Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{7}{2}\right) -\left(\frac{5}{-4}\right) +\left(\frac{-11}{-12}\right)\\= \frac{7}{2}+ \frac{5}{4}+\frac{11}{12}\\=\frac{42}{12}+\frac{15}{12}+\frac{11}{12}\\=\frac{42+15+11}{12}\\=\frac{68}{12}\\=\frac{17}{3}\)
2. \(-\left(\frac{6}{-7}\right) -\left(\frac{-2}{2}\right) -\left(\frac{5}{-8}\right)\\= \frac{6}{7}+ \frac{2}{2}+\frac{5}{8}\\=\frac{6}{7}+\frac{1}{1}+\frac{5}{8}\\=\frac{48}{56}+\frac{56}{56}+\frac{35}{56}\\=\frac{48+56+35}{56}\\=\frac{139}{56}\)
3. \(-\left(\frac{5}{6}\right) -\left(\frac{3}{-9}\right) -\left(\frac{-10}{-5}\right)\\= \frac{-5}{6}+ \frac{3}{9}-\frac{10}{5}\\=\frac{-5}{6}+\frac{1}{3}-\frac{2}{1}\\=\frac{-5+1-2}{6}\\=\frac{-6}{6}\\=\frac{-1}{1}\)
4. \(+\left(\frac{-2}{-7}\right) +\left(\frac{2}{-3}\right) -\left(\frac{-8}{-12}\right)\\= \frac{2}{7}- \frac{2}{3}-\frac{8}{12}\\=\frac{2}{7}-\frac{2}{3}-\frac{2}{3}\\=\frac{6}{21}-\frac{14}{21}-\frac{14}{21}\\=\frac{6-14-14}{21}\\=\frac{-22}{21}\)
5. \(+\left(\frac{-8}{-5}\right) -\left(\frac{-9}{-10}\right) +\left(\frac{-5}{5}\right)\\= \frac{8}{5}- \frac{9}{10}-\frac{5}{5}\\=\frac{8}{5}-\frac{9}{10}-\frac{1}{1}\\=\frac{16}{10}-\frac{9}{10}-\frac{10}{10}\\=\frac{16-9-10}{10}\\=\frac{-3}{10}\)
6. \(+\left(\frac{4}{5}\right) -\left(\frac{7}{8}\right) +\left(\frac{9}{11}\right)\\= \frac{4}{5}- \frac{7}{8}+\frac{9}{11}\\=\frac{352}{440}-\frac{385}{440}+\frac{360}{440}\\=\frac{352-385+360}{440}\\=\frac{327}{440}\)
7. \(-\left(\frac{-5}{-7}\right) +\left(\frac{-8}{8}\right) -\left(\frac{5}{-6}\right)\\= \frac{-5}{7}- \frac{8}{8}+\frac{5}{6}\\=\frac{-5}{7}-\frac{1}{1}+\frac{5}{6}\\=\frac{-30}{42}-\frac{42}{42}+\frac{35}{42}\\=\frac{-30-42+35}{42}\\=\frac{-37}{42}\)
8. \(-\left(\frac{9}{-4}\right) -\left(\frac{-2}{7}\right) +\left(\frac{7}{-11}\right)\\= \frac{9}{4}+ \frac{2}{7}-\frac{7}{11}\\=\frac{693}{308}+\frac{88}{308}-\frac{196}{308}\\=\frac{693+88-196}{308}\\=\frac{585}{308}\)
9. \(-\left(\frac{-7}{-2}\right) +\left(\frac{6}{6}\right) +\left(\frac{-12}{9}\right)\\= \frac{-7}{2}+ \frac{6}{6}-\frac{12}{9}\\=\frac{-7}{2}+\frac{1}{1}-\frac{4}{3}\\=\frac{-21}{6}+\frac{6}{6}-\frac{8}{6}\\=\frac{-21+6-8}{6}\\=\frac{-23}{6}\)
10. \(-\left(\frac{7}{4}\right) +\left(\frac{-10}{9}\right) +\left(\frac{9}{4}\right)\\= \frac{-7}{4}- \frac{10}{9}+\frac{9}{4}\\=\frac{-63}{36}-\frac{40}{36}+\frac{81}{36}\\=\frac{-63-40+81}{36}\\=\frac{-22}{36}\\=\frac{-11}{18}\)
11. \(+\left(\frac{-2}{-3}\right) +\left(\frac{-8}{-3}\right) +\left(\frac{12}{-9}\right)\\= \frac{2}{3}+ \frac{8}{3}-\frac{12}{9}\\=\frac{2}{3}+\frac{8}{3}-\frac{4}{3}\\=\frac{2+8-4}{3}\\=\frac{6}{3}\\=\frac{2}{1}\)
12. \(-\left(\frac{10}{7}\right) -\left(\frac{-3}{7}\right) +\left(\frac{-12}{-8}\right)\\= \frac{-10}{7}+ \frac{3}{7}+\frac{12}{8}\\=\frac{-10}{7}+\frac{3}{7}+\frac{3}{2}\\=\frac{-20}{14}+\frac{6}{14}+\frac{21}{14}\\=\frac{-20+6+21}{14}\\=\frac{7}{14}\\=\frac{1}{2}\)