Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{-5}\right) +\left(\frac{3}{-8}\right) -\left(\frac{-5}{-3}\right)\\= \frac{-2}{5}- \frac{3}{8}-\frac{5}{3}\\=\frac{-48}{120}-\frac{45}{120}-\frac{200}{120}\\=\frac{-48-45-200}{120}\\=\frac{-293}{120}\)
2. \(+\left(\frac{7}{2}\right) -\left(\frac{3}{5}\right) +\left(\frac{11}{-2}\right)\\= \frac{7}{2}- \frac{3}{5}-\frac{11}{2}\\=\frac{35}{10}-\frac{6}{10}-\frac{55}{10}\\=\frac{35-6-55}{10}\\=\frac{-26}{10}\\=\frac{-13}{5}\)
3. \(-\left(\frac{2}{-9}\right) -\left(\frac{10}{7}\right) -\left(\frac{5}{11}\right)\\= \frac{2}{9}- \frac{10}{7}-\frac{5}{11}\\=\frac{154}{693}-\frac{990}{693}-\frac{315}{693}\\=\frac{154-990-315}{693}\\=\frac{-1151}{693}\)
4. \(+\left(\frac{4}{-9}\right) +\left(\frac{6}{-2}\right) +\left(\frac{-8}{9}\right)\\= \frac{-4}{9}- \frac{6}{2}-\frac{8}{9}\\=\frac{-4}{9}-\frac{3}{1}-\frac{8}{9}\\=\frac{-4-3-8}{9}\\=\frac{-15}{9}\\=\frac{-5}{3}\)
5. \(-\left(\frac{-3}{2}\right) -\left(\frac{6}{5}\right) -\left(\frac{10}{12}\right)\\= \frac{3}{2}- \frac{6}{5}-\frac{10}{12}\\=\frac{3}{2}-\frac{6}{5}-\frac{5}{6}\\=\frac{45}{30}-\frac{36}{30}-\frac{25}{30}\\=\frac{45-36-25}{30}\\=\frac{-16}{30}\\=\frac{-8}{15}\)
6. \(+\left(\frac{-9}{-2}\right) +\left(\frac{4}{7}\right) -\left(\frac{-12}{9}\right)\\= \frac{9}{2}+ \frac{4}{7}+\frac{12}{9}\\=\frac{9}{2}+\frac{4}{7}+\frac{4}{3}\\=\frac{189}{42}+\frac{24}{42}+\frac{56}{42}\\=\frac{189+24+56}{42}\\=\frac{269}{42}\)
7. \(-\left(\frac{-6}{-5}\right) +\left(\frac{10}{-4}\right) -\left(\frac{7}{8}\right)\\= \frac{-6}{5}- \frac{10}{4}-\frac{7}{8}\\=\frac{-6}{5}-\frac{5}{2}-\frac{7}{8}\\=\frac{-48}{40}-\frac{100}{40}-\frac{35}{40}\\=\frac{-48-100-35}{40}\\=\frac{-183}{40}\)
8. \(-\left(\frac{3}{-8}\right) +\left(\frac{-7}{3}\right) -\left(\frac{6}{9}\right)\\= \frac{3}{8}- \frac{7}{3}-\frac{6}{9}\\=\frac{3}{8}-\frac{7}{3}-\frac{2}{3}\\=\frac{9}{24}-\frac{56}{24}-\frac{16}{24}\\=\frac{9-56-16}{24}\\=\frac{-63}{24}\\=\frac{-21}{8}\)
9. \(+\left(\frac{2}{7}\right) +\left(\frac{6}{3}\right) +\left(\frac{8}{3}\right)\\= \frac{2}{7}+ \frac{6}{3}+\frac{8}{3}\\=\frac{2}{7}+\frac{2}{1}+\frac{8}{3}\\=\frac{6}{21}+\frac{42}{21}+\frac{56}{21}\\=\frac{6+42+56}{21}\\=\frac{104}{21}\)
10. \(-\left(\frac{5}{6}\right) -\left(\frac{-5}{2}\right) -\left(\frac{-5}{-7}\right)\\= \frac{-5}{6}+ \frac{5}{2}-\frac{5}{7}\\=\frac{-35}{42}+\frac{105}{42}-\frac{30}{42}\\=\frac{-35+105-30}{42}\\=\frac{40}{42}\\=\frac{20}{21}\)
11. \(+\left(\frac{-2}{3}\right) -\left(\frac{6}{-2}\right) -\left(\frac{10}{-10}\right)\\= \frac{-2}{3}+ \frac{6}{2}+\frac{10}{10}\\=\frac{-2}{3}+\frac{3}{1}+\frac{1}{1}\\=\frac{-2+3+1}{3}\\=\frac{2}{3}\)
12. \(+\left(\frac{-4}{3}\right) -\left(\frac{-2}{-4}\right) -\left(\frac{5}{7}\right)\\= \frac{-4}{3}- \frac{2}{4}-\frac{5}{7}\\=\frac{-4}{3}-\frac{1}{2}-\frac{5}{7}\\=\frac{-56}{42}-\frac{21}{42}-\frac{30}{42}\\=\frac{-56-21-30}{42}\\=\frac{-107}{42}\)