Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{8}{9}\right) -\left(\frac{9}{-4}\right) +\left(\frac{-3}{-4}\right)\\= \frac{8}{9}+ \frac{9}{4}+\frac{3}{4}\\=\frac{32}{36}+\frac{81}{36}+\frac{27}{36}\\=\frac{32+81+27}{36}\\=\frac{140}{36}\\=\frac{35}{9}\)
2. \(+\left(\frac{3}{-8}\right) -\left(\frac{6}{8}\right) +\left(\frac{-2}{9}\right)\\= \frac{-3}{8}- \frac{6}{8}-\frac{2}{9}\\=\frac{-3}{8}-\frac{3}{4}-\frac{2}{9}\\=\frac{-27}{72}-\frac{54}{72}-\frac{16}{72}\\=\frac{-27-54-16}{72}\\=\frac{-97}{72}\)
3. \(+\left(\frac{-9}{7}\right) +\left(\frac{2}{2}\right) -\left(\frac{-12}{11}\right)\\= \frac{-9}{7}+ \frac{2}{2}+\frac{12}{11}\\=\frac{-9}{7}+\frac{1}{1}+\frac{12}{11}\\=\frac{-99}{77}+\frac{77}{77}+\frac{84}{77}\\=\frac{-99+77+84}{77}\\=\frac{62}{77}\)
4. \(+\left(\frac{-10}{7}\right) -\left(\frac{8}{-4}\right) -\left(\frac{-8}{-9}\right)\\= \frac{-10}{7}+ \frac{8}{4}-\frac{8}{9}\\=\frac{-10}{7}+\frac{2}{1}-\frac{8}{9}\\=\frac{-90}{63}+\frac{126}{63}-\frac{56}{63}\\=\frac{-90+126-56}{63}\\=\frac{-20}{63}\)
5. \(-\left(\frac{-3}{2}\right) -\left(\frac{4}{-5}\right) +\left(\frac{7}{11}\right)\\= \frac{3}{2}+ \frac{4}{5}+\frac{7}{11}\\=\frac{165}{110}+\frac{88}{110}+\frac{70}{110}\\=\frac{165+88+70}{110}\\=\frac{323}{110}\)
6. \(-\left(\frac{-3}{-2}\right) -\left(\frac{9}{4}\right) -\left(\frac{6}{-8}\right)\\= \frac{-3}{2}- \frac{9}{4}+\frac{6}{8}\\=\frac{-3}{2}-\frac{9}{4}+\frac{3}{4}\\=\frac{-6}{4}-\frac{9}{4}+\frac{3}{4}\\=\frac{-6-9+3}{4}\\=\frac{-12}{4}\\=\frac{-3}{1}\)
7. \(+\left(\frac{5}{2}\right) +\left(\frac{-2}{-2}\right) +\left(\frac{3}{11}\right)\\= \frac{5}{2}+ \frac{2}{2}+\frac{3}{11}\\=\frac{5}{2}+\frac{1}{1}+\frac{3}{11}\\=\frac{55}{22}+\frac{22}{22}+\frac{6}{22}\\=\frac{55+22+6}{22}\\=\frac{83}{22}\)
8. \(-\left(\frac{-7}{-3}\right) -\left(\frac{5}{-7}\right) +\left(\frac{4}{8}\right)\\= \frac{-7}{3}+ \frac{5}{7}+\frac{4}{8}\\=\frac{-7}{3}+\frac{5}{7}+\frac{1}{2}\\=\frac{-98}{42}+\frac{30}{42}+\frac{21}{42}\\=\frac{-98+30+21}{42}\\=\frac{-47}{42}\)
9. \(-\left(\frac{10}{-7}\right) +\left(\frac{-10}{7}\right) -\left(\frac{-9}{-10}\right)\\= \frac{10}{7}- \frac{10}{7}-\frac{9}{10}\\=\frac{100}{70}-\frac{100}{70}-\frac{63}{70}\\=\frac{100-100-63}{70}\\=\frac{-63}{70}\\=\frac{-9}{10}\)
10. \(+\left(\frac{-9}{-5}\right) +\left(\frac{5}{-4}\right) +\left(\frac{-4}{-7}\right)\\= \frac{9}{5}- \frac{5}{4}+\frac{4}{7}\\=\frac{252}{140}-\frac{175}{140}+\frac{80}{140}\\=\frac{252-175+80}{140}\\=\frac{157}{140}\)
11. \(-\left(\frac{-7}{5}\right) -\left(\frac{7}{5}\right) +\left(\frac{-2}{3}\right)\\= \frac{7}{5}- \frac{7}{5}-\frac{2}{3}\\=\frac{21}{15}-\frac{21}{15}-\frac{10}{15}\\=\frac{21-21-10}{15}\\=\frac{-10}{15}\\=\frac{-2}{3}\)
12. \(+\left(\frac{5}{-8}\right) +\left(\frac{-5}{9}\right) +\left(\frac{-3}{7}\right)\\= \frac{-5}{8}- \frac{5}{9}-\frac{3}{7}\\=\frac{-315}{504}-\frac{280}{504}-\frac{216}{504}\\=\frac{-315-280-216}{504}\\=\frac{-811}{504}\)