Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-4}{-7}\right) +\left(\frac{2}{10}\right) -\left(\frac{-4}{-12}\right)\\= \frac{4}{7}+ \frac{2}{10}-\frac{4}{12}\\=\frac{4}{7}+\frac{1}{5}-\frac{1}{3}\\=\frac{60}{105}+\frac{21}{105}-\frac{35}{105}\\=\frac{60+21-35}{105}\\=\frac{46}{105}\)
2. \(+\left(\frac{7}{8}\right) +\left(\frac{-10}{5}\right) +\left(\frac{5}{-12}\right)\\= \frac{7}{8}- \frac{10}{5}-\frac{5}{12}\\=\frac{7}{8}-\frac{2}{1}-\frac{5}{12}\\=\frac{21}{24}-\frac{48}{24}-\frac{10}{24}\\=\frac{21-48-10}{24}\\=\frac{-37}{24}\)
3. \(+\left(\frac{-8}{9}\right) -\left(\frac{8}{-8}\right) +\left(\frac{-12}{9}\right)\\= \frac{-8}{9}+ \frac{8}{8}-\frac{12}{9}\\=\frac{-8}{9}+\frac{1}{1}-\frac{4}{3}\\=\frac{-8+1-4}{9}\\=\frac{-11}{9}\)
4. \(-\left(\frac{6}{-7}\right) +\left(\frac{-8}{7}\right) -\left(\frac{6}{-10}\right)\\= \frac{6}{7}- \frac{8}{7}+\frac{6}{10}\\=\frac{6}{7}-\frac{8}{7}+\frac{3}{5}\\=\frac{30}{35}-\frac{40}{35}+\frac{21}{35}\\=\frac{30-40+21}{35}\\=\frac{11}{35}\)
5. \(+\left(\frac{-2}{3}\right) +\left(\frac{-7}{-4}\right) +\left(\frac{-7}{-3}\right)\\= \frac{-2}{3}+ \frac{7}{4}+\frac{7}{3}\\=\frac{-8}{12}+\frac{21}{12}+\frac{28}{12}\\=\frac{-8+21+28}{12}\\=\frac{41}{12}\)
6. \(+\left(\frac{3}{4}\right) +\left(\frac{-9}{5}\right) -\left(\frac{9}{4}\right)\\= \frac{3}{4}- \frac{9}{5}-\frac{9}{4}\\=\frac{15}{20}-\frac{36}{20}-\frac{45}{20}\\=\frac{15-36-45}{20}\\=\frac{-66}{20}\\=\frac{-33}{10}\)
7. \(-\left(\frac{-9}{2}\right) -\left(\frac{-6}{4}\right) -\left(\frac{6}{-8}\right)\\= \frac{9}{2}+ \frac{6}{4}+\frac{6}{8}\\=\frac{9}{2}+\frac{3}{2}+\frac{3}{4}\\=\frac{18}{4}+\frac{6}{4}+\frac{3}{4}\\=\frac{18+6+3}{4}\\=\frac{27}{4}\)
8. \(-\left(\frac{4}{-5}\right) -\left(\frac{-7}{9}\right) -\left(\frac{11}{2}\right)\\= \frac{4}{5}+ \frac{7}{9}-\frac{11}{2}\\=\frac{72}{90}+\frac{70}{90}-\frac{495}{90}\\=\frac{72+70-495}{90}\\=\frac{-353}{90}\)
9. \(+\left(\frac{9}{-2}\right) -\left(\frac{3}{10}\right) +\left(\frac{-9}{5}\right)\\= \frac{-9}{2}- \frac{3}{10}-\frac{9}{5}\\=\frac{-45}{10}-\frac{3}{10}-\frac{18}{10}\\=\frac{-45-3-18}{10}\\=\frac{-66}{10}\\=\frac{-33}{5}\)
10. \(+\left(\frac{-2}{9}\right) -\left(\frac{7}{-9}\right) -\left(\frac{7}{-4}\right)\\= \frac{-2}{9}+ \frac{7}{9}+\frac{7}{4}\\=\frac{-8}{36}+\frac{28}{36}+\frac{63}{36}\\=\frac{-8+28+63}{36}\\=\frac{83}{36}\)
11. \(+\left(\frac{-2}{9}\right) -\left(\frac{8}{7}\right) +\left(\frac{6}{-2}\right)\\= \frac{-2}{9}- \frac{8}{7}-\frac{6}{2}\\=\frac{-2}{9}-\frac{8}{7}-\frac{3}{1}\\=\frac{-14}{63}-\frac{72}{63}-\frac{189}{63}\\=\frac{-14-72-189}{63}\\=\frac{-275}{63}\)
12. \(+\left(\frac{-5}{-4}\right) +\left(\frac{-5}{-3}\right) -\left(\frac{8}{12}\right)\\= \frac{5}{4}+ \frac{5}{3}-\frac{8}{12}\\=\frac{5}{4}+\frac{5}{3}-\frac{2}{3}\\=\frac{15}{12}+\frac{20}{12}-\frac{8}{12}\\=\frac{15+20-8}{12}\\=\frac{27}{12}\\=\frac{9}{4}\)