Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{-2}\right) +\left(\frac{4}{9}\right) -\left(\frac{9}{2}\right)\\= \frac{-9}{2}+ \frac{4}{9}-\frac{9}{2}\\=\frac{-81}{18}+\frac{8}{18}-\frac{81}{18}\\=\frac{-81+8-81}{18}\\=\frac{-154}{18}\\=\frac{-77}{9}\)
2. \(-\left(\frac{-3}{2}\right) -\left(\frac{9}{-7}\right) +\left(\frac{-4}{11}\right)\\= \frac{3}{2}+ \frac{9}{7}-\frac{4}{11}\\=\frac{231}{154}+\frac{198}{154}-\frac{56}{154}\\=\frac{231+198-56}{154}\\=\frac{373}{154}\)
3. \(+\left(\frac{-2}{3}\right) +\left(\frac{-3}{-5}\right) +\left(\frac{5}{-12}\right)\\= \frac{-2}{3}+ \frac{3}{5}-\frac{5}{12}\\=\frac{-40}{60}+\frac{36}{60}-\frac{25}{60}\\=\frac{-40+36-25}{60}\\=\frac{-29}{60}\)
4. \(-\left(\frac{6}{5}\right) +\left(\frac{8}{-4}\right) +\left(\frac{-7}{-2}\right)\\= \frac{-6}{5}- \frac{8}{4}+\frac{7}{2}\\=\frac{-6}{5}-\frac{2}{1}+\frac{7}{2}\\=\frac{-12}{10}-\frac{20}{10}+\frac{35}{10}\\=\frac{-12-20+35}{10}\\=\frac{3}{10}\)
5. \(+\left(\frac{2}{-3}\right) +\left(\frac{3}{7}\right) -\left(\frac{-6}{-5}\right)\\= \frac{-2}{3}+ \frac{3}{7}-\frac{6}{5}\\=\frac{-70}{105}+\frac{45}{105}-\frac{126}{105}\\=\frac{-70+45-126}{105}\\=\frac{-151}{105}\)
6. \(+\left(\frac{-3}{2}\right) -\left(\frac{6}{-10}\right) +\left(\frac{9}{-8}\right)\\= \frac{-3}{2}+ \frac{6}{10}-\frac{9}{8}\\=\frac{-3}{2}+\frac{3}{5}-\frac{9}{8}\\=\frac{-60}{40}+\frac{24}{40}-\frac{45}{40}\\=\frac{-60+24-45}{40}\\=\frac{-81}{40}\)
7. \(-\left(\frac{-9}{-7}\right) +\left(\frac{8}{-6}\right) -\left(\frac{-11}{5}\right)\\= \frac{-9}{7}- \frac{8}{6}+\frac{11}{5}\\=\frac{-9}{7}-\frac{4}{3}+\frac{11}{5}\\=\frac{-135}{105}-\frac{140}{105}+\frac{231}{105}\\=\frac{-135-140+231}{105}\\=\frac{-44}{105}\)
8. \(-\left(\frac{-9}{-4}\right) -\left(\frac{4}{-7}\right) -\left(\frac{7}{-6}\right)\\= \frac{-9}{4}+ \frac{4}{7}+\frac{7}{6}\\=\frac{-189}{84}+\frac{48}{84}+\frac{98}{84}\\=\frac{-189+48+98}{84}\\=\frac{-43}{84}\)
9. \(+\left(\frac{10}{3}\right) +\left(\frac{-8}{-8}\right) -\left(\frac{5}{11}\right)\\= \frac{10}{3}+ \frac{8}{8}-\frac{5}{11}\\=\frac{10}{3}+\frac{1}{1}-\frac{5}{11}\\=\frac{110}{33}+\frac{33}{33}-\frac{15}{33}\\=\frac{110+33-15}{33}\\=\frac{128}{33}\)
10. \(-\left(\frac{9}{4}\right) +\left(\frac{-7}{-3}\right) +\left(\frac{-5}{-4}\right)\\= \frac{-9}{4}+ \frac{7}{3}+\frac{5}{4}\\=\frac{-27}{12}+\frac{28}{12}+\frac{15}{12}\\=\frac{-27+28+15}{12}\\=\frac{16}{12}\\=\frac{4}{3}\)
11. \(+\left(\frac{10}{-9}\right) +\left(\frac{8}{10}\right) +\left(\frac{11}{9}\right)\\= \frac{-10}{9}+ \frac{8}{10}+\frac{11}{9}\\=\frac{-10}{9}+\frac{4}{5}+\frac{11}{9}\\=\frac{-50}{45}+\frac{36}{45}+\frac{55}{45}\\=\frac{-50+36+55}{45}\\=\frac{41}{45}\)
12. \(-\left(\frac{2}{3}\right) +\left(\frac{9}{-6}\right) -\left(\frac{-2}{3}\right)\\= \frac{-2}{3}- \frac{9}{6}+\frac{2}{3}\\=\frac{-2}{3}-\frac{3}{2}+\frac{2}{3}\\=\frac{-4}{6}-\frac{9}{6}+\frac{4}{6}\\=\frac{-4-9+4}{6}\\=\frac{-9}{6}\\=\frac{-3}{2}\)