Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{6}\right) -\left(\frac{2}{-8}\right) -\left(\frac{-3}{-11}\right)\\= \frac{-5}{6}+ \frac{2}{8}-\frac{3}{11}\\=\frac{-5}{6}+\frac{1}{4}-\frac{3}{11}\\=\frac{-110}{132}+\frac{33}{132}-\frac{36}{132}\\=\frac{-110+33-36}{132}\\=\frac{-113}{132}\)
2. \(+\left(\frac{-9}{-4}\right) +\left(\frac{-4}{9}\right) -\left(\frac{-3}{-2}\right)\\= \frac{9}{4}- \frac{4}{9}-\frac{3}{2}\\=\frac{81}{36}-\frac{16}{36}-\frac{54}{36}\\=\frac{81-16-54}{36}\\=\frac{11}{36}\)
3. \(-\left(\frac{-6}{-7}\right) +\left(\frac{-10}{-4}\right) +\left(\frac{-7}{6}\right)\\= \frac{-6}{7}+ \frac{10}{4}-\frac{7}{6}\\=\frac{-6}{7}+\frac{5}{2}-\frac{7}{6}\\=\frac{-36}{42}+\frac{105}{42}-\frac{49}{42}\\=\frac{-36+105-49}{42}\\=\frac{20}{42}\\=\frac{10}{21}\)
4. \(+\left(\frac{-5}{-9}\right) +\left(\frac{-10}{4}\right) +\left(\frac{5}{-4}\right)\\= \frac{5}{9}- \frac{10}{4}-\frac{5}{4}\\=\frac{5}{9}-\frac{5}{2}-\frac{5}{4}\\=\frac{20}{36}-\frac{90}{36}-\frac{45}{36}\\=\frac{20-90-45}{36}\\=\frac{-115}{36}\)
5. \(-\left(\frac{5}{6}\right) +\left(\frac{6}{-5}\right) +\left(\frac{9}{6}\right)\\= \frac{-5}{6}- \frac{6}{5}+\frac{9}{6}\\=\frac{-5}{6}-\frac{6}{5}+\frac{3}{2}\\=\frac{-25}{30}-\frac{36}{30}+\frac{45}{30}\\=\frac{-25-36+45}{30}\\=\frac{-16}{30}\\=\frac{-8}{15}\)
6. \(+\left(\frac{-7}{-6}\right) -\left(\frac{-10}{7}\right) -\left(\frac{10}{-12}\right)\\= \frac{7}{6}+ \frac{10}{7}+\frac{10}{12}\\=\frac{7}{6}+\frac{10}{7}+\frac{5}{6}\\=\frac{49}{42}+\frac{60}{42}+\frac{35}{42}\\=\frac{49+60+35}{42}\\=\frac{144}{42}\\=\frac{24}{7}\)
7. \(-\left(\frac{6}{5}\right) +\left(\frac{7}{3}\right) +\left(\frac{5}{9}\right)\\= \frac{-6}{5}+ \frac{7}{3}+\frac{5}{9}\\=\frac{-54}{45}+\frac{105}{45}+\frac{25}{45}\\=\frac{-54+105+25}{45}\\=\frac{76}{45}\)
8. \(+\left(\frac{2}{-5}\right) +\left(\frac{10}{-5}\right) +\left(\frac{-7}{-3}\right)\\= \frac{-2}{5}- \frac{10}{5}+\frac{7}{3}\\=\frac{-2}{5}-\frac{2}{1}+\frac{7}{3}\\=\frac{-6}{15}-\frac{30}{15}+\frac{35}{15}\\=\frac{-6-30+35}{15}\\=\frac{-1}{15}\)
9. \(-\left(\frac{3}{-2}\right) -\left(\frac{10}{-7}\right) -\left(\frac{-7}{-2}\right)\\= \frac{3}{2}+ \frac{10}{7}-\frac{7}{2}\\=\frac{21}{14}+\frac{20}{14}-\frac{49}{14}\\=\frac{21+20-49}{14}\\=\frac{-8}{14}\\=\frac{-4}{7}\)
10. \(+\left(\frac{10}{3}\right) +\left(\frac{-10}{-6}\right) +\left(\frac{12}{-11}\right)\\= \frac{10}{3}+ \frac{10}{6}-\frac{12}{11}\\=\frac{10}{3}+\frac{5}{3}-\frac{12}{11}\\=\frac{110}{33}+\frac{55}{33}-\frac{36}{33}\\=\frac{110+55-36}{33}\\=\frac{129}{33}\\=\frac{43}{11}\)
11. \(+\left(\frac{-4}{-7}\right) -\left(\frac{7}{-3}\right) -\left(\frac{-10}{-3}\right)\\= \frac{4}{7}+ \frac{7}{3}-\frac{10}{3}\\=\frac{12}{21}+\frac{49}{21}-\frac{70}{21}\\=\frac{12+49-70}{21}\\=\frac{-9}{21}\\=\frac{-3}{7}\)
12. \(-\left(\frac{6}{7}\right) +\left(\frac{-5}{-7}\right) +\left(\frac{6}{12}\right)\\= \frac{-6}{7}+ \frac{5}{7}+\frac{6}{12}\\=\frac{-6}{7}+\frac{5}{7}+\frac{1}{2}\\=\frac{-12}{14}+\frac{10}{14}+\frac{7}{14}\\=\frac{-12+10+7}{14}\\=\frac{5}{14}\)