Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{4}{9}\right) -\left(\frac{3}{10}\right) +\left(\frac{8}{-7}\right)\\= \frac{4}{9}- \frac{3}{10}-\frac{8}{7}\\=\frac{280}{630}-\frac{189}{630}-\frac{720}{630}\\=\frac{280-189-720}{630}\\=\frac{-629}{630}\)
2. \(+\left(\frac{-8}{-9}\right) +\left(\frac{3}{-9}\right) +\left(\frac{-4}{-6}\right)\\= \frac{8}{9}- \frac{3}{9}+\frac{4}{6}\\=\frac{8}{9}-\frac{1}{3}+\frac{2}{3}\\=\frac{8-1+2}{9}\\=\frac{9}{9}\\=\frac{1}{1}\)
3. \(-\left(\frac{6}{-5}\right) +\left(\frac{-9}{4}\right) -\left(\frac{6}{3}\right)\\= \frac{6}{5}- \frac{9}{4}-\frac{6}{3}\\=\frac{6}{5}-\frac{9}{4}-\frac{2}{1}\\=\frac{24}{20}-\frac{45}{20}-\frac{40}{20}\\=\frac{24-45-40}{20}\\=\frac{-61}{20}\)
4. \(-\left(\frac{-7}{-6}\right) -\left(\frac{4}{4}\right) +\left(\frac{-11}{-8}\right)\\= \frac{-7}{6}- \frac{4}{4}+\frac{11}{8}\\=\frac{-7}{6}-\frac{1}{1}+\frac{11}{8}\\=\frac{-28}{24}-\frac{24}{24}+\frac{33}{24}\\=\frac{-28-24+33}{24}\\=\frac{-19}{24}\)
5. \(-\left(\frac{5}{8}\right) +\left(\frac{6}{-10}\right) -\left(\frac{12}{-3}\right)\\= \frac{-5}{8}- \frac{6}{10}+\frac{12}{3}\\=\frac{-5}{8}-\frac{3}{5}+\frac{4}{1}\\=\frac{-25}{40}-\frac{24}{40}+\frac{160}{40}\\=\frac{-25-24+160}{40}\\=\frac{111}{40}\)
6. \(+\left(\frac{6}{5}\right) -\left(\frac{4}{-2}\right) +\left(\frac{-9}{-3}\right)\\= \frac{6}{5}+ \frac{4}{2}+\frac{9}{3}\\=\frac{6}{5}+\frac{2}{1}+\frac{3}{1}\\=\frac{6+2+3}{5}\\=\frac{11}{5}\)
7. \(+\left(\frac{9}{2}\right) +\left(\frac{10}{-7}\right) +\left(\frac{6}{3}\right)\\= \frac{9}{2}- \frac{10}{7}+\frac{6}{3}\\=\frac{9}{2}-\frac{10}{7}+\frac{2}{1}\\=\frac{63}{14}-\frac{20}{14}+\frac{28}{14}\\=\frac{63-20+28}{14}\\=\frac{71}{14}\)
8. \(-\left(\frac{-10}{-7}\right) -\left(\frac{4}{2}\right) +\left(\frac{6}{-6}\right)\\= \frac{-10}{7}- \frac{4}{2}-\frac{6}{6}\\=\frac{-10}{7}-\frac{2}{1}-\frac{1}{1}\\=\frac{-10-2-1}{7}\\=\frac{-13}{7}\)
9. \(-\left(\frac{9}{7}\right) +\left(\frac{7}{-8}\right) -\left(\frac{12}{-11}\right)\\= \frac{-9}{7}- \frac{7}{8}+\frac{12}{11}\\=\frac{-792}{616}-\frac{539}{616}+\frac{672}{616}\\=\frac{-792-539+672}{616}\\=\frac{-659}{616}\)
10. \(-\left(\frac{-7}{8}\right) -\left(\frac{-8}{-9}\right) -\left(\frac{11}{11}\right)\\= \frac{7}{8}- \frac{8}{9}-\frac{11}{11}\\=\frac{7}{8}-\frac{8}{9}-\frac{1}{1}\\=\frac{63}{72}-\frac{64}{72}-\frac{72}{72}\\=\frac{63-64-72}{72}\\=\frac{-73}{72}\)
11. \(-\left(\frac{-6}{-5}\right) +\left(\frac{9}{5}\right) +\left(\frac{-9}{7}\right)\\= \frac{-6}{5}+ \frac{9}{5}-\frac{9}{7}\\=\frac{-42}{35}+\frac{63}{35}-\frac{45}{35}\\=\frac{-42+63-45}{35}\\=\frac{-24}{35}\)
12. \(-\left(\frac{2}{5}\right) +\left(\frac{4}{10}\right) -\left(\frac{10}{2}\right)\\= \frac{-2}{5}+ \frac{4}{10}-\frac{10}{2}\\=\frac{-2}{5}+\frac{2}{5}-\frac{5}{1}\\=\frac{-2+2-5}{5}\\=\frac{-5}{5}\\=\frac{-1}{1}\)