Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-7}\right) -\left(\frac{-4}{10}\right) -\left(\frac{10}{-9}\right)\\= \frac{10}{7}+ \frac{4}{10}+\frac{10}{9}\\=\frac{10}{7}+\frac{2}{5}+\frac{10}{9}\\=\frac{450}{315}+\frac{126}{315}+\frac{350}{315}\\=\frac{450+126+350}{315}\\=\frac{926}{315}\)
2. \(+\left(\frac{7}{-6}\right) +\left(\frac{9}{-4}\right) -\left(\frac{12}{-4}\right)\\= \frac{-7}{6}- \frac{9}{4}+\frac{12}{4}\\=\frac{-7}{6}-\frac{9}{4}+\frac{3}{1}\\=\frac{-14}{12}-\frac{27}{12}+\frac{36}{12}\\=\frac{-14-27+36}{12}\\=\frac{-5}{12}\)
3. \(+\left(\frac{-10}{-3}\right) -\left(\frac{-2}{6}\right) +\left(\frac{-5}{12}\right)\\= \frac{10}{3}+ \frac{2}{6}-\frac{5}{12}\\=\frac{10}{3}+\frac{1}{3}-\frac{5}{12}\\=\frac{40}{12}+\frac{4}{12}-\frac{5}{12}\\=\frac{40+4-5}{12}\\=\frac{39}{12}\\=\frac{13}{4}\)
4. \(-\left(\frac{7}{-2}\right) +\left(\frac{-9}{-5}\right) -\left(\frac{12}{-11}\right)\\= \frac{7}{2}+ \frac{9}{5}+\frac{12}{11}\\=\frac{385}{110}+\frac{198}{110}+\frac{120}{110}\\=\frac{385+198+120}{110}\\=\frac{703}{110}\)
5. \(-\left(\frac{-8}{3}\right) +\left(\frac{3}{3}\right) -\left(\frac{4}{8}\right)\\= \frac{8}{3}+ \frac{3}{3}-\frac{4}{8}\\=\frac{8}{3}+\frac{1}{1}-\frac{1}{2}\\=\frac{16}{6}+\frac{6}{6}-\frac{3}{6}\\=\frac{16+6-3}{6}\\=\frac{19}{6}\)
6. \(+\left(\frac{6}{5}\right) -\left(\frac{-7}{-4}\right) -\left(\frac{5}{-4}\right)\\= \frac{6}{5}- \frac{7}{4}+\frac{5}{4}\\=\frac{24}{20}-\frac{35}{20}+\frac{25}{20}\\=\frac{24-35+25}{20}\\=\frac{14}{20}\\=\frac{7}{10}\)
7. \(-\left(\frac{-9}{-7}\right) -\left(\frac{10}{7}\right) +\left(\frac{-5}{2}\right)\\= \frac{-9}{7}- \frac{10}{7}-\frac{5}{2}\\=\frac{-18}{14}-\frac{20}{14}-\frac{35}{14}\\=\frac{-18-20-35}{14}\\=\frac{-73}{14}\)
8. \(+\left(\frac{5}{2}\right) +\left(\frac{-6}{-8}\right) -\left(\frac{-5}{12}\right)\\= \frac{5}{2}+ \frac{6}{8}+\frac{5}{12}\\=\frac{5}{2}+\frac{3}{4}+\frac{5}{12}\\=\frac{30}{12}+\frac{9}{12}+\frac{5}{12}\\=\frac{30+9+5}{12}\\=\frac{44}{12}\\=\frac{11}{3}\)
9. \(-\left(\frac{-10}{-7}\right) -\left(\frac{-6}{5}\right) +\left(\frac{-8}{-6}\right)\\= \frac{-10}{7}+ \frac{6}{5}+\frac{8}{6}\\=\frac{-10}{7}+\frac{6}{5}+\frac{4}{3}\\=\frac{-150}{105}+\frac{126}{105}+\frac{140}{105}\\=\frac{-150+126+140}{105}\\=\frac{116}{105}\)
10. \(-\left(\frac{7}{8}\right) +\left(\frac{-7}{8}\right) +\left(\frac{8}{2}\right)\\= \frac{-7}{8}- \frac{7}{8}+\frac{8}{2}\\=\frac{-7}{8}-\frac{7}{8}+\frac{4}{1}\\=\frac{-7-7+4}{8}\\=\frac{-10}{8}\\=\frac{-5}{4}\)
11. \(-\left(\frac{8}{5}\right) +\left(\frac{3}{-4}\right) -\left(\frac{6}{-5}\right)\\= \frac{-8}{5}- \frac{3}{4}+\frac{6}{5}\\=\frac{-32}{20}-\frac{15}{20}+\frac{24}{20}\\=\frac{-32-15+24}{20}\\=\frac{-23}{20}\)
12. \(+\left(\frac{2}{-3}\right) +\left(\frac{-2}{-6}\right) -\left(\frac{-2}{-7}\right)\\= \frac{-2}{3}+ \frac{2}{6}-\frac{2}{7}\\=\frac{-2}{3}+\frac{1}{3}-\frac{2}{7}\\=\frac{-14}{21}+\frac{7}{21}-\frac{6}{21}\\=\frac{-14+7-6}{21}\\=\frac{-13}{21}\)