Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{5}\right) +\left(\frac{6}{10}\right) +\left(\frac{-8}{5}\right)\\= \frac{6}{5}+ \frac{6}{10}-\frac{8}{5}\\=\frac{6}{5}+\frac{3}{5}-\frac{8}{5}\\=\frac{6+3-8}{5}\\=\frac{1}{5}\)
2. \(-\left(\frac{-9}{-7}\right) -\left(\frac{-6}{9}\right) -\left(\frac{-5}{6}\right)\\= \frac{-9}{7}+ \frac{6}{9}+\frac{5}{6}\\=\frac{-9}{7}+\frac{2}{3}+\frac{5}{6}\\=\frac{-54}{42}+\frac{28}{42}+\frac{35}{42}\\=\frac{-54+28+35}{42}\\=\frac{9}{42}\\=\frac{3}{14}\)
3. \(+\left(\frac{9}{-5}\right) -\left(\frac{2}{7}\right) -\left(\frac{-7}{-10}\right)\\= \frac{-9}{5}- \frac{2}{7}-\frac{7}{10}\\=\frac{-126}{70}-\frac{20}{70}-\frac{49}{70}\\=\frac{-126-20-49}{70}\\=\frac{-195}{70}\\=\frac{-39}{14}\)
4. \(+\left(\frac{10}{-9}\right) +\left(\frac{5}{5}\right) -\left(\frac{-7}{-7}\right)\\= \frac{-10}{9}+ \frac{5}{5}-\frac{7}{7}\\=\frac{-10}{9}+\frac{1}{1}-\frac{1}{1}\\=\frac{-10+1-1}{9}\\=\frac{-10}{9}\)
5. \(+\left(\frac{-4}{3}\right) -\left(\frac{-8}{6}\right) +\left(\frac{-5}{-6}\right)\\= \frac{-4}{3}+ \frac{8}{6}+\frac{5}{6}\\=\frac{-4}{3}+\frac{4}{3}+\frac{5}{6}\\=\frac{-8}{6}+\frac{8}{6}+\frac{5}{6}\\=\frac{-8+8+5}{6}\\=\frac{5}{6}\)
6. \(+\left(\frac{-2}{-5}\right) -\left(\frac{-5}{10}\right) +\left(\frac{-3}{10}\right)\\= \frac{2}{5}+ \frac{5}{10}-\frac{3}{10}\\=\frac{2}{5}+\frac{1}{2}-\frac{3}{10}\\=\frac{4}{10}+\frac{5}{10}-\frac{3}{10}\\=\frac{4+5-3}{10}\\=\frac{6}{10}\\=\frac{3}{5}\)
7. \(-\left(\frac{8}{-5}\right) -\left(\frac{8}{6}\right) +\left(\frac{12}{3}\right)\\= \frac{8}{5}- \frac{8}{6}+\frac{12}{3}\\=\frac{8}{5}-\frac{4}{3}+\frac{4}{1}\\=\frac{24}{15}-\frac{20}{15}+\frac{60}{15}\\=\frac{24-20+60}{15}\\=\frac{64}{15}\)
8. \(-\left(\frac{4}{-9}\right) -\left(\frac{7}{-7}\right) +\left(\frac{9}{-7}\right)\\= \frac{4}{9}+ \frac{7}{7}-\frac{9}{7}\\=\frac{4}{9}+\frac{1}{1}-\frac{9}{7}\\=\frac{28}{63}+\frac{63}{63}-\frac{81}{63}\\=\frac{28+63-81}{63}\\=\frac{10}{63}\)
9. \(+\left(\frac{-2}{7}\right) -\left(\frac{-9}{-3}\right) -\left(\frac{11}{7}\right)\\= \frac{-2}{7}- \frac{9}{3}-\frac{11}{7}\\=\frac{-2}{7}-\frac{3}{1}-\frac{11}{7}\\=\frac{-2-3-11}{7}\\=\frac{-16}{7}\)
10. \(-\left(\frac{-3}{4}\right) +\left(\frac{-7}{10}\right) +\left(\frac{2}{8}\right)\\= \frac{3}{4}- \frac{7}{10}+\frac{2}{8}\\=\frac{3}{4}-\frac{7}{10}+\frac{1}{4}\\=\frac{15}{20}-\frac{14}{20}+\frac{5}{20}\\=\frac{15-14+5}{20}\\=\frac{6}{20}\\=\frac{3}{10}\)
11. \(+\left(\frac{-3}{-4}\right) -\left(\frac{-2}{-9}\right) +\left(\frac{10}{-4}\right)\\= \frac{3}{4}- \frac{2}{9}-\frac{10}{4}\\=\frac{3}{4}-\frac{2}{9}-\frac{5}{2}\\=\frac{27}{36}-\frac{8}{36}-\frac{90}{36}\\=\frac{27-8-90}{36}\\=\frac{-71}{36}\)
12. \(+\left(\frac{7}{-9}\right) +\left(\frac{7}{-10}\right) +\left(\frac{2}{4}\right)\\= \frac{-7}{9}- \frac{7}{10}+\frac{2}{4}\\=\frac{-7}{9}-\frac{7}{10}+\frac{1}{2}\\=\frac{-70}{90}-\frac{63}{90}+\frac{45}{90}\\=\frac{-70-63+45}{90}\\=\frac{-88}{90}\\=\frac{-44}{45}\)