Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{-4}\right) -\left(\frac{8}{4}\right) +\left(\frac{6}{9}\right)\\= \frac{-9}{4}- \frac{8}{4}+\frac{6}{9}\\=\frac{-9}{4}-\frac{2}{1}+\frac{2}{3}\\=\frac{-27}{12}-\frac{24}{12}+\frac{8}{12}\\=\frac{-27-24+8}{12}\\=\frac{-43}{12}\)
2. \(+\left(\frac{-8}{-3}\right) +\left(\frac{7}{-3}\right) +\left(\frac{-5}{-2}\right)\\= \frac{8}{3}- \frac{7}{3}+\frac{5}{2}\\=\frac{16}{6}-\frac{14}{6}+\frac{15}{6}\\=\frac{16-14+15}{6}\\=\frac{17}{6}\)
3. \(-\left(\frac{-10}{7}\right) -\left(\frac{-2}{-6}\right) +\left(\frac{4}{-7}\right)\\= \frac{10}{7}- \frac{2}{6}-\frac{4}{7}\\=\frac{10}{7}-\frac{1}{3}-\frac{4}{7}\\=\frac{30}{21}-\frac{7}{21}-\frac{12}{21}\\=\frac{30-7-12}{21}\\=\frac{11}{21}\)
4. \(+\left(\frac{7}{6}\right) -\left(\frac{10}{-3}\right) -\left(\frac{2}{-5}\right)\\= \frac{7}{6}+ \frac{10}{3}+\frac{2}{5}\\=\frac{35}{30}+\frac{100}{30}+\frac{12}{30}\\=\frac{35+100+12}{30}\\=\frac{147}{30}\\=\frac{49}{10}\)
5. \(-\left(\frac{-3}{-8}\right) +\left(\frac{-9}{-2}\right) -\left(\frac{9}{7}\right)\\= \frac{-3}{8}+ \frac{9}{2}-\frac{9}{7}\\=\frac{-21}{56}+\frac{252}{56}-\frac{72}{56}\\=\frac{-21+252-72}{56}\\=\frac{159}{56}\)
6. \(+\left(\frac{-2}{-9}\right) +\left(\frac{10}{2}\right) +\left(\frac{-2}{-5}\right)\\= \frac{2}{9}+ \frac{10}{2}+\frac{2}{5}\\=\frac{2}{9}+\frac{5}{1}+\frac{2}{5}\\=\frac{10}{45}+\frac{225}{45}+\frac{18}{45}\\=\frac{10+225+18}{45}\\=\frac{253}{45}\)
7. \(+\left(\frac{-8}{-7}\right) -\left(\frac{-8}{-7}\right) +\left(\frac{2}{-6}\right)\\= \frac{8}{7}- \frac{8}{7}-\frac{2}{6}\\=\frac{8}{7}-\frac{8}{7}-\frac{1}{3}\\=\frac{24}{21}-\frac{24}{21}-\frac{7}{21}\\=\frac{24-24-7}{21}\\=\frac{-7}{21}\\=\frac{-1}{3}\)
8. \(+\left(\frac{-4}{9}\right) +\left(\frac{-9}{-10}\right) +\left(\frac{11}{9}\right)\\= \frac{-4}{9}+ \frac{9}{10}+\frac{11}{9}\\=\frac{-40}{90}+\frac{81}{90}+\frac{110}{90}\\=\frac{-40+81+110}{90}\\=\frac{151}{90}\)
9. \(-\left(\frac{8}{-5}\right) +\left(\frac{6}{9}\right) +\left(\frac{5}{-7}\right)\\= \frac{8}{5}+ \frac{6}{9}-\frac{5}{7}\\=\frac{8}{5}+\frac{2}{3}-\frac{5}{7}\\=\frac{168}{105}+\frac{70}{105}-\frac{75}{105}\\=\frac{168+70-75}{105}\\=\frac{163}{105}\)
10. \(-\left(\frac{10}{3}\right) +\left(\frac{10}{3}\right) -\left(\frac{12}{-11}\right)\\= \frac{-10}{3}+ \frac{10}{3}+\frac{12}{11}\\=\frac{-110}{33}+\frac{110}{33}+\frac{36}{33}\\=\frac{-110+110+36}{33}\\=\frac{36}{33}\\=\frac{12}{11}\)
11. \(+\left(\frac{-3}{-2}\right) +\left(\frac{7}{-8}\right) -\left(\frac{9}{6}\right)\\= \frac{3}{2}- \frac{7}{8}-\frac{9}{6}\\=\frac{3}{2}-\frac{7}{8}-\frac{3}{2}\\=\frac{12}{8}-\frac{7}{8}-\frac{12}{8}\\=\frac{12-7-12}{8}\\=\frac{-7}{8}\)
12. \(-\left(\frac{6}{-5}\right) +\left(\frac{7}{4}\right) -\left(\frac{12}{5}\right)\\= \frac{6}{5}+ \frac{7}{4}-\frac{12}{5}\\=\frac{24}{20}+\frac{35}{20}-\frac{48}{20}\\=\frac{24+35-48}{20}\\=\frac{11}{20}\)