Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-4}{3}\right) +\left(\frac{-5}{-3}\right) +\left(\frac{7}{6}\right)\\= \frac{-4}{3}+ \frac{5}{3}+\frac{7}{6}\\=\frac{-8}{6}+\frac{10}{6}+\frac{7}{6}\\=\frac{-8+10+7}{6}\\=\frac{9}{6}\\=\frac{3}{2}\)
2. \(+\left(\frac{-2}{-9}\right) -\left(\frac{-6}{3}\right) -\left(\frac{-12}{10}\right)\\= \frac{2}{9}+ \frac{6}{3}+\frac{12}{10}\\=\frac{2}{9}+\frac{2}{1}+\frac{6}{5}\\=\frac{10}{45}+\frac{90}{45}+\frac{54}{45}\\=\frac{10+90+54}{45}\\=\frac{154}{45}\)
3. \(+\left(\frac{7}{8}\right) -\left(\frac{6}{2}\right) +\left(\frac{3}{2}\right)\\= \frac{7}{8}- \frac{6}{2}+\frac{3}{2}\\=\frac{7}{8}-\frac{3}{1}+\frac{3}{2}\\=\frac{7-3+3}{8}\\=\frac{7}{8}\)
4. \(+\left(\frac{-9}{8}\right) -\left(\frac{-4}{3}\right) -\left(\frac{-2}{-12}\right)\\= \frac{-9}{8}+ \frac{4}{3}-\frac{2}{12}\\=\frac{-9}{8}+\frac{4}{3}-\frac{1}{6}\\=\frac{-27}{24}+\frac{32}{24}-\frac{4}{24}\\=\frac{-27+32-4}{24}\\=\frac{1}{24}\)
5. \(-\left(\frac{-9}{4}\right) -\left(\frac{-9}{-10}\right) +\left(\frac{-4}{-12}\right)\\= \frac{9}{4}- \frac{9}{10}+\frac{4}{12}\\=\frac{9}{4}-\frac{9}{10}+\frac{1}{3}\\=\frac{135}{60}-\frac{54}{60}+\frac{20}{60}\\=\frac{135-54+20}{60}\\=\frac{101}{60}\)
6. \(+\left(\frac{-5}{-2}\right) -\left(\frac{8}{7}\right) -\left(\frac{-12}{-9}\right)\\= \frac{5}{2}- \frac{8}{7}-\frac{12}{9}\\=\frac{5}{2}-\frac{8}{7}-\frac{4}{3}\\=\frac{105}{42}-\frac{48}{42}-\frac{56}{42}\\=\frac{105-48-56}{42}\\=\frac{1}{42}\)
7. \(-\left(\frac{-2}{-5}\right) +\left(\frac{3}{-7}\right) -\left(\frac{10}{11}\right)\\= \frac{-2}{5}- \frac{3}{7}-\frac{10}{11}\\=\frac{-154}{385}-\frac{165}{385}-\frac{350}{385}\\=\frac{-154-165-350}{385}\\=\frac{-669}{385}\)
8. \(-\left(\frac{-6}{5}\right) +\left(\frac{2}{6}\right) -\left(\frac{9}{-7}\right)\\= \frac{6}{5}+ \frac{2}{6}+\frac{9}{7}\\=\frac{6}{5}+\frac{1}{3}+\frac{9}{7}\\=\frac{126}{105}+\frac{35}{105}+\frac{135}{105}\\=\frac{126+35+135}{105}\\=\frac{296}{105}\)
9. \(-\left(\frac{-10}{-3}\right) +\left(\frac{-2}{-8}\right) +\left(\frac{-6}{6}\right)\\= \frac{-10}{3}+ \frac{2}{8}-\frac{6}{6}\\=\frac{-10}{3}+\frac{1}{4}-\frac{1}{1}\\=\frac{-40}{12}+\frac{3}{12}-\frac{12}{12}\\=\frac{-40+3-12}{12}\\=\frac{-49}{12}\)
10. \(+\left(\frac{2}{-3}\right) +\left(\frac{5}{8}\right) +\left(\frac{12}{-3}\right)\\= \frac{-2}{3}+ \frac{5}{8}-\frac{12}{3}\\=\frac{-2}{3}+\frac{5}{8}-\frac{4}{1}\\=\frac{-16}{24}+\frac{15}{24}-\frac{96}{24}\\=\frac{-16+15-96}{24}\\=\frac{-97}{24}\)
11. \(-\left(\frac{2}{5}\right) -\left(\frac{-4}{-10}\right) +\left(\frac{-4}{8}\right)\\= \frac{-2}{5}- \frac{4}{10}-\frac{4}{8}\\=\frac{-2}{5}-\frac{2}{5}-\frac{1}{2}\\=\frac{-4}{10}-\frac{4}{10}-\frac{5}{10}\\=\frac{-4-4-5}{10}\\=\frac{-13}{10}\)
12. \(-\left(\frac{-7}{2}\right) +\left(\frac{4}{-9}\right) +\left(\frac{-10}{4}\right)\\= \frac{7}{2}- \frac{4}{9}-\frac{10}{4}\\=\frac{7}{2}-\frac{4}{9}-\frac{5}{2}\\=\frac{63}{18}-\frac{8}{18}-\frac{45}{18}\\=\frac{63-8-45}{18}\\=\frac{10}{18}\\=\frac{5}{9}\)