Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{-7}\right) -\left(\frac{5}{-10}\right) +\left(\frac{-3}{-6}\right)\\= \frac{9}{7}+ \frac{5}{10}+\frac{3}{6}\\=\frac{9}{7}+\frac{1}{2}+\frac{1}{2}\\=\frac{18}{14}+\frac{7}{14}+\frac{7}{14}\\=\frac{18+7+7}{14}\\=\frac{32}{14}\\=\frac{16}{7}\)
2. \(-\left(\frac{2}{3}\right) +\left(\frac{-4}{10}\right) +\left(\frac{3}{-3}\right)\\= \frac{-2}{3}- \frac{4}{10}-\frac{3}{3}\\=\frac{-2}{3}-\frac{2}{5}-\frac{1}{1}\\=\frac{-10}{15}-\frac{6}{15}-\frac{15}{15}\\=\frac{-10-6-15}{15}\\=\frac{-31}{15}\)
3. \(+\left(\frac{-9}{-2}\right) +\left(\frac{2}{-5}\right) -\left(\frac{-10}{-8}\right)\\= \frac{9}{2}- \frac{2}{5}-\frac{10}{8}\\=\frac{9}{2}-\frac{2}{5}-\frac{5}{4}\\=\frac{90}{20}-\frac{8}{20}-\frac{25}{20}\\=\frac{90-8-25}{20}\\=\frac{57}{20}\)
4. \(-\left(\frac{8}{-9}\right) -\left(\frac{7}{2}\right) -\left(\frac{6}{3}\right)\\= \frac{8}{9}- \frac{7}{2}-\frac{6}{3}\\=\frac{8}{9}-\frac{7}{2}-\frac{2}{1}\\=\frac{16}{18}-\frac{63}{18}-\frac{36}{18}\\=\frac{16-63-36}{18}\\=\frac{-83}{18}\)
5. \(+\left(\frac{2}{5}\right) -\left(\frac{-6}{9}\right) -\left(\frac{2}{6}\right)\\= \frac{2}{5}+ \frac{6}{9}-\frac{2}{6}\\=\frac{2}{5}+\frac{2}{3}-\frac{1}{3}\\=\frac{6}{15}+\frac{10}{15}-\frac{5}{15}\\=\frac{6+10-5}{15}\\=\frac{11}{15}\)
6. \(+\left(\frac{-7}{2}\right) +\left(\frac{-6}{-8}\right) -\left(\frac{-7}{-4}\right)\\= \frac{-7}{2}+ \frac{6}{8}-\frac{7}{4}\\=\frac{-7}{2}+\frac{3}{4}-\frac{7}{4}\\=\frac{-14}{4}+\frac{3}{4}-\frac{7}{4}\\=\frac{-14+3-7}{4}\\=\frac{-18}{4}\\=\frac{-9}{2}\)
7. \(+\left(\frac{-5}{8}\right) -\left(\frac{7}{-7}\right) +\left(\frac{6}{-6}\right)\\= \frac{-5}{8}+ \frac{7}{7}-\frac{6}{6}\\=\frac{-5}{8}+\frac{1}{1}-\frac{1}{1}\\=\frac{-5+1-1}{8}\\=\frac{-5}{8}\)
8. \(-\left(\frac{-5}{3}\right) -\left(\frac{-4}{-9}\right) +\left(\frac{-10}{2}\right)\\= \frac{5}{3}- \frac{4}{9}-\frac{10}{2}\\=\frac{5}{3}-\frac{4}{9}-\frac{5}{1}\\=\frac{15}{9}-\frac{4}{9}-\frac{45}{9}\\=\frac{15-4-45}{9}\\=\frac{-34}{9}\)
9. \(+\left(\frac{-6}{5}\right) +\left(\frac{-7}{8}\right) +\left(\frac{-11}{-3}\right)\\= \frac{-6}{5}- \frac{7}{8}+\frac{11}{3}\\=\frac{-144}{120}-\frac{105}{120}+\frac{440}{120}\\=\frac{-144-105+440}{120}\\=\frac{191}{120}\)
10. \(+\left(\frac{-7}{-6}\right) +\left(\frac{-10}{3}\right) -\left(\frac{-10}{-7}\right)\\= \frac{7}{6}- \frac{10}{3}-\frac{10}{7}\\=\frac{49}{42}-\frac{140}{42}-\frac{60}{42}\\=\frac{49-140-60}{42}\\=\frac{-151}{42}\)
11. \(-\left(\frac{3}{-2}\right) -\left(\frac{5}{7}\right) -\left(\frac{-7}{10}\right)\\= \frac{3}{2}- \frac{5}{7}+\frac{7}{10}\\=\frac{105}{70}-\frac{50}{70}+\frac{49}{70}\\=\frac{105-50+49}{70}\\=\frac{104}{70}\\=\frac{52}{35}\)
12. \(+\left(\frac{8}{-9}\right) +\left(\frac{-9}{-3}\right) -\left(\frac{-11}{11}\right)\\= \frac{-8}{9}+ \frac{9}{3}+\frac{11}{11}\\=\frac{-8}{9}+\frac{3}{1}+\frac{1}{1}\\=\frac{-8+3+1}{9}\\=\frac{-4}{9}\)