Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{-2}\right) +\left(\frac{-3}{7}\right) -\left(\frac{6}{11}\right)\\= \frac{9}{2}- \frac{3}{7}-\frac{6}{11}\\=\frac{693}{154}-\frac{66}{154}-\frac{84}{154}\\=\frac{693-66-84}{154}\\=\frac{543}{154}\)
2. \(-\left(\frac{-8}{9}\right) -\left(\frac{5}{6}\right) +\left(\frac{12}{4}\right)\\= \frac{8}{9}- \frac{5}{6}+\frac{12}{4}\\=\frac{8}{9}-\frac{5}{6}+\frac{3}{1}\\=\frac{16}{18}-\frac{15}{18}+\frac{54}{18}\\=\frac{16-15+54}{18}\\=\frac{55}{18}\)
3. \(-\left(\frac{2}{3}\right) -\left(\frac{8}{6}\right) +\left(\frac{-9}{-4}\right)\\= \frac{-2}{3}- \frac{8}{6}+\frac{9}{4}\\=\frac{-2}{3}-\frac{4}{3}+\frac{9}{4}\\=\frac{-8}{12}-\frac{16}{12}+\frac{27}{12}\\=\frac{-8-16+27}{12}\\=\frac{3}{12}\\=\frac{1}{4}\)
4. \(+\left(\frac{3}{2}\right) +\left(\frac{-9}{-4}\right) -\left(\frac{4}{-9}\right)\\= \frac{3}{2}+ \frac{9}{4}+\frac{4}{9}\\=\frac{54}{36}+\frac{81}{36}+\frac{16}{36}\\=\frac{54+81+16}{36}\\=\frac{151}{36}\)
5. \(+\left(\frac{-9}{-2}\right) +\left(\frac{4}{8}\right) -\left(\frac{-8}{-4}\right)\\= \frac{9}{2}+ \frac{4}{8}-\frac{8}{4}\\=\frac{9}{2}+\frac{1}{2}-\frac{2}{1}\\=\frac{9+1-2}{2}\\=\frac{8}{2}\\=\frac{4}{1}\)
6. \(+\left(\frac{-6}{-5}\right) +\left(\frac{7}{2}\right) +\left(\frac{4}{-12}\right)\\= \frac{6}{5}+ \frac{7}{2}-\frac{4}{12}\\=\frac{6}{5}+\frac{7}{2}-\frac{1}{3}\\=\frac{36}{30}+\frac{105}{30}-\frac{10}{30}\\=\frac{36+105-10}{30}\\=\frac{131}{30}\)
7. \(+\left(\frac{-3}{-2}\right) -\left(\frac{-8}{5}\right) -\left(\frac{-10}{11}\right)\\= \frac{3}{2}+ \frac{8}{5}+\frac{10}{11}\\=\frac{165}{110}+\frac{176}{110}+\frac{100}{110}\\=\frac{165+176+100}{110}\\=\frac{441}{110}\)
8. \(+\left(\frac{-9}{-7}\right) -\left(\frac{-9}{10}\right) +\left(\frac{-11}{2}\right)\\= \frac{9}{7}+ \frac{9}{10}-\frac{11}{2}\\=\frac{90}{70}+\frac{63}{70}-\frac{385}{70}\\=\frac{90+63-385}{70}\\=\frac{-232}{70}\\=\frac{-116}{35}\)
9. \(-\left(\frac{4}{7}\right) +\left(\frac{10}{-3}\right) -\left(\frac{5}{9}\right)\\= \frac{-4}{7}- \frac{10}{3}-\frac{5}{9}\\=\frac{-36}{63}-\frac{210}{63}-\frac{35}{63}\\=\frac{-36-210-35}{63}\\=\frac{-281}{63}\)
10. \(-\left(\frac{7}{8}\right) +\left(\frac{4}{-9}\right) -\left(\frac{4}{-2}\right)\\= \frac{-7}{8}- \frac{4}{9}+\frac{4}{2}\\=\frac{-7}{8}-\frac{4}{9}+\frac{2}{1}\\=\frac{-63}{72}-\frac{32}{72}+\frac{144}{72}\\=\frac{-63-32+144}{72}\\=\frac{49}{72}\)
11. \(-\left(\frac{9}{-5}\right) -\left(\frac{-10}{-7}\right) +\left(\frac{-10}{10}\right)\\= \frac{9}{5}- \frac{10}{7}-\frac{10}{10}\\=\frac{9}{5}-\frac{10}{7}-\frac{1}{1}\\=\frac{63}{35}-\frac{50}{35}-\frac{35}{35}\\=\frac{63-50-35}{35}\\=\frac{-22}{35}\)
12. \(+\left(\frac{7}{-3}\right) +\left(\frac{6}{-4}\right) +\left(\frac{11}{-7}\right)\\= \frac{-7}{3}- \frac{6}{4}-\frac{11}{7}\\=\frac{-7}{3}-\frac{3}{2}-\frac{11}{7}\\=\frac{-98}{42}-\frac{63}{42}-\frac{66}{42}\\=\frac{-98-63-66}{42}\\=\frac{-227}{42}\)