Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{-9}\right) -\left(\frac{-7}{-8}\right) -\left(\frac{3}{-4}\right)\\= \frac{2}{9}- \frac{7}{8}+\frac{3}{4}\\=\frac{16}{72}-\frac{63}{72}+\frac{54}{72}\\=\frac{16-63+54}{72}\\=\frac{7}{72}\)
2. \(-\left(\frac{-2}{-3}\right) -\left(\frac{-10}{2}\right) +\left(\frac{12}{-12}\right)\\= \frac{-2}{3}+ \frac{10}{2}-\frac{12}{12}\\=\frac{-2}{3}+\frac{5}{1}-\frac{1}{1}\\=\frac{-2+5-1}{3}\\=\frac{2}{3}\)
3. \(+\left(\frac{2}{-9}\right) -\left(\frac{-9}{4}\right) +\left(\frac{-3}{-4}\right)\\= \frac{-2}{9}+ \frac{9}{4}+\frac{3}{4}\\=\frac{-8}{36}+\frac{81}{36}+\frac{27}{36}\\=\frac{-8+81+27}{36}\\=\frac{100}{36}\\=\frac{25}{9}\)
4. \(+\left(\frac{2}{3}\right) +\left(\frac{5}{9}\right) -\left(\frac{11}{4}\right)\\= \frac{2}{3}+ \frac{5}{9}-\frac{11}{4}\\=\frac{24}{36}+\frac{20}{36}-\frac{99}{36}\\=\frac{24+20-99}{36}\\=\frac{-55}{36}\)
5. \(+\left(\frac{-3}{4}\right) -\left(\frac{6}{-3}\right) -\left(\frac{-11}{-6}\right)\\= \frac{-3}{4}+ \frac{6}{3}-\frac{11}{6}\\=\frac{-3}{4}+\frac{2}{1}-\frac{11}{6}\\=\frac{-9}{12}+\frac{24}{12}-\frac{22}{12}\\=\frac{-9+24-22}{12}\\=\frac{-7}{12}\)
6. \(-\left(\frac{3}{-2}\right) -\left(\frac{7}{-5}\right) -\left(\frac{8}{-6}\right)\\= \frac{3}{2}+ \frac{7}{5}+\frac{8}{6}\\=\frac{3}{2}+\frac{7}{5}+\frac{4}{3}\\=\frac{45}{30}+\frac{42}{30}+\frac{40}{30}\\=\frac{45+42+40}{30}\\=\frac{127}{30}\)
7. \(+\left(\frac{-9}{4}\right) +\left(\frac{9}{7}\right) -\left(\frac{-5}{-2}\right)\\= \frac{-9}{4}+ \frac{9}{7}-\frac{5}{2}\\=\frac{-63}{28}+\frac{36}{28}-\frac{70}{28}\\=\frac{-63+36-70}{28}\\=\frac{-97}{28}\)
8. \(+\left(\frac{-8}{5}\right) -\left(\frac{-3}{7}\right) +\left(\frac{-11}{11}\right)\\= \frac{-8}{5}+ \frac{3}{7}-\frac{11}{11}\\=\frac{-8}{5}+\frac{3}{7}-\frac{1}{1}\\=\frac{-56}{35}+\frac{15}{35}-\frac{35}{35}\\=\frac{-56+15-35}{35}\\=\frac{-76}{35}\)
9. \(+\left(\frac{-3}{-8}\right) +\left(\frac{-10}{4}\right) +\left(\frac{5}{3}\right)\\= \frac{3}{8}- \frac{10}{4}+\frac{5}{3}\\=\frac{3}{8}-\frac{5}{2}+\frac{5}{3}\\=\frac{9}{24}-\frac{60}{24}+\frac{40}{24}\\=\frac{9-60+40}{24}\\=\frac{-11}{24}\)
10. \(+\left(\frac{8}{-5}\right) +\left(\frac{4}{-8}\right) +\left(\frac{7}{-6}\right)\\= \frac{-8}{5}- \frac{4}{8}-\frac{7}{6}\\=\frac{-8}{5}-\frac{1}{2}-\frac{7}{6}\\=\frac{-48}{30}-\frac{15}{30}-\frac{35}{30}\\=\frac{-48-15-35}{30}\\=\frac{-98}{30}\\=\frac{-49}{15}\)
11. \(+\left(\frac{-7}{-4}\right) +\left(\frac{8}{7}\right) +\left(\frac{-7}{-7}\right)\\= \frac{7}{4}+ \frac{8}{7}+\frac{7}{7}\\=\frac{7}{4}+\frac{8}{7}+\frac{1}{1}\\=\frac{49}{28}+\frac{32}{28}+\frac{28}{28}\\=\frac{49+32+28}{28}\\=\frac{109}{28}\)
12. \(+\left(\frac{7}{-3}\right) -\left(\frac{2}{10}\right) +\left(\frac{8}{7}\right)\\= \frac{-7}{3}- \frac{2}{10}+\frac{8}{7}\\=\frac{-7}{3}-\frac{1}{5}+\frac{8}{7}\\=\frac{-245}{105}-\frac{21}{105}+\frac{120}{105}\\=\frac{-245-21+120}{105}\\=\frac{-146}{105}\)