Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{3}\right) +\left(\frac{4}{-7}\right) +\left(\frac{6}{8}\right)\\= \frac{-10}{3}- \frac{4}{7}+\frac{6}{8}\\=\frac{-10}{3}-\frac{4}{7}+\frac{3}{4}\\=\frac{-280}{84}-\frac{48}{84}+\frac{63}{84}\\=\frac{-280-48+63}{84}\\=\frac{-265}{84}\)
2. \(+\left(\frac{8}{-5}\right) -\left(\frac{7}{-10}\right) +\left(\frac{-6}{6}\right)\\= \frac{-8}{5}+ \frac{7}{10}-\frac{6}{6}\\=\frac{-8}{5}+\frac{7}{10}-\frac{1}{1}\\=\frac{-16}{10}+\frac{7}{10}-\frac{10}{10}\\=\frac{-16+7-10}{10}\\=\frac{-19}{10}\)
3. \(+\left(\frac{6}{5}\right) -\left(\frac{2}{-3}\right) -\left(\frac{-4}{-10}\right)\\= \frac{6}{5}+ \frac{2}{3}-\frac{4}{10}\\=\frac{6}{5}+\frac{2}{3}-\frac{2}{5}\\=\frac{18}{15}+\frac{10}{15}-\frac{6}{15}\\=\frac{18+10-6}{15}\\=\frac{22}{15}\)
4. \(+\left(\frac{-8}{-5}\right) +\left(\frac{7}{-2}\right) +\left(\frac{-2}{3}\right)\\= \frac{8}{5}- \frac{7}{2}-\frac{2}{3}\\=\frac{48}{30}-\frac{105}{30}-\frac{20}{30}\\=\frac{48-105-20}{30}\\=\frac{-77}{30}\)
5. \(-\left(\frac{-10}{-3}\right) +\left(\frac{9}{9}\right) -\left(\frac{-4}{3}\right)\\= \frac{-10}{3}+ \frac{9}{9}+\frac{4}{3}\\=\frac{-10}{3}+\frac{1}{1}+\frac{4}{3}\\=\frac{-10+1+4}{3}\\=\frac{-5}{3}\)
6. \(-\left(\frac{10}{-9}\right) +\left(\frac{4}{4}\right) -\left(\frac{4}{-6}\right)\\= \frac{10}{9}+ \frac{4}{4}+\frac{4}{6}\\=\frac{10}{9}+\frac{1}{1}+\frac{2}{3}\\=\frac{10+1+2}{9}\\=\frac{13}{9}\)
7. \(+\left(\frac{3}{8}\right) -\left(\frac{5}{-7}\right) -\left(\frac{9}{12}\right)\\= \frac{3}{8}+ \frac{5}{7}-\frac{9}{12}\\=\frac{3}{8}+\frac{5}{7}-\frac{3}{4}\\=\frac{21}{56}+\frac{40}{56}-\frac{42}{56}\\=\frac{21+40-42}{56}\\=\frac{19}{56}\)
8. \(-\left(\frac{5}{9}\right) -\left(\frac{-6}{7}\right) +\left(\frac{11}{-12}\right)\\= \frac{-5}{9}+ \frac{6}{7}-\frac{11}{12}\\=\frac{-140}{252}+\frac{216}{252}-\frac{231}{252}\\=\frac{-140+216-231}{252}\\=\frac{-155}{252}\)
9. \(-\left(\frac{-9}{10}\right) +\left(\frac{-6}{6}\right) +\left(\frac{-5}{-2}\right)\\= \frac{9}{10}- \frac{6}{6}+\frac{5}{2}\\=\frac{9}{10}-\frac{1}{1}+\frac{5}{2}\\=\frac{9-1+5}{10}\\=\frac{13}{10}\)
10. \(-\left(\frac{-6}{-7}\right) +\left(\frac{2}{2}\right) -\left(\frac{8}{-12}\right)\\= \frac{-6}{7}+ \frac{2}{2}+\frac{8}{12}\\=\frac{-6}{7}+\frac{1}{1}+\frac{2}{3}\\=\frac{-18}{21}+\frac{21}{21}+\frac{14}{21}\\=\frac{-18+21+14}{21}\\=\frac{17}{21}\)
11. \(-\left(\frac{-6}{-7}\right) -\left(\frac{-6}{-4}\right) -\left(\frac{-8}{-7}\right)\\= \frac{-6}{7}- \frac{6}{4}-\frac{8}{7}\\=\frac{-6}{7}-\frac{3}{2}-\frac{8}{7}\\=\frac{-12}{14}-\frac{21}{14}-\frac{16}{14}\\=\frac{-12-21-16}{14}\\=\frac{-49}{14}\\=\frac{-7}{2}\)
12. \(-\left(\frac{6}{-7}\right) +\left(\frac{-7}{7}\right) +\left(\frac{-7}{-7}\right)\\= \frac{6}{7}- \frac{7}{7}+\frac{7}{7}\\=\frac{6}{7}-\frac{1}{1}+\frac{1}{1}\\=\frac{6-1+1}{7}\\=\frac{6}{7}\)