Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-8}{3}\right) -\left(\frac{5}{-4}\right) -\left(\frac{-8}{6}\right)\\= \frac{8}{3}+ \frac{5}{4}+\frac{8}{6}\\=\frac{8}{3}+\frac{5}{4}+\frac{4}{3}\\=\frac{32}{12}+\frac{15}{12}+\frac{16}{12}\\=\frac{32+15+16}{12}\\=\frac{63}{12}\\=\frac{21}{4}\)
2. \(-\left(\frac{-6}{7}\right) -\left(\frac{-10}{-8}\right) +\left(\frac{-2}{10}\right)\\= \frac{6}{7}- \frac{10}{8}-\frac{2}{10}\\=\frac{6}{7}-\frac{5}{4}-\frac{1}{5}\\=\frac{120}{140}-\frac{175}{140}-\frac{28}{140}\\=\frac{120-175-28}{140}\\=\frac{-83}{140}\)
3. \(-\left(\frac{2}{-9}\right) -\left(\frac{-5}{4}\right) -\left(\frac{2}{-2}\right)\\= \frac{2}{9}+ \frac{5}{4}+\frac{2}{2}\\=\frac{2}{9}+\frac{5}{4}+\frac{1}{1}\\=\frac{8}{36}+\frac{45}{36}+\frac{36}{36}\\=\frac{8+45+36}{36}\\=\frac{89}{36}\)
4. \(-\left(\frac{4}{3}\right) -\left(\frac{6}{2}\right) +\left(\frac{9}{-6}\right)\\= \frac{-4}{3}- \frac{6}{2}-\frac{9}{6}\\=\frac{-4}{3}-\frac{3}{1}-\frac{3}{2}\\=\frac{-8}{6}-\frac{18}{6}-\frac{9}{6}\\=\frac{-8-18-9}{6}\\=\frac{-35}{6}\)
5. \(-\left(\frac{9}{2}\right) +\left(\frac{6}{6}\right) +\left(\frac{4}{11}\right)\\= \frac{-9}{2}+ \frac{6}{6}+\frac{4}{11}\\=\frac{-9}{2}+\frac{1}{1}+\frac{4}{11}\\=\frac{-99}{22}+\frac{22}{22}+\frac{8}{22}\\=\frac{-99+22+8}{22}\\=\frac{-69}{22}\)
6. \(-\left(\frac{6}{7}\right) +\left(\frac{7}{7}\right) +\left(\frac{-11}{5}\right)\\= \frac{-6}{7}+ \frac{7}{7}-\frac{11}{5}\\=\frac{-6}{7}+\frac{1}{1}-\frac{11}{5}\\=\frac{-30}{35}+\frac{35}{35}-\frac{77}{35}\\=\frac{-30+35-77}{35}\\=\frac{-72}{35}\)
7. \(-\left(\frac{-9}{4}\right) +\left(\frac{6}{-3}\right) +\left(\frac{6}{8}\right)\\= \frac{9}{4}- \frac{6}{3}+\frac{6}{8}\\=\frac{9}{4}-\frac{2}{1}+\frac{3}{4}\\=\frac{9-2+3}{4}\\=\frac{10}{4}\\=\frac{5}{2}\)
8. \(-\left(\frac{5}{-2}\right) +\left(\frac{-8}{-3}\right) +\left(\frac{-8}{4}\right)\\= \frac{5}{2}+ \frac{8}{3}-\frac{8}{4}\\=\frac{5}{2}+\frac{8}{3}-\frac{2}{1}\\=\frac{15}{6}+\frac{16}{6}-\frac{12}{6}\\=\frac{15+16-12}{6}\\=\frac{19}{6}\)
9. \(-\left(\frac{-7}{6}\right) +\left(\frac{-3}{6}\right) -\left(\frac{5}{-3}\right)\\= \frac{7}{6}- \frac{3}{6}+\frac{5}{3}\\=\frac{7}{6}-\frac{1}{2}+\frac{5}{3}\\=\frac{7-1+5}{6}\\=\frac{11}{6}\)
10. \(+\left(\frac{3}{7}\right) +\left(\frac{-3}{-9}\right) +\left(\frac{-7}{11}\right)\\= \frac{3}{7}+ \frac{3}{9}-\frac{7}{11}\\=\frac{3}{7}+\frac{1}{3}-\frac{7}{11}\\=\frac{99}{231}+\frac{77}{231}-\frac{147}{231}\\=\frac{99+77-147}{231}\\=\frac{29}{231}\)
11. \(-\left(\frac{4}{3}\right) +\left(\frac{3}{-2}\right) -\left(\frac{-11}{3}\right)\\= \frac{-4}{3}- \frac{3}{2}+\frac{11}{3}\\=\frac{-8}{6}-\frac{9}{6}+\frac{22}{6}\\=\frac{-8-9+22}{6}\\=\frac{5}{6}\)
12. \(+\left(\frac{-9}{7}\right) -\left(\frac{-9}{2}\right) -\left(\frac{-3}{-4}\right)\\= \frac{-9}{7}+ \frac{9}{2}-\frac{3}{4}\\=\frac{-36}{28}+\frac{126}{28}-\frac{21}{28}\\=\frac{-36+126-21}{28}\\=\frac{69}{28}\)