{-6}{8}\right) -\left(\frac{7}{-9}\right)\\= \frac{6}{7}- \frac{6}{8}+\frac{7}{9}\\=\frac{6}{7}-\frac{3}{4}+\frac{7}{9}\\=\frac{216}{252}-\frac{189}{252}+\frac{196}{252}\\=\frac{216-189+196}{252}\\=\frac{223}{252}\)
2. \(-\left(\frac{-6}{-5}\right) -\left(\frac{6}{2}\right) +\left(\frac{-8}{-10}\right)\\= \frac{-6}{5}- \frac{6}{2}+\frac{8}{10}\\=\frac{-6}{5}-\frac{3}{1}+\frac{4}{5}\\=\frac{-6-3+4}{5}\\=\frac{-5}{5}\\=\frac{-1}{1}\)
3. \(-\left(\frac{7}{8}\right) -\left(\frac{-5}{10}\right) -\left(\frac{-6}{9}\right)\\= \frac{-7}{8}+ \frac{5}{10}+\frac{6}{9}\\=\frac{-7}{8}+\frac{1}{2}+\frac{2}{3}\\=\frac{-21}{24}+\frac{12}{24}+\frac{16}{24}\\=\frac{-21+12+16}{24}\\=\frac{7}{24}\)
4. \(+\left(\frac{-5}{9}\right) -\left(\frac{6}{6}\right) -\left(\frac{-5}{2}\right)\\= \frac{-5}{9}- \frac{6}{6}+\frac{5}{2}\\=\frac{-5}{9}-\frac{1}{1}+\frac{5}{2}\\=\frac{-10}{18}-\frac{18}{18}+\frac{45}{18}\\=\frac{-10-18+45}{18}\\=\frac{17}{18}\)
5. \(-\left(\frac{-2}{7}\right) -\left(\frac{5}{2}\right) +\left(\frac{-9}{-3}\right)\\= \frac{2}{7}- \frac{5}{2}+\frac{9}{3}\\=\frac{2}{7}-\frac{5}{2}+\frac{3}{1}\\=\frac{4}{14}-\frac{35}{14}+\frac{42}{14}\\=\frac{4-35+42}{14}\\=\frac{11}{14}\)
6. \(-\left(\frac{10}{-9}\right) +\left(\frac{-7}{8}\right) +\left(\frac{-2}{12}\right)\\= \frac{10}{9}- \frac{7}{8}-\frac{2}{12}\\=\frac{10}{9}-\frac{7}{8}-\frac{1}{6}\\=\frac{80}{72}-\frac{63}{72}-\frac{12}{72}\\=\frac{80-63-12}{72}\\=\frac{5}{72}\)
7. \(-\left(\frac{-5}{2}\right) +\left(\frac{-6}{8}\right) -\left(\frac{7}{4}\right)\\= \frac{5}{2}- \frac{6}{8}-\frac{7}{4}\\=\frac{5}{2}-\frac{3}{4}-\frac{7}{4}\\=\frac{10}{4}-\frac{3}{4}-\frac{7}{4}\\=\frac{10-3-7}{4}\\=\frac{0}{4}\\=\frac{0}{1}\)
8. \(+\left(\frac{-5}{4}\right) -\left(\frac{7}{4}\right) +\left(\frac{3}{6}\right)\\= \frac{-5}{4}- \frac{7}{4}+\frac{3}{6}\\=\frac{-5}{4}-\frac{7}{4}+\frac{1}{2}\\=\frac{-5-7+1}{4}\\=\frac{-11}{4}\)
9. \(+\left(\frac{-5}{6}\right) -\left(\frac{5}{-3}\right) +\left(\frac{5}{-9}\right)\\= \frac{-5}{6}+ \frac{5}{3}-\frac{5}{9}\\=\frac{-15}{18}+\frac{30}{18}-\frac{10}{18}\\=\frac{-15+30-10}{18}\\=\frac{5}{18}\)
10. \(+\left(\frac{-5}{-6}\right) -\left(\frac{-2}{-9}\right) -\left(\frac{11}{4}\right)\\= \frac{5}{6}- \frac{2}{9}-\frac{11}{4}\\=\frac{30}{36}-\frac{8}{36}-\frac{99}{36}\\=\frac{30-8-99}{36}\\=\frac{-77}{36}\)
11. \(-\left(\frac{-3}{-4}\right) -\left(\frac{3}{-3}\right) +\left(\frac{-8}{12}\right)\\= \frac{-3}{4}+ \frac{3}{3}-\frac{8}{12}\\=\frac{-3}{4}+\frac{1}{1}-\frac{2}{3}\\=\frac{-9}{12}+\frac{12}{12}-\frac{8}{12}\\=\frac{-9+12-8}{12}\\=\frac{-5}{12}\)
12. \(-\left(\frac{-3}{-4}\right) +\left(\frac{-6}{-9}\right) -\left(\frac{9}{12}\right)\\= \frac{-3}{4}+ \frac{6}{9}-\frac{9}{12}\\=\frac{-3}{4}+\frac{2}{3}-\frac{3}{4}\\=\frac{-9}{12}+\frac{8}{12}-\frac{9}{12}\\=\frac{-9+8-9}{12}\\=\frac{-10}{12}\\=\frac{-5}{6}\)