Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{10}{-7}\right) +\left(\frac{-6}{9}\right) +\left(\frac{4}{10}\right)\\= \frac{-10}{7}- \frac{6}{9}+\frac{4}{10}\\=\frac{-10}{7}-\frac{2}{3}+\frac{2}{5}\\=\frac{-150}{105}-\frac{70}{105}+\frac{42}{105}\\=\frac{-150-70+42}{105}\\=\frac{-178}{105}\)
2. \(-\left(\frac{6}{-5}\right) +\left(\frac{6}{6}\right) +\left(\frac{-12}{12}\right)\\= \frac{6}{5}+ \frac{6}{6}-\frac{12}{12}\\=\frac{6}{5}+\frac{1}{1}-\frac{1}{1}\\=\frac{6+1-1}{5}\\=\frac{6}{5}\)
3. \(-\left(\frac{3}{-7}\right) -\left(\frac{2}{8}\right) +\left(\frac{-6}{8}\right)\\= \frac{3}{7}- \frac{2}{8}-\frac{6}{8}\\=\frac{3}{7}-\frac{1}{4}-\frac{3}{4}\\=\frac{12}{28}-\frac{7}{28}-\frac{21}{28}\\=\frac{12-7-21}{28}\\=\frac{-16}{28}\\=\frac{-4}{7}\)
4. \(+\left(\frac{7}{-2}\right) -\left(\frac{4}{-7}\right) +\left(\frac{-2}{6}\right)\\= \frac{-7}{2}+ \frac{4}{7}-\frac{2}{6}\\=\frac{-7}{2}+\frac{4}{7}-\frac{1}{3}\\=\frac{-147}{42}+\frac{24}{42}-\frac{14}{42}\\=\frac{-147+24-14}{42}\\=\frac{-137}{42}\)
5. \(+\left(\frac{3}{2}\right) +\left(\frac{-2}{2}\right) +\left(\frac{4}{8}\right)\\= \frac{3}{2}- \frac{2}{2}+\frac{4}{8}\\=\frac{3}{2}-\frac{1}{1}+\frac{1}{2}\\=\frac{3-1+1}{2}\\=\frac{3}{2}\)
6. \(-\left(\frac{-8}{-9}\right) -\left(\frac{-6}{-6}\right) -\left(\frac{5}{12}\right)\\= \frac{-8}{9}- \frac{6}{6}-\frac{5}{12}\\=\frac{-8}{9}-\frac{1}{1}-\frac{5}{12}\\=\frac{-32}{36}-\frac{36}{36}-\frac{15}{36}\\=\frac{-32-36-15}{36}\\=\frac{-83}{36}\)
7. \(-\left(\frac{-2}{-9}\right) +\left(\frac{-5}{-7}\right) +\left(\frac{-9}{6}\right)\\= \frac{-2}{9}+ \frac{5}{7}-\frac{9}{6}\\=\frac{-2}{9}+\frac{5}{7}-\frac{3}{2}\\=\frac{-28}{126}+\frac{90}{126}-\frac{189}{126}\\=\frac{-28+90-189}{126}\\=\frac{-127}{126}\)
8. \(-\left(\frac{-4}{-3}\right) +\left(\frac{2}{2}\right) -\left(\frac{4}{-10}\right)\\= \frac{-4}{3}+ \frac{2}{2}+\frac{4}{10}\\=\frac{-4}{3}+\frac{1}{1}+\frac{2}{5}\\=\frac{-20}{15}+\frac{15}{15}+\frac{6}{15}\\=\frac{-20+15+6}{15}\\=\frac{1}{15}\)
9. \(-\left(\frac{-5}{6}\right) +\left(\frac{-2}{6}\right) -\left(\frac{-12}{-11}\right)\\= \frac{5}{6}- \frac{2}{6}-\frac{12}{11}\\=\frac{5}{6}-\frac{1}{3}-\frac{12}{11}\\=\frac{55}{66}-\frac{22}{66}-\frac{72}{66}\\=\frac{55-22-72}{66}\\=\frac{-39}{66}\\=\frac{-13}{22}\)
10. \(+\left(\frac{7}{5}\right) -\left(\frac{2}{-3}\right) -\left(\frac{-3}{-4}\right)\\= \frac{7}{5}+ \frac{2}{3}-\frac{3}{4}\\=\frac{84}{60}+\frac{40}{60}-\frac{45}{60}\\=\frac{84+40-45}{60}\\=\frac{79}{60}\)
11. \(-\left(\frac{6}{7}\right) +\left(\frac{3}{-6}\right) +\left(\frac{3}{-11}\right)\\= \frac{-6}{7}- \frac{3}{6}-\frac{3}{11}\\=\frac{-6}{7}-\frac{1}{2}-\frac{3}{11}\\=\frac{-132}{154}-\frac{77}{154}-\frac{42}{154}\\=\frac{-132-77-42}{154}\\=\frac{-251}{154}\)
12. \(-\left(\frac{6}{-5}\right) +\left(\frac{-4}{-9}\right) +\left(\frac{5}{8}\right)\\= \frac{6}{5}+ \frac{4}{9}+\frac{5}{8}\\=\frac{432}{360}+\frac{160}{360}+\frac{225}{360}\\=\frac{432+160+225}{360}\\=\frac{817}{360}\)