Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{6}\right) +\left(\frac{4}{-5}\right) -\left(\frac{-2}{11}\right)\\= \frac{-7}{6}- \frac{4}{5}+\frac{2}{11}\\=\frac{-385}{330}-\frac{264}{330}+\frac{60}{330}\\=\frac{-385-264+60}{330}\\=\frac{-589}{330}\)
2. \(-\left(\frac{5}{9}\right) +\left(\frac{8}{10}\right) +\left(\frac{5}{10}\right)\\= \frac{-5}{9}+ \frac{8}{10}+\frac{5}{10}\\=\frac{-5}{9}+\frac{4}{5}+\frac{1}{2}\\=\frac{-50}{90}+\frac{72}{90}+\frac{45}{90}\\=\frac{-50+72+45}{90}\\=\frac{67}{90}\)
3. \(+\left(\frac{-4}{-9}\right) +\left(\frac{-3}{-5}\right) -\left(\frac{-6}{8}\right)\\= \frac{4}{9}+ \frac{3}{5}+\frac{6}{8}\\=\frac{4}{9}+\frac{3}{5}+\frac{3}{4}\\=\frac{80}{180}+\frac{108}{180}+\frac{135}{180}\\=\frac{80+108+135}{180}\\=\frac{323}{180}\)
4. \(+\left(\frac{5}{-9}\right) +\left(\frac{6}{-2}\right) +\left(\frac{-3}{6}\right)\\= \frac{-5}{9}- \frac{6}{2}-\frac{3}{6}\\=\frac{-5}{9}-\frac{3}{1}-\frac{1}{2}\\=\frac{-10}{18}-\frac{54}{18}-\frac{9}{18}\\=\frac{-10-54-9}{18}\\=\frac{-73}{18}\)
5. \(+\left(\frac{-9}{2}\right) +\left(\frac{4}{9}\right) -\left(\frac{-11}{3}\right)\\= \frac{-9}{2}+ \frac{4}{9}+\frac{11}{3}\\=\frac{-81}{18}+\frac{8}{18}+\frac{66}{18}\\=\frac{-81+8+66}{18}\\=\frac{-7}{18}\)
6. \(+\left(\frac{6}{5}\right) +\left(\frac{-2}{10}\right) +\left(\frac{-12}{-4}\right)\\= \frac{6}{5}- \frac{2}{10}+\frac{12}{4}\\=\frac{6}{5}-\frac{1}{5}+\frac{3}{1}\\=\frac{6-1+3}{5}\\=\frac{8}{5}\)
7. \(-\left(\frac{-2}{-9}\right) -\left(\frac{8}{9}\right) -\left(\frac{-2}{-2}\right)\\= \frac{-2}{9}- \frac{8}{9}-\frac{2}{2}\\=\frac{-2}{9}-\frac{8}{9}-\frac{1}{1}\\=\frac{-2-8-1}{9}\\=\frac{-11}{9}\)
8. \(+\left(\frac{-7}{-6}\right) -\left(\frac{-4}{10}\right) +\left(\frac{9}{-5}\right)\\= \frac{7}{6}+ \frac{4}{10}-\frac{9}{5}\\=\frac{7}{6}+\frac{2}{5}-\frac{9}{5}\\=\frac{35}{30}+\frac{12}{30}-\frac{54}{30}\\=\frac{35+12-54}{30}\\=\frac{-7}{30}\)
9. \(+\left(\frac{4}{-9}\right) -\left(\frac{-4}{6}\right) +\left(\frac{-7}{-7}\right)\\= \frac{-4}{9}+ \frac{4}{6}+\frac{7}{7}\\=\frac{-4}{9}+\frac{2}{3}+\frac{1}{1}\\=\frac{-4+2+1}{9}\\=\frac{-1}{9}\)
10. \(+\left(\frac{7}{6}\right) -\left(\frac{4}{6}\right) -\left(\frac{5}{3}\right)\\= \frac{7}{6}- \frac{4}{6}-\frac{5}{3}\\=\frac{7}{6}-\frac{2}{3}-\frac{5}{3}\\=\frac{7-2-5}{6}\\=\frac{0}{6}\\=\frac{0}{1}\)
11. \(+\left(\frac{5}{-4}\right) -\left(\frac{-9}{-9}\right) +\left(\frac{4}{9}\right)\\= \frac{-5}{4}- \frac{9}{9}+\frac{4}{9}\\=\frac{-5}{4}-\frac{1}{1}+\frac{4}{9}\\=\frac{-45}{36}-\frac{36}{36}+\frac{16}{36}\\=\frac{-45-36+16}{36}\\=\frac{-65}{36}\)
12. \(-\left(\frac{-2}{5}\right) +\left(\frac{6}{2}\right) -\left(\frac{11}{5}\right)\\= \frac{2}{5}+ \frac{6}{2}-\frac{11}{5}\\=\frac{2}{5}+\frac{3}{1}-\frac{11}{5}\\=\frac{2+3-11}{5}\\=\frac{-6}{5}\)