Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{8}{7}\right) -\left(\frac{2}{7}\right) +\left(\frac{6}{-4}\right)\\= \frac{8}{7}- \frac{2}{7}-\frac{6}{4}\\=\frac{8}{7}-\frac{2}{7}-\frac{3}{2}\\=\frac{16}{14}-\frac{4}{14}-\frac{21}{14}\\=\frac{16-4-21}{14}\\=\frac{-9}{14}\)
2. \(+\left(\frac{-9}{4}\right) -\left(\frac{8}{2}\right) -\left(\frac{-8}{-9}\right)\\= \frac{-9}{4}- \frac{8}{2}-\frac{8}{9}\\=\frac{-9}{4}-\frac{4}{1}-\frac{8}{9}\\=\frac{-81}{36}-\frac{144}{36}-\frac{32}{36}\\=\frac{-81-144-32}{36}\\=\frac{-257}{36}\)
3. \(-\left(\frac{-4}{3}\right) +\left(\frac{-7}{-3}\right) +\left(\frac{8}{9}\right)\\= \frac{4}{3}+ \frac{7}{3}+\frac{8}{9}\\=\frac{12}{9}+\frac{21}{9}+\frac{8}{9}\\=\frac{12+21+8}{9}\\=\frac{41}{9}\)
4. \(+\left(\frac{-10}{7}\right) +\left(\frac{5}{8}\right) +\left(\frac{-8}{-3}\right)\\= \frac{-10}{7}+ \frac{5}{8}+\frac{8}{3}\\=\frac{-240}{168}+\frac{105}{168}+\frac{448}{168}\\=\frac{-240+105+448}{168}\\=\frac{313}{168}\)
5. \(+\left(\frac{-3}{8}\right) -\left(\frac{-3}{8}\right) +\left(\frac{-5}{-2}\right)\\= \frac{-3}{8}+ \frac{3}{8}+\frac{5}{2}\\=\frac{-3+3+5}{8}\\=\frac{5}{8}\)
6. \(-\left(\frac{3}{2}\right) +\left(\frac{-2}{-4}\right) -\left(\frac{-3}{6}\right)\\= \frac{-3}{2}+ \frac{2}{4}+\frac{3}{6}\\=\frac{-3}{2}+\frac{1}{2}+\frac{1}{2}\\=\frac{-3+1+1}{2}\\=\frac{-1}{2}\)
7. \(+\left(\frac{-3}{-5}\right) +\left(\frac{-7}{-2}\right) +\left(\frac{12}{-2}\right)\\= \frac{3}{5}+ \frac{7}{2}-\frac{12}{2}\\=\frac{3}{5}+\frac{7}{2}-\frac{6}{1}\\=\frac{6}{10}+\frac{35}{10}-\frac{60}{10}\\=\frac{6+35-60}{10}\\=\frac{-19}{10}\)
8. \(+\left(\frac{6}{5}\right) -\left(\frac{-8}{10}\right) +\left(\frac{-2}{2}\right)\\= \frac{6}{5}+ \frac{8}{10}-\frac{2}{2}\\=\frac{6}{5}+\frac{4}{5}-\frac{1}{1}\\=\frac{6+4-1}{5}\\=\frac{9}{5}\)
9. \(-\left(\frac{7}{6}\right) -\left(\frac{9}{9}\right) +\left(\frac{-7}{-7}\right)\\= \frac{-7}{6}- \frac{9}{9}+\frac{7}{7}\\=\frac{-7}{6}-\frac{1}{1}+\frac{1}{1}\\=\frac{-7-1+1}{6}\\=\frac{-7}{6}\)
10. \(+\left(\frac{-10}{-3}\right) -\left(\frac{10}{5}\right) -\left(\frac{5}{-11}\right)\\= \frac{10}{3}- \frac{10}{5}+\frac{5}{11}\\=\frac{10}{3}-\frac{2}{1}+\frac{5}{11}\\=\frac{110}{33}-\frac{66}{33}+\frac{15}{33}\\=\frac{110-66+15}{33}\\=\frac{59}{33}\)
11. \(-\left(\frac{7}{6}\right) -\left(\frac{5}{6}\right) -\left(\frac{6}{4}\right)\\= \frac{-7}{6}- \frac{5}{6}-\frac{6}{4}\\=\frac{-7}{6}-\frac{5}{6}-\frac{3}{2}\\=\frac{-7-5-3}{6}\\=\frac{-15}{6}\\=\frac{-5}{2}\)
12. \(+\left(\frac{-5}{-9}\right) -\left(\frac{-7}{-9}\right) -\left(\frac{-2}{-3}\right)\\= \frac{5}{9}- \frac{7}{9}-\frac{2}{3}\\=\frac{5-7-2}{9}\\=\frac{-4}{9}\)