Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{-3}\right) -\left(\frac{-7}{-7}\right) +\left(\frac{-3}{12}\right)\\= \frac{-10}{3}- \frac{7}{7}-\frac{3}{12}\\=\frac{-10}{3}-\frac{1}{1}-\frac{1}{4}\\=\frac{-40}{12}-\frac{12}{12}-\frac{3}{12}\\=\frac{-40-12-3}{12}\\=\frac{-55}{12}\)
2. \(+\left(\frac{6}{5}\right) -\left(\frac{-9}{-10}\right) +\left(\frac{-10}{10}\right)\\= \frac{6}{5}- \frac{9}{10}-\frac{10}{10}\\=\frac{6}{5}-\frac{9}{10}-\frac{1}{1}\\=\frac{12}{10}-\frac{9}{10}-\frac{10}{10}\\=\frac{12-9-10}{10}\\=\frac{-7}{10}\)
3. \(-\left(\frac{7}{3}\right) +\left(\frac{7}{5}\right) +\left(\frac{12}{7}\right)\\= \frac{-7}{3}+ \frac{7}{5}+\frac{12}{7}\\=\frac{-245}{105}+\frac{147}{105}+\frac{180}{105}\\=\frac{-245+147+180}{105}\\=\frac{82}{105}\)
4. \(-\left(\frac{9}{4}\right) +\left(\frac{-2}{-4}\right) -\left(\frac{8}{-9}\right)\\= \frac{-9}{4}+ \frac{2}{4}+\frac{8}{9}\\=\frac{-9}{4}+\frac{1}{2}+\frac{8}{9}\\=\frac{-81}{36}+\frac{18}{36}+\frac{32}{36}\\=\frac{-81+18+32}{36}\\=\frac{-31}{36}\)
5. \(+\left(\frac{4}{9}\right) -\left(\frac{-3}{-8}\right) -\left(\frac{11}{-7}\right)\\= \frac{4}{9}- \frac{3}{8}+\frac{11}{7}\\=\frac{224}{504}-\frac{189}{504}+\frac{792}{504}\\=\frac{224-189+792}{504}\\=\frac{827}{504}\)
6. \(+\left(\frac{6}{5}\right) -\left(\frac{7}{-10}\right) +\left(\frac{4}{-6}\right)\\= \frac{6}{5}+ \frac{7}{10}-\frac{4}{6}\\=\frac{6}{5}+\frac{7}{10}-\frac{2}{3}\\=\frac{36}{30}+\frac{21}{30}-\frac{20}{30}\\=\frac{36+21-20}{30}\\=\frac{37}{30}\)
7. \(-\left(\frac{8}{-9}\right) +\left(\frac{-3}{-7}\right) -\left(\frac{-11}{-9}\right)\\= \frac{8}{9}+ \frac{3}{7}-\frac{11}{9}\\=\frac{56}{63}+\frac{27}{63}-\frac{77}{63}\\=\frac{56+27-77}{63}\\=\frac{6}{63}\\=\frac{2}{21}\)
8. \(-\left(\frac{-2}{-3}\right) -\left(\frac{6}{5}\right) +\left(\frac{-8}{-7}\right)\\= \frac{-2}{3}- \frac{6}{5}+\frac{8}{7}\\=\frac{-70}{105}-\frac{126}{105}+\frac{120}{105}\\=\frac{-70-126+120}{105}\\=\frac{-76}{105}\)
9. \(+\left(\frac{7}{4}\right) -\left(\frac{5}{9}\right) +\left(\frac{-2}{6}\right)\\= \frac{7}{4}- \frac{5}{9}-\frac{2}{6}\\=\frac{7}{4}-\frac{5}{9}-\frac{1}{3}\\=\frac{63}{36}-\frac{20}{36}-\frac{12}{36}\\=\frac{63-20-12}{36}\\=\frac{31}{36}\)
10. \(+\left(\frac{-7}{-8}\right) +\left(\frac{-7}{-2}\right) -\left(\frac{11}{4}\right)\\= \frac{7}{8}+ \frac{7}{2}-\frac{11}{4}\\=\frac{7+7-11}{8}\\=\frac{3}{8}\)
11. \(+\left(\frac{-5}{-2}\right) +\left(\frac{2}{-10}\right) -\left(\frac{10}{9}\right)\\= \frac{5}{2}- \frac{2}{10}-\frac{10}{9}\\=\frac{5}{2}-\frac{1}{5}-\frac{10}{9}\\=\frac{225}{90}-\frac{18}{90}-\frac{100}{90}\\=\frac{225-18-100}{90}\\=\frac{107}{90}\)
12. \(-\left(\frac{-8}{9}\right) -\left(\frac{7}{-2}\right) -\left(\frac{-2}{2}\right)\\= \frac{8}{9}+ \frac{7}{2}+\frac{2}{2}\\=\frac{8}{9}+\frac{7}{2}+\frac{1}{1}\\=\frac{16}{18}+\frac{63}{18}+\frac{18}{18}\\=\frac{16+63+18}{18}\\=\frac{97}{18}\)