Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{6}{-7}\right) +\left(\frac{-9}{-8}\right) +\left(\frac{-5}{4}\right)\\= \frac{-6}{7}+ \frac{9}{8}-\frac{5}{4}\\=\frac{-48}{56}+\frac{63}{56}-\frac{70}{56}\\=\frac{-48+63-70}{56}\\=\frac{-55}{56}\)
2. \(-\left(\frac{-9}{-2}\right) -\left(\frac{6}{3}\right) -\left(\frac{-11}{-7}\right)\\= \frac{-9}{2}- \frac{6}{3}-\frac{11}{7}\\=\frac{-9}{2}-\frac{2}{1}-\frac{11}{7}\\=\frac{-63}{14}-\frac{28}{14}-\frac{22}{14}\\=\frac{-63-28-22}{14}\\=\frac{-113}{14}\)
3. \(-\left(\frac{8}{-7}\right) -\left(\frac{2}{2}\right) +\left(\frac{7}{3}\right)\\= \frac{8}{7}- \frac{2}{2}+\frac{7}{3}\\=\frac{8}{7}-\frac{1}{1}+\frac{7}{3}\\=\frac{24}{21}-\frac{21}{21}+\frac{49}{21}\\=\frac{24-21+49}{21}\\=\frac{52}{21}\)
4. \(+\left(\frac{-7}{-2}\right) +\left(\frac{-4}{-2}\right) -\left(\frac{11}{2}\right)\\= \frac{7}{2}+ \frac{4}{2}-\frac{11}{2}\\=\frac{7}{2}+\frac{2}{1}-\frac{11}{2}\\=\frac{7+2-11}{2}\\=\frac{-2}{2}\\=\frac{-1}{1}\)
5. \(+\left(\frac{-7}{3}\right) +\left(\frac{-3}{-4}\right) +\left(\frac{8}{6}\right)\\= \frac{-7}{3}+ \frac{3}{4}+\frac{8}{6}\\=\frac{-7}{3}+\frac{3}{4}+\frac{4}{3}\\=\frac{-28}{12}+\frac{9}{12}+\frac{16}{12}\\=\frac{-28+9+16}{12}\\=\frac{-3}{12}\\=\frac{-1}{4}\)
6. \(+\left(\frac{9}{-2}\right) +\left(\frac{8}{-7}\right) -\left(\frac{-12}{-6}\right)\\= \frac{-9}{2}- \frac{8}{7}-\frac{12}{6}\\=\frac{-9}{2}-\frac{8}{7}-\frac{2}{1}\\=\frac{-63}{14}-\frac{16}{14}-\frac{28}{14}\\=\frac{-63-16-28}{14}\\=\frac{-107}{14}\)
7. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-10}{-9}\right) +\left(\frac{-9}{-3}\right)\\= \frac{-6}{5}+ \frac{10}{9}+\frac{9}{3}\\=\frac{-6}{5}+\frac{10}{9}+\frac{3}{1}\\=\frac{-54}{45}+\frac{50}{45}+\frac{135}{45}\\=\frac{-54+50+135}{45}\\=\frac{131}{45}\)
8. \(-\left(\frac{-6}{-5}\right) -\left(\frac{10}{-6}\right) +\left(\frac{-5}{6}\right)\\= \frac{-6}{5}+ \frac{10}{6}-\frac{5}{6}\\=\frac{-6}{5}+\frac{5}{3}-\frac{5}{6}\\=\frac{-36}{30}+\frac{50}{30}-\frac{25}{30}\\=\frac{-36+50-25}{30}\\=\frac{-11}{30}\)
9. \(-\left(\frac{10}{-9}\right) +\left(\frac{9}{-8}\right) -\left(\frac{3}{10}\right)\\= \frac{10}{9}- \frac{9}{8}-\frac{3}{10}\\=\frac{400}{360}-\frac{405}{360}-\frac{108}{360}\\=\frac{400-405-108}{360}\\=\frac{-113}{360}\)
10. \(+\left(\frac{-6}{7}\right) +\left(\frac{9}{2}\right) +\left(\frac{11}{3}\right)\\= \frac{-6}{7}+ \frac{9}{2}+\frac{11}{3}\\=\frac{-36}{42}+\frac{189}{42}+\frac{154}{42}\\=\frac{-36+189+154}{42}\\=\frac{307}{42}\)
11. \(+\left(\frac{-2}{3}\right) +\left(\frac{10}{5}\right) +\left(\frac{-10}{8}\right)\\= \frac{-2}{3}+ \frac{10}{5}-\frac{10}{8}\\=\frac{-2}{3}+\frac{2}{1}-\frac{5}{4}\\=\frac{-8}{12}+\frac{24}{12}-\frac{15}{12}\\=\frac{-8+24-15}{12}\\=\frac{1}{12}\)
12. \(+\left(\frac{-2}{-5}\right) +\left(\frac{-4}{2}\right) -\left(\frac{-6}{-2}\right)\\= \frac{2}{5}- \frac{4}{2}-\frac{6}{2}\\=\frac{2}{5}-\frac{2}{1}-\frac{3}{1}\\=\frac{2-2-3}{5}\\=\frac{-3}{5}\)