Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{3}\right) +\left(\frac{7}{10}\right) -\left(\frac{-5}{7}\right)\\= \frac{10}{3}+ \frac{7}{10}+\frac{5}{7}\\=\frac{700}{210}+\frac{147}{210}+\frac{150}{210}\\=\frac{700+147+150}{210}\\=\frac{997}{210}\)
2. \(-\left(\frac{-6}{5}\right) -\left(\frac{-7}{-6}\right) -\left(\frac{2}{10}\right)\\= \frac{6}{5}- \frac{7}{6}-\frac{2}{10}\\=\frac{6}{5}-\frac{7}{6}-\frac{1}{5}\\=\frac{36}{30}-\frac{35}{30}-\frac{6}{30}\\=\frac{36-35-6}{30}\\=\frac{-5}{30}\\=\frac{-1}{6}\)
3. \(-\left(\frac{3}{-8}\right) -\left(\frac{-2}{5}\right) -\left(\frac{8}{6}\right)\\= \frac{3}{8}+ \frac{2}{5}-\frac{8}{6}\\=\frac{3}{8}+\frac{2}{5}-\frac{4}{3}\\=\frac{45}{120}+\frac{48}{120}-\frac{160}{120}\\=\frac{45+48-160}{120}\\=\frac{-67}{120}\)
4. \(+\left(\frac{8}{9}\right) -\left(\frac{-4}{4}\right) +\left(\frac{8}{-11}\right)\\= \frac{8}{9}+ \frac{4}{4}-\frac{8}{11}\\=\frac{8}{9}+\frac{1}{1}-\frac{8}{11}\\=\frac{88}{99}+\frac{99}{99}-\frac{72}{99}\\=\frac{88+99-72}{99}\\=\frac{115}{99}\)
5. \(+\left(\frac{8}{-7}\right) -\left(\frac{-5}{5}\right) +\left(\frac{4}{-3}\right)\\= \frac{-8}{7}+ \frac{5}{5}-\frac{4}{3}\\=\frac{-8}{7}+\frac{1}{1}-\frac{4}{3}\\=\frac{-24}{21}+\frac{21}{21}-\frac{28}{21}\\=\frac{-24+21-28}{21}\\=\frac{-31}{21}\)
6. \(+\left(\frac{-5}{-7}\right) +\left(\frac{-3}{6}\right) -\left(\frac{-9}{2}\right)\\= \frac{5}{7}- \frac{3}{6}+\frac{9}{2}\\=\frac{5}{7}-\frac{1}{2}+\frac{9}{2}\\=\frac{10}{14}-\frac{7}{14}+\frac{63}{14}\\=\frac{10-7+63}{14}\\=\frac{66}{14}\\=\frac{33}{7}\)
7. \(+\left(\frac{-4}{9}\right) -\left(\frac{-7}{-10}\right) +\left(\frac{10}{-7}\right)\\= \frac{-4}{9}- \frac{7}{10}-\frac{10}{7}\\=\frac{-280}{630}-\frac{441}{630}-\frac{900}{630}\\=\frac{-280-441-900}{630}\\=\frac{-1621}{630}\)
8. \(+\left(\frac{9}{-2}\right) -\left(\frac{10}{3}\right) -\left(\frac{-2}{-5}\right)\\= \frac{-9}{2}- \frac{10}{3}-\frac{2}{5}\\=\frac{-135}{30}-\frac{100}{30}-\frac{12}{30}\\=\frac{-135-100-12}{30}\\=\frac{-247}{30}\)
9. \(+\left(\frac{5}{4}\right) +\left(\frac{3}{-2}\right) -\left(\frac{10}{9}\right)\\= \frac{5}{4}- \frac{3}{2}-\frac{10}{9}\\=\frac{45}{36}-\frac{54}{36}-\frac{40}{36}\\=\frac{45-54-40}{36}\\=\frac{-49}{36}\)
10. \(-\left(\frac{8}{-5}\right) -\left(\frac{2}{5}\right) +\left(\frac{-4}{5}\right)\\= \frac{8}{5}- \frac{2}{5}-\frac{4}{5}\\=\frac{8-2-4}{5}\\=\frac{2}{5}\)
11. \(-\left(\frac{5}{8}\right) +\left(\frac{-8}{4}\right) +\left(\frac{-5}{-6}\right)\\= \frac{-5}{8}- \frac{8}{4}+\frac{5}{6}\\=\frac{-5}{8}-\frac{2}{1}+\frac{5}{6}\\=\frac{-15}{24}-\frac{48}{24}+\frac{20}{24}\\=\frac{-15-48+20}{24}\\=\frac{-43}{24}\)
12. \(+\left(\frac{-6}{-5}\right) +\left(\frac{2}{-8}\right) -\left(\frac{-7}{6}\right)\\= \frac{6}{5}- \frac{2}{8}+\frac{7}{6}\\=\frac{6}{5}-\frac{1}{4}+\frac{7}{6}\\=\frac{72}{60}-\frac{15}{60}+\frac{70}{60}\\=\frac{72-15+70}{60}\\=\frac{127}{60}\)