Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{2}\right) +\left(\frac{-5}{-3}\right) -\left(\frac{6}{-12}\right)\\= \frac{3}{2}+ \frac{5}{3}+\frac{6}{12}\\=\frac{3}{2}+\frac{5}{3}+\frac{1}{2}\\=\frac{9}{6}+\frac{10}{6}+\frac{3}{6}\\=\frac{9+10+3}{6}\\=\frac{22}{6}\\=\frac{11}{3}\)
2. \(-\left(\frac{3}{-2}\right) -\left(\frac{4}{-8}\right) -\left(\frac{-7}{-8}\right)\\= \frac{3}{2}+ \frac{4}{8}-\frac{7}{8}\\=\frac{3}{2}+\frac{1}{2}-\frac{7}{8}\\=\frac{12}{8}+\frac{4}{8}-\frac{7}{8}\\=\frac{12+4-7}{8}\\=\frac{9}{8}\)
3. \(-\left(\frac{10}{7}\right) +\left(\frac{-10}{3}\right) +\left(\frac{6}{-3}\right)\\= \frac{-10}{7}- \frac{10}{3}-\frac{6}{3}\\=\frac{-10}{7}-\frac{10}{3}-\frac{2}{1}\\=\frac{-30}{21}-\frac{70}{21}-\frac{42}{21}\\=\frac{-30-70-42}{21}\\=\frac{-142}{21}\)
4. \(+\left(\frac{-10}{7}\right) -\left(\frac{-10}{7}\right) -\left(\frac{-7}{8}\right)\\= \frac{-10}{7}+ \frac{10}{7}+\frac{7}{8}\\=\frac{-80}{56}+\frac{80}{56}+\frac{49}{56}\\=\frac{-80+80+49}{56}\\=\frac{49}{56}\\=\frac{7}{8}\)
5. \(-\left(\frac{-3}{-7}\right) +\left(\frac{6}{4}\right) -\left(\frac{-2}{8}\right)\\= \frac{-3}{7}+ \frac{6}{4}+\frac{2}{8}\\=\frac{-3}{7}+\frac{3}{2}+\frac{1}{4}\\=\frac{-12}{28}+\frac{42}{28}+\frac{7}{28}\\=\frac{-12+42+7}{28}\\=\frac{37}{28}\)
6. \(+\left(\frac{6}{7}\right) -\left(\frac{-6}{-10}\right) +\left(\frac{-10}{-10}\right)\\= \frac{6}{7}- \frac{6}{10}+\frac{10}{10}\\=\frac{6}{7}-\frac{3}{5}+\frac{1}{1}\\=\frac{30}{35}-\frac{21}{35}+\frac{35}{35}\\=\frac{30-21+35}{35}\\=\frac{44}{35}\)
7. \(+\left(\frac{7}{4}\right) -\left(\frac{-6}{8}\right) +\left(\frac{11}{-3}\right)\\= \frac{7}{4}+ \frac{6}{8}-\frac{11}{3}\\=\frac{7}{4}+\frac{3}{4}-\frac{11}{3}\\=\frac{21}{12}+\frac{9}{12}-\frac{44}{12}\\=\frac{21+9-44}{12}\\=\frac{-14}{12}\\=\frac{-7}{6}\)
8. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-6}{-4}\right) -\left(\frac{12}{-5}\right)\\= \frac{-6}{5}- \frac{6}{4}+\frac{12}{5}\\=\frac{-6}{5}-\frac{3}{2}+\frac{12}{5}\\=\frac{-12}{10}-\frac{15}{10}+\frac{24}{10}\\=\frac{-12-15+24}{10}\\=\frac{-3}{10}\)
9. \(+\left(\frac{3}{2}\right) -\left(\frac{-10}{4}\right) -\left(\frac{-12}{12}\right)\\= \frac{3}{2}+ \frac{10}{4}+\frac{12}{12}\\=\frac{3}{2}+\frac{5}{2}+\frac{1}{1}\\=\frac{3+5+1}{2}\\=\frac{9}{2}\)
10. \(+\left(\frac{5}{2}\right) +\left(\frac{2}{-9}\right) +\left(\frac{3}{-5}\right)\\= \frac{5}{2}- \frac{2}{9}-\frac{3}{5}\\=\frac{225}{90}-\frac{20}{90}-\frac{54}{90}\\=\frac{225-20-54}{90}\\=\frac{151}{90}\)
11. \(+\left(\frac{4}{-3}\right) +\left(\frac{-2}{10}\right) -\left(\frac{-4}{2}\right)\\= \frac{-4}{3}- \frac{2}{10}+\frac{4}{2}\\=\frac{-4}{3}-\frac{1}{5}+\frac{2}{1}\\=\frac{-20}{15}-\frac{3}{15}+\frac{30}{15}\\=\frac{-20-3+30}{15}\\=\frac{7}{15}\)
12. \(+\left(\frac{6}{-5}\right) -\left(\frac{10}{9}\right) +\left(\frac{-10}{6}\right)\\= \frac{-6}{5}- \frac{10}{9}-\frac{10}{6}\\=\frac{-6}{5}-\frac{10}{9}-\frac{5}{3}\\=\frac{-54}{45}-\frac{50}{45}-\frac{75}{45}\\=\frac{-54-50-75}{45}\\=\frac{-179}{45}\)