Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{4}{3}\right) +\left(\frac{10}{6}\right) -\left(\frac{-11}{9}\right)\\= \frac{4}{3}+ \frac{10}{6}+\frac{11}{9}\\=\frac{4}{3}+\frac{5}{3}+\frac{11}{9}\\=\frac{12}{9}+\frac{15}{9}+\frac{11}{9}\\=\frac{12+15+11}{9}\\=\frac{38}{9}\)
2. \(+\left(\frac{-8}{-3}\right) -\left(\frac{-9}{-10}\right) +\left(\frac{-11}{-3}\right)\\= \frac{8}{3}- \frac{9}{10}+\frac{11}{3}\\=\frac{80}{30}-\frac{27}{30}+\frac{110}{30}\\=\frac{80-27+110}{30}\\=\frac{163}{30}\)
3. \(-\left(\frac{-8}{-3}\right) -\left(\frac{8}{-3}\right) -\left(\frac{2}{4}\right)\\= \frac{-8}{3}+ \frac{8}{3}-\frac{2}{4}\\=\frac{-8}{3}+\frac{8}{3}-\frac{1}{2}\\=\frac{-16}{6}+\frac{16}{6}-\frac{3}{6}\\=\frac{-16+16-3}{6}\\=\frac{-3}{6}\\=\frac{-1}{2}\)
4. \(+\left(\frac{4}{-9}\right) -\left(\frac{-2}{-6}\right) -\left(\frac{4}{-10}\right)\\= \frac{-4}{9}- \frac{2}{6}+\frac{4}{10}\\=\frac{-4}{9}-\frac{1}{3}+\frac{2}{5}\\=\frac{-20}{45}-\frac{15}{45}+\frac{18}{45}\\=\frac{-20-15+18}{45}\\=\frac{-17}{45}\)
5. \(-\left(\frac{4}{5}\right) +\left(\frac{10}{7}\right) -\left(\frac{-7}{-6}\right)\\= \frac{-4}{5}+ \frac{10}{7}-\frac{7}{6}\\=\frac{-168}{210}+\frac{300}{210}-\frac{245}{210}\\=\frac{-168+300-245}{210}\\=\frac{-113}{210}\)
6. \(-\left(\frac{-3}{-2}\right) +\left(\frac{-7}{-2}\right) -\left(\frac{-11}{3}\right)\\= \frac{-3}{2}+ \frac{7}{2}+\frac{11}{3}\\=\frac{-9}{6}+\frac{21}{6}+\frac{22}{6}\\=\frac{-9+21+22}{6}\\=\frac{34}{6}\\=\frac{17}{3}\)
7. \(+\left(\frac{9}{-2}\right) +\left(\frac{-5}{4}\right) -\left(\frac{11}{-6}\right)\\= \frac{-9}{2}- \frac{5}{4}+\frac{11}{6}\\=\frac{-54}{12}-\frac{15}{12}+\frac{22}{12}\\=\frac{-54-15+22}{12}\\=\frac{-47}{12}\)
8. \(+\left(\frac{6}{-7}\right) -\left(\frac{-9}{7}\right) -\left(\frac{12}{7}\right)\\= \frac{-6}{7}+ \frac{9}{7}-\frac{12}{7}\\=\frac{-6+9-12}{7}\\=\frac{-9}{7}\)
9. \(-\left(\frac{-10}{3}\right) -\left(\frac{-2}{7}\right) -\left(\frac{6}{10}\right)\\= \frac{10}{3}+ \frac{2}{7}-\frac{6}{10}\\=\frac{10}{3}+\frac{2}{7}-\frac{3}{5}\\=\frac{350}{105}+\frac{30}{105}-\frac{63}{105}\\=\frac{350+30-63}{105}\\=\frac{317}{105}\)
10. \(+\left(\frac{-7}{-5}\right) -\left(\frac{2}{-7}\right) +\left(\frac{-12}{4}\right)\\= \frac{7}{5}+ \frac{2}{7}-\frac{12}{4}\\=\frac{7}{5}+\frac{2}{7}-\frac{3}{1}\\=\frac{49}{35}+\frac{10}{35}-\frac{105}{35}\\=\frac{49+10-105}{35}\\=\frac{-46}{35}\)
11. \(+\left(\frac{-2}{-3}\right) +\left(\frac{6}{-7}\right) -\left(\frac{6}{-9}\right)\\= \frac{2}{3}- \frac{6}{7}+\frac{6}{9}\\=\frac{2}{3}-\frac{6}{7}+\frac{2}{3}\\=\frac{14}{21}-\frac{18}{21}+\frac{14}{21}\\=\frac{14-18+14}{21}\\=\frac{10}{21}\)
12. \(+\left(\frac{8}{-7}\right) -\left(\frac{3}{-2}\right) +\left(\frac{4}{-12}\right)\\= \frac{-8}{7}+ \frac{3}{2}-\frac{4}{12}\\=\frac{-8}{7}+\frac{3}{2}-\frac{1}{3}\\=\frac{-48}{42}+\frac{63}{42}-\frac{14}{42}\\=\frac{-48+63-14}{42}\\=\frac{1}{42}\)