Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{2}\right) -\left(\frac{5}{3}\right) -\left(\frac{-4}{-4}\right)\\= \frac{3}{2}- \frac{5}{3}-\frac{4}{4}\\=\frac{3}{2}-\frac{5}{3}-\frac{1}{1}\\=\frac{9}{6}-\frac{10}{6}-\frac{6}{6}\\=\frac{9-10-6}{6}\\=\frac{-7}{6}\)
2. \(+\left(\frac{9}{8}\right) -\left(\frac{-9}{10}\right) +\left(\frac{3}{-6}\right)\\= \frac{9}{8}+ \frac{9}{10}-\frac{3}{6}\\=\frac{9}{8}+\frac{9}{10}-\frac{1}{2}\\=\frac{45}{40}+\frac{36}{40}-\frac{20}{40}\\=\frac{45+36-20}{40}\\=\frac{61}{40}\)
3. \(+\left(\frac{5}{-8}\right) -\left(\frac{-3}{-7}\right) +\left(\frac{8}{6}\right)\\= \frac{-5}{8}- \frac{3}{7}+\frac{8}{6}\\=\frac{-5}{8}-\frac{3}{7}+\frac{4}{3}\\=\frac{-105}{168}-\frac{72}{168}+\frac{224}{168}\\=\frac{-105-72+224}{168}\\=\frac{47}{168}\)
4. \(+\left(\frac{-5}{-4}\right) -\left(\frac{9}{9}\right) -\left(\frac{-4}{-7}\right)\\= \frac{5}{4}- \frac{9}{9}-\frac{4}{7}\\=\frac{5}{4}-\frac{1}{1}-\frac{4}{7}\\=\frac{35}{28}-\frac{28}{28}-\frac{16}{28}\\=\frac{35-28-16}{28}\\=\frac{-9}{28}\)
5. \(-\left(\frac{-2}{-7}\right) +\left(\frac{-3}{-8}\right) -\left(\frac{4}{5}\right)\\= \frac{-2}{7}+ \frac{3}{8}-\frac{4}{5}\\=\frac{-80}{280}+\frac{105}{280}-\frac{224}{280}\\=\frac{-80+105-224}{280}\\=\frac{-199}{280}\)
6. \(-\left(\frac{-9}{-8}\right) +\left(\frac{2}{8}\right) +\left(\frac{4}{6}\right)\\= \frac{-9}{8}+ \frac{2}{8}+\frac{4}{6}\\=\frac{-9}{8}+\frac{1}{4}+\frac{2}{3}\\=\frac{-27}{24}+\frac{6}{24}+\frac{16}{24}\\=\frac{-27+6+16}{24}\\=\frac{-5}{24}\)
7. \(+\left(\frac{4}{-5}\right) -\left(\frac{10}{4}\right) +\left(\frac{7}{9}\right)\\= \frac{-4}{5}- \frac{10}{4}+\frac{7}{9}\\=\frac{-4}{5}-\frac{5}{2}+\frac{7}{9}\\=\frac{-72}{90}-\frac{225}{90}+\frac{70}{90}\\=\frac{-72-225+70}{90}\\=\frac{-227}{90}\)
8. \(-\left(\frac{7}{-4}\right) -\left(\frac{5}{-6}\right) +\left(\frac{8}{-8}\right)\\= \frac{7}{4}+ \frac{5}{6}-\frac{8}{8}\\=\frac{7}{4}+\frac{5}{6}-\frac{1}{1}\\=\frac{21}{12}+\frac{10}{12}-\frac{12}{12}\\=\frac{21+10-12}{12}\\=\frac{19}{12}\)
9. \(-\left(\frac{-4}{3}\right) -\left(\frac{-6}{-5}\right) -\left(\frac{6}{8}\right)\\= \frac{4}{3}- \frac{6}{5}-\frac{6}{8}\\=\frac{4}{3}-\frac{6}{5}-\frac{3}{4}\\=\frac{80}{60}-\frac{72}{60}-\frac{45}{60}\\=\frac{80-72-45}{60}\\=\frac{-37}{60}\)
10. \(-\left(\frac{9}{-2}\right) +\left(\frac{7}{-10}\right) -\left(\frac{-2}{9}\right)\\= \frac{9}{2}- \frac{7}{10}+\frac{2}{9}\\=\frac{405}{90}-\frac{63}{90}+\frac{20}{90}\\=\frac{405-63+20}{90}\\=\frac{362}{90}\\=\frac{181}{45}\)
11. \(-\left(\frac{4}{3}\right) +\left(\frac{9}{-10}\right) -\left(\frac{2}{-11}\right)\\= \frac{-4}{3}- \frac{9}{10}+\frac{2}{11}\\=\frac{-440}{330}-\frac{297}{330}+\frac{60}{330}\\=\frac{-440-297+60}{330}\\=\frac{-677}{330}\)
12. \(-\left(\frac{8}{-9}\right) +\left(\frac{2}{-6}\right) +\left(\frac{2}{12}\right)\\= \frac{8}{9}- \frac{2}{6}+\frac{2}{12}\\=\frac{8}{9}-\frac{1}{3}+\frac{1}{6}\\=\frac{16}{18}-\frac{6}{18}+\frac{3}{18}\\=\frac{16-6+3}{18}\\=\frac{13}{18}\)