Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{6}{-5}\right) +\left(\frac{-3}{7}\right) +\left(\frac{2}{3}\right)\\= \frac{6}{5}- \frac{3}{7}+\frac{2}{3}\\=\frac{126}{105}-\frac{45}{105}+\frac{70}{105}\\=\frac{126-45+70}{105}\\=\frac{151}{105}\)
2. \(-\left(\frac{7}{2}\right) -\left(\frac{-3}{7}\right) +\left(\frac{-3}{-12}\right)\\= \frac{-7}{2}+ \frac{3}{7}+\frac{3}{12}\\=\frac{-7}{2}+\frac{3}{7}+\frac{1}{4}\\=\frac{-98}{28}+\frac{12}{28}+\frac{7}{28}\\=\frac{-98+12+7}{28}\\=\frac{-79}{28}\)
3. \(+\left(\frac{3}{2}\right) -\left(\frac{-2}{-8}\right) +\left(\frac{11}{12}\right)\\= \frac{3}{2}- \frac{2}{8}+\frac{11}{12}\\=\frac{3}{2}-\frac{1}{4}+\frac{11}{12}\\=\frac{18}{12}-\frac{3}{12}+\frac{11}{12}\\=\frac{18-3+11}{12}\\=\frac{26}{12}\\=\frac{13}{6}\)
4. \(-\left(\frac{-10}{-3}\right) +\left(\frac{-4}{10}\right) -\left(\frac{-12}{12}\right)\\= \frac{-10}{3}- \frac{4}{10}+\frac{12}{12}\\=\frac{-10}{3}-\frac{2}{5}+\frac{1}{1}\\=\frac{-50}{15}-\frac{6}{15}+\frac{15}{15}\\=\frac{-50-6+15}{15}\\=\frac{-41}{15}\)
5. \(-\left(\frac{8}{9}\right) +\left(\frac{2}{9}\right) +\left(\frac{9}{8}\right)\\= \frac{-8}{9}+ \frac{2}{9}+\frac{9}{8}\\=\frac{-64}{72}+\frac{16}{72}+\frac{81}{72}\\=\frac{-64+16+81}{72}\\=\frac{33}{72}\\=\frac{11}{24}\)
6. \(-\left(\frac{-4}{3}\right) -\left(\frac{6}{-7}\right) +\left(\frac{-12}{10}\right)\\= \frac{4}{3}+ \frac{6}{7}-\frac{12}{10}\\=\frac{4}{3}+\frac{6}{7}-\frac{6}{5}\\=\frac{140}{105}+\frac{90}{105}-\frac{126}{105}\\=\frac{140+90-126}{105}\\=\frac{104}{105}\)
7. \(+\left(\frac{-10}{-7}\right) -\left(\frac{-6}{6}\right) -\left(\frac{2}{12}\right)\\= \frac{10}{7}+ \frac{6}{6}-\frac{2}{12}\\=\frac{10}{7}+\frac{1}{1}-\frac{1}{6}\\=\frac{60}{42}+\frac{42}{42}-\frac{7}{42}\\=\frac{60+42-7}{42}\\=\frac{95}{42}\)
8. \(+\left(\frac{-9}{2}\right) -\left(\frac{2}{5}\right) -\left(\frac{-4}{6}\right)\\= \frac{-9}{2}- \frac{2}{5}+\frac{4}{6}\\=\frac{-9}{2}-\frac{2}{5}+\frac{2}{3}\\=\frac{-135}{30}-\frac{12}{30}+\frac{20}{30}\\=\frac{-135-12+20}{30}\\=\frac{-127}{30}\)
9. \(+\left(\frac{-10}{3}\right) +\left(\frac{10}{3}\right) +\left(\frac{-2}{-5}\right)\\= \frac{-10}{3}+ \frac{10}{3}+\frac{2}{5}\\=\frac{-50}{15}+\frac{50}{15}+\frac{6}{15}\\=\frac{-50+50+6}{15}\\=\frac{6}{15}\\=\frac{2}{5}\)
10. \(+\left(\frac{5}{6}\right) +\left(\frac{7}{-3}\right) +\left(\frac{-6}{-7}\right)\\= \frac{5}{6}- \frac{7}{3}+\frac{6}{7}\\=\frac{35}{42}-\frac{98}{42}+\frac{36}{42}\\=\frac{35-98+36}{42}\\=\frac{-27}{42}\\=\frac{-9}{14}\)
11. \(+\left(\frac{-9}{-2}\right) -\left(\frac{9}{9}\right) +\left(\frac{-8}{6}\right)\\= \frac{9}{2}- \frac{9}{9}-\frac{8}{6}\\=\frac{9}{2}-\frac{1}{1}-\frac{4}{3}\\=\frac{27}{6}-\frac{6}{6}-\frac{8}{6}\\=\frac{27-6-8}{6}\\=\frac{13}{6}\)
12. \(-\left(\frac{-3}{4}\right) -\left(\frac{-10}{-3}\right) -\left(\frac{5}{-3}\right)\\= \frac{3}{4}- \frac{10}{3}+\frac{5}{3}\\=\frac{9}{12}-\frac{40}{12}+\frac{20}{12}\\=\frac{9-40+20}{12}\\=\frac{-11}{12}\)