Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{5}\right) -\left(\frac{7}{3}\right) -\left(\frac{-7}{-12}\right)\\= \frac{6}{5}- \frac{7}{3}-\frac{7}{12}\\=\frac{72}{60}-\frac{140}{60}-\frac{35}{60}\\=\frac{72-140-35}{60}\\=\frac{-103}{60}\)
2. \(+\left(\frac{-7}{9}\right) -\left(\frac{6}{5}\right) +\left(\frac{7}{-6}\right)\\= \frac{-7}{9}- \frac{6}{5}-\frac{7}{6}\\=\frac{-70}{90}-\frac{108}{90}-\frac{105}{90}\\=\frac{-70-108-105}{90}\\=\frac{-283}{90}\)
3. \(+\left(\frac{5}{2}\right) +\left(\frac{-4}{3}\right) -\left(\frac{3}{-7}\right)\\= \frac{5}{2}- \frac{4}{3}+\frac{3}{7}\\=\frac{105}{42}-\frac{56}{42}+\frac{18}{42}\\=\frac{105-56+18}{42}\\=\frac{67}{42}\)
4. \(-\left(\frac{-7}{2}\right) -\left(\frac{2}{2}\right) -\left(\frac{10}{-5}\right)\\= \frac{7}{2}- \frac{2}{2}+\frac{10}{5}\\=\frac{7}{2}-\frac{1}{1}+\frac{2}{1}\\=\frac{7-1+2}{2}\\=\frac{8}{2}\\=\frac{4}{1}\)
5. \(+\left(\frac{5}{-2}\right) +\left(\frac{-5}{2}\right) +\left(\frac{6}{8}\right)\\= \frac{-5}{2}- \frac{5}{2}+\frac{6}{8}\\=\frac{-5}{2}-\frac{5}{2}+\frac{3}{4}\\=\frac{-10}{4}-\frac{10}{4}+\frac{3}{4}\\=\frac{-10-10+3}{4}\\=\frac{-17}{4}\)
6. \(+\left(\frac{8}{3}\right) +\left(\frac{2}{-5}\right) +\left(\frac{-6}{-5}\right)\\= \frac{8}{3}- \frac{2}{5}+\frac{6}{5}\\=\frac{40}{15}-\frac{6}{15}+\frac{18}{15}\\=\frac{40-6+18}{15}\\=\frac{52}{15}\)
7. \(-\left(\frac{10}{9}\right) +\left(\frac{8}{-2}\right) -\left(\frac{9}{-10}\right)\\= \frac{-10}{9}- \frac{8}{2}+\frac{9}{10}\\=\frac{-10}{9}-\frac{4}{1}+\frac{9}{10}\\=\frac{-100}{90}-\frac{360}{90}+\frac{81}{90}\\=\frac{-100-360+81}{90}\\=\frac{-379}{90}\)
8. \(+\left(\frac{-8}{7}\right) -\left(\frac{-5}{5}\right) -\left(\frac{7}{3}\right)\\= \frac{-8}{7}+ \frac{5}{5}-\frac{7}{3}\\=\frac{-8}{7}+\frac{1}{1}-\frac{7}{3}\\=\frac{-24}{21}+\frac{21}{21}-\frac{49}{21}\\=\frac{-24+21-49}{21}\\=\frac{-52}{21}\)
9. \(-\left(\frac{-5}{-4}\right) +\left(\frac{7}{-6}\right) +\left(\frac{3}{-11}\right)\\= \frac{-5}{4}- \frac{7}{6}-\frac{3}{11}\\=\frac{-165}{132}-\frac{154}{132}-\frac{36}{132}\\=\frac{-165-154-36}{132}\\=\frac{-355}{132}\)
10. \(-\left(\frac{-10}{3}\right) -\left(\frac{-7}{-5}\right) -\left(\frac{2}{11}\right)\\= \frac{10}{3}- \frac{7}{5}-\frac{2}{11}\\=\frac{550}{165}-\frac{231}{165}-\frac{30}{165}\\=\frac{550-231-30}{165}\\=\frac{289}{165}\)
11. \(+\left(\frac{2}{-9}\right) +\left(\frac{-5}{-9}\right) +\left(\frac{-6}{-9}\right)\\= \frac{-2}{9}+ \frac{5}{9}+\frac{6}{9}\\=\frac{-2}{9}+\frac{5}{9}+\frac{2}{3}\\=\frac{-2+5+2}{9}\\=\frac{5}{9}\)
12. \(-\left(\frac{-8}{-5}\right) -\left(\frac{2}{-3}\right) -\left(\frac{4}{5}\right)\\= \frac{-8}{5}+ \frac{2}{3}-\frac{4}{5}\\=\frac{-24}{15}+\frac{10}{15}-\frac{12}{15}\\=\frac{-24+10-12}{15}\\=\frac{-26}{15}\)