Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{2}\right) -\left(\frac{-5}{9}\right) -\left(\frac{-9}{-4}\right)\\= \frac{3}{2}+ \frac{5}{9}-\frac{9}{4}\\=\frac{54}{36}+\frac{20}{36}-\frac{81}{36}\\=\frac{54+20-81}{36}\\=\frac{-7}{36}\)
2. \(-\left(\frac{-4}{-9}\right) -\left(\frac{7}{9}\right) +\left(\frac{2}{3}\right)\\= \frac{-4}{9}- \frac{7}{9}+\frac{2}{3}\\=\frac{-4-7+2}{9}\\=\frac{-9}{9}\\=\frac{-1}{1}\)
3. \(-\left(\frac{-7}{-8}\right) +\left(\frac{-9}{-2}\right) -\left(\frac{-5}{-10}\right)\\= \frac{-7}{8}+ \frac{9}{2}-\frac{5}{10}\\=\frac{-7}{8}+\frac{9}{2}-\frac{1}{2}\\=\frac{-7+9-1}{8}\\=\frac{1}{8}\)
4. \(-\left(\frac{4}{-7}\right) -\left(\frac{-3}{-9}\right) +\left(\frac{4}{4}\right)\\= \frac{4}{7}- \frac{3}{9}+\frac{4}{4}\\=\frac{4}{7}-\frac{1}{3}+\frac{1}{1}\\=\frac{12}{21}-\frac{7}{21}+\frac{21}{21}\\=\frac{12-7+21}{21}\\=\frac{26}{21}\)
5. \(-\left(\frac{-7}{-8}\right) -\left(\frac{2}{4}\right) +\left(\frac{-4}{-5}\right)\\= \frac{-7}{8}- \frac{2}{4}+\frac{4}{5}\\=\frac{-7}{8}-\frac{1}{2}+\frac{4}{5}\\=\frac{-35}{40}-\frac{20}{40}+\frac{32}{40}\\=\frac{-35-20+32}{40}\\=\frac{-23}{40}\)
6. \(-\left(\frac{-7}{6}\right) -\left(\frac{-8}{8}\right) -\left(\frac{-12}{7}\right)\\= \frac{7}{6}+ \frac{8}{8}+\frac{12}{7}\\=\frac{7}{6}+\frac{1}{1}+\frac{12}{7}\\=\frac{49}{42}+\frac{42}{42}+\frac{72}{42}\\=\frac{49+42+72}{42}\\=\frac{163}{42}\)
7. \(-\left(\frac{2}{9}\right) -\left(\frac{6}{2}\right) -\left(\frac{-4}{2}\right)\\= \frac{-2}{9}- \frac{6}{2}+\frac{4}{2}\\=\frac{-2}{9}-\frac{3}{1}+\frac{2}{1}\\=\frac{-2-3+2}{9}\\=\frac{-3}{9}\\=\frac{-1}{3}\)
8. \(-\left(\frac{7}{-8}\right) -\left(\frac{6}{-5}\right) -\left(\frac{2}{-8}\right)\\= \frac{7}{8}+ \frac{6}{5}+\frac{2}{8}\\=\frac{7}{8}+\frac{6}{5}+\frac{1}{4}\\=\frac{35}{40}+\frac{48}{40}+\frac{10}{40}\\=\frac{35+48+10}{40}\\=\frac{93}{40}\)
9. \(+\left(\frac{3}{-2}\right) -\left(\frac{9}{5}\right) -\left(\frac{12}{-5}\right)\\= \frac{-3}{2}- \frac{9}{5}+\frac{12}{5}\\=\frac{-15}{10}-\frac{18}{10}+\frac{24}{10}\\=\frac{-15-18+24}{10}\\=\frac{-9}{10}\)
10. \(+\left(\frac{10}{-7}\right) -\left(\frac{4}{7}\right) -\left(\frac{7}{4}\right)\\= \frac{-10}{7}- \frac{4}{7}-\frac{7}{4}\\=\frac{-40}{28}-\frac{16}{28}-\frac{49}{28}\\=\frac{-40-16-49}{28}\\=\frac{-105}{28}\\=\frac{-15}{4}\)
11. \(+\left(\frac{-5}{-3}\right) +\left(\frac{8}{-4}\right) +\left(\frac{7}{6}\right)\\= \frac{5}{3}- \frac{8}{4}+\frac{7}{6}\\=\frac{5}{3}-\frac{2}{1}+\frac{7}{6}\\=\frac{10}{6}-\frac{12}{6}+\frac{7}{6}\\=\frac{10-12+7}{6}\\=\frac{5}{6}\)
12. \(+\left(\frac{-7}{-8}\right) +\left(\frac{-9}{2}\right) +\left(\frac{-5}{-2}\right)\\= \frac{7}{8}- \frac{9}{2}+\frac{5}{2}\\=\frac{7-9+5}{8}\\=\frac{3}{8}\)