Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{7}\right) +\left(\frac{-7}{4}\right) +\left(\frac{-3}{11}\right)\\= \frac{9}{7}- \frac{7}{4}-\frac{3}{11}\\=\frac{396}{308}-\frac{539}{308}-\frac{84}{308}\\=\frac{396-539-84}{308}\\=\frac{-227}{308}\)
2. \(-\left(\frac{-2}{-9}\right) -\left(\frac{6}{7}\right) +\left(\frac{-4}{-4}\right)\\= \frac{-2}{9}- \frac{6}{7}+\frac{4}{4}\\=\frac{-2}{9}-\frac{6}{7}+\frac{1}{1}\\=\frac{-14}{63}-\frac{54}{63}+\frac{63}{63}\\=\frac{-14-54+63}{63}\\=\frac{-5}{63}\)
3. \(-\left(\frac{-7}{-3}\right) +\left(\frac{7}{2}\right) -\left(\frac{11}{2}\right)\\= \frac{-7}{3}+ \frac{7}{2}-\frac{11}{2}\\=\frac{-14}{6}+\frac{21}{6}-\frac{33}{6}\\=\frac{-14+21-33}{6}\\=\frac{-26}{6}\\=\frac{-13}{3}\)
4. \(-\left(\frac{6}{-7}\right) +\left(\frac{-3}{-8}\right) -\left(\frac{10}{2}\right)\\= \frac{6}{7}+ \frac{3}{8}-\frac{10}{2}\\=\frac{6}{7}+\frac{3}{8}-\frac{5}{1}\\=\frac{48}{56}+\frac{21}{56}-\frac{280}{56}\\=\frac{48+21-280}{56}\\=\frac{-211}{56}\)
5. \(+\left(\frac{-9}{7}\right) -\left(\frac{6}{5}\right) -\left(\frac{-8}{6}\right)\\= \frac{-9}{7}- \frac{6}{5}+\frac{8}{6}\\=\frac{-9}{7}-\frac{6}{5}+\frac{4}{3}\\=\frac{-135}{105}-\frac{126}{105}+\frac{140}{105}\\=\frac{-135-126+140}{105}\\=\frac{-121}{105}\)
6. \(+\left(\frac{-7}{5}\right) +\left(\frac{8}{9}\right) +\left(\frac{8}{-10}\right)\\= \frac{-7}{5}+ \frac{8}{9}-\frac{8}{10}\\=\frac{-7}{5}+\frac{8}{9}-\frac{4}{5}\\=\frac{-63}{45}+\frac{40}{45}-\frac{36}{45}\\=\frac{-63+40-36}{45}\\=\frac{-59}{45}\)
7. \(-\left(\frac{2}{3}\right) +\left(\frac{7}{-3}\right) -\left(\frac{-9}{3}\right)\\= \frac{-2}{3}- \frac{7}{3}+\frac{9}{3}\\=\frac{-2}{3}-\frac{7}{3}+\frac{3}{1}\\=\frac{-2-7+3}{3}\\=\frac{-6}{3}\\=\frac{-2}{1}\)
8. \(-\left(\frac{-10}{9}\right) +\left(\frac{3}{6}\right) -\left(\frac{-5}{-12}\right)\\= \frac{10}{9}+ \frac{3}{6}-\frac{5}{12}\\=\frac{10}{9}+\frac{1}{2}-\frac{5}{12}\\=\frac{40}{36}+\frac{18}{36}-\frac{15}{36}\\=\frac{40+18-15}{36}\\=\frac{43}{36}\)
9. \(-\left(\frac{-3}{-4}\right) +\left(\frac{-4}{5}\right) -\left(\frac{-2}{8}\right)\\= \frac{-3}{4}- \frac{4}{5}+\frac{2}{8}\\=\frac{-3}{4}-\frac{4}{5}+\frac{1}{4}\\=\frac{-15}{20}-\frac{16}{20}+\frac{5}{20}\\=\frac{-15-16+5}{20}\\=\frac{-26}{20}\\=\frac{-13}{10}\)
10. \(-\left(\frac{-3}{-5}\right) -\left(\frac{9}{8}\right) -\left(\frac{-8}{-11}\right)\\= \frac{-3}{5}- \frac{9}{8}-\frac{8}{11}\\=\frac{-264}{440}-\frac{495}{440}-\frac{320}{440}\\=\frac{-264-495-320}{440}\\=\frac{-1079}{440}\)
11. \(-\left(\frac{3}{4}\right) +\left(\frac{7}{-4}\right) -\left(\frac{-12}{-4}\right)\\= \frac{-3}{4}- \frac{7}{4}-\frac{12}{4}\\=\frac{-3}{4}-\frac{7}{4}-\frac{3}{1}\\=\frac{-3-7-3}{4}\\=\frac{-13}{4}\)
12. \(+\left(\frac{2}{5}\right) +\left(\frac{7}{-5}\right) -\left(\frac{-3}{10}\right)\\= \frac{2}{5}- \frac{7}{5}+\frac{3}{10}\\=\frac{4}{10}-\frac{14}{10}+\frac{3}{10}\\=\frac{4-14+3}{10}\\=\frac{-7}{10}\)