Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{4}{-7}\right) +\left(\frac{-9}{-6}\right) -\left(\frac{7}{-2}\right)\\= \frac{-4}{7}+ \frac{9}{6}+\frac{7}{2}\\=\frac{-4}{7}+\frac{3}{2}+\frac{7}{2}\\=\frac{-8}{14}+\frac{21}{14}+\frac{49}{14}\\=\frac{-8+21+49}{14}\\=\frac{62}{14}\\=\frac{31}{7}\)
2. \(-\left(\frac{9}{-4}\right) +\left(\frac{-9}{8}\right) -\left(\frac{10}{10}\right)\\= \frac{9}{4}- \frac{9}{8}-\frac{10}{10}\\=\frac{9}{4}-\frac{9}{8}-\frac{1}{1}\\=\frac{18}{8}-\frac{9}{8}-\frac{8}{8}\\=\frac{18-9-8}{8}\\=\frac{1}{8}\)
3. \(-\left(\frac{5}{3}\right) +\left(\frac{-5}{5}\right) -\left(\frac{-5}{7}\right)\\= \frac{-5}{3}- \frac{5}{5}+\frac{5}{7}\\=\frac{-5}{3}-\frac{1}{1}+\frac{5}{7}\\=\frac{-35}{21}-\frac{21}{21}+\frac{15}{21}\\=\frac{-35-21+15}{21}\\=\frac{-41}{21}\)
4. \(-\left(\frac{10}{3}\right) -\left(\frac{-9}{-7}\right) -\left(\frac{-5}{3}\right)\\= \frac{-10}{3}- \frac{9}{7}+\frac{5}{3}\\=\frac{-70}{21}-\frac{27}{21}+\frac{35}{21}\\=\frac{-70-27+35}{21}\\=\frac{-62}{21}\)
5. \(+\left(\frac{-2}{7}\right) -\left(\frac{-8}{-8}\right) -\left(\frac{5}{-11}\right)\\= \frac{-2}{7}- \frac{8}{8}+\frac{5}{11}\\=\frac{-2}{7}-\frac{1}{1}+\frac{5}{11}\\=\frac{-22}{77}-\frac{77}{77}+\frac{35}{77}\\=\frac{-22-77+35}{77}\\=\frac{-64}{77}\)
6. \(-\left(\frac{-2}{-5}\right) -\left(\frac{-5}{-8}\right) -\left(\frac{9}{-12}\right)\\= \frac{-2}{5}- \frac{5}{8}+\frac{9}{12}\\=\frac{-2}{5}-\frac{5}{8}+\frac{3}{4}\\=\frac{-16}{40}-\frac{25}{40}+\frac{30}{40}\\=\frac{-16-25+30}{40}\\=\frac{-11}{40}\)
7. \(+\left(\frac{-4}{-3}\right) +\left(\frac{9}{4}\right) +\left(\frac{-11}{-5}\right)\\= \frac{4}{3}+ \frac{9}{4}+\frac{11}{5}\\=\frac{80}{60}+\frac{135}{60}+\frac{132}{60}\\=\frac{80+135+132}{60}\\=\frac{347}{60}\)
8. \(+\left(\frac{-8}{-3}\right) -\left(\frac{3}{7}\right) -\left(\frac{7}{7}\right)\\= \frac{8}{3}- \frac{3}{7}-\frac{7}{7}\\=\frac{8}{3}-\frac{3}{7}-\frac{1}{1}\\=\frac{56}{21}-\frac{9}{21}-\frac{21}{21}\\=\frac{56-9-21}{21}\\=\frac{26}{21}\)
9. \(+\left(\frac{5}{-6}\right) +\left(\frac{8}{10}\right) +\left(\frac{10}{-10}\right)\\= \frac{-5}{6}+ \frac{8}{10}-\frac{10}{10}\\=\frac{-5}{6}+\frac{4}{5}-\frac{1}{1}\\=\frac{-25}{30}+\frac{24}{30}-\frac{30}{30}\\=\frac{-25+24-30}{30}\\=\frac{-31}{30}\)
10. \(+\left(\frac{8}{9}\right) +\left(\frac{-9}{-8}\right) +\left(\frac{-2}{-9}\right)\\= \frac{8}{9}+ \frac{9}{8}+\frac{2}{9}\\=\frac{64}{72}+\frac{81}{72}+\frac{16}{72}\\=\frac{64+81+16}{72}\\=\frac{161}{72}\)
11. \(+\left(\frac{8}{-9}\right) -\left(\frac{-9}{-7}\right) +\left(\frac{3}{3}\right)\\= \frac{-8}{9}- \frac{9}{7}+\frac{3}{3}\\=\frac{-8}{9}-\frac{9}{7}+\frac{1}{1}\\=\frac{-56}{63}-\frac{81}{63}+\frac{63}{63}\\=\frac{-56-81+63}{63}\\=\frac{-74}{63}\)
12. \(-\left(\frac{-3}{4}\right) +\left(\frac{4}{5}\right) -\left(\frac{4}{9}\right)\\= \frac{3}{4}+ \frac{4}{5}-\frac{4}{9}\\=\frac{135}{180}+\frac{144}{180}-\frac{80}{180}\\=\frac{135+144-80}{180}\\=\frac{199}{180}\)