Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{8}\right) +\left(\frac{-2}{10}\right) +\left(\frac{8}{11}\right)\\= \frac{-3}{8}- \frac{2}{10}+\frac{8}{11}\\=\frac{-3}{8}-\frac{1}{5}+\frac{8}{11}\\=\frac{-165}{440}-\frac{88}{440}+\frac{320}{440}\\=\frac{-165-88+320}{440}\\=\frac{67}{440}\)
2. \(-\left(\frac{5}{9}\right) +\left(\frac{7}{5}\right) +\left(\frac{-5}{-11}\right)\\= \frac{-5}{9}+ \frac{7}{5}+\frac{5}{11}\\=\frac{-275}{495}+\frac{693}{495}+\frac{225}{495}\\=\frac{-275+693+225}{495}\\=\frac{643}{495}\)
3. \(+\left(\frac{-10}{7}\right) -\left(\frac{-6}{-10}\right) -\left(\frac{10}{-12}\right)\\= \frac{-10}{7}- \frac{6}{10}+\frac{10}{12}\\=\frac{-10}{7}-\frac{3}{5}+\frac{5}{6}\\=\frac{-300}{210}-\frac{126}{210}+\frac{175}{210}\\=\frac{-300-126+175}{210}\\=\frac{-251}{210}\)
4. \(+\left(\frac{-5}{6}\right) -\left(\frac{2}{8}\right) -\left(\frac{-10}{-11}\right)\\= \frac{-5}{6}- \frac{2}{8}-\frac{10}{11}\\=\frac{-5}{6}-\frac{1}{4}-\frac{10}{11}\\=\frac{-110}{132}-\frac{33}{132}-\frac{120}{132}\\=\frac{-110-33-120}{132}\\=\frac{-263}{132}\)
5. \(+\left(\frac{-4}{-3}\right) +\left(\frac{-2}{2}\right) -\left(\frac{-2}{-10}\right)\\= \frac{4}{3}- \frac{2}{2}-\frac{2}{10}\\=\frac{4}{3}-\frac{1}{1}-\frac{1}{5}\\=\frac{20}{15}-\frac{15}{15}-\frac{3}{15}\\=\frac{20-15-3}{15}\\=\frac{2}{15}\)
6. \(+\left(\frac{6}{5}\right) -\left(\frac{-5}{-7}\right) -\left(\frac{-7}{-12}\right)\\= \frac{6}{5}- \frac{5}{7}-\frac{7}{12}\\=\frac{504}{420}-\frac{300}{420}-\frac{245}{420}\\=\frac{504-300-245}{420}\\=\frac{-41}{420}\)
7. \(-\left(\frac{5}{2}\right) -\left(\frac{8}{-8}\right) +\left(\frac{3}{-2}\right)\\= \frac{-5}{2}+ \frac{8}{8}-\frac{3}{2}\\=\frac{-5}{2}+\frac{1}{1}-\frac{3}{2}\\=\frac{-5+1-3}{2}\\=\frac{-7}{2}\)
8. \(+\left(\frac{7}{-6}\right) -\left(\frac{-2}{-9}\right) +\left(\frac{-12}{12}\right)\\= \frac{-7}{6}- \frac{2}{9}-\frac{12}{12}\\=\frac{-7}{6}-\frac{2}{9}-\frac{1}{1}\\=\frac{-21}{18}-\frac{4}{18}-\frac{18}{18}\\=\frac{-21-4-18}{18}\\=\frac{-43}{18}\)
9. \(-\left(\frac{6}{7}\right) -\left(\frac{-9}{9}\right) -\left(\frac{-8}{-11}\right)\\= \frac{-6}{7}+ \frac{9}{9}-\frac{8}{11}\\=\frac{-6}{7}+\frac{1}{1}-\frac{8}{11}\\=\frac{-66}{77}+\frac{77}{77}-\frac{56}{77}\\=\frac{-66+77-56}{77}\\=\frac{-45}{77}\)
10. \(-\left(\frac{-7}{4}\right) -\left(\frac{-7}{-9}\right) +\left(\frac{5}{8}\right)\\= \frac{7}{4}- \frac{7}{9}+\frac{5}{8}\\=\frac{126}{72}-\frac{56}{72}+\frac{45}{72}\\=\frac{126-56+45}{72}\\=\frac{115}{72}\)
11. \(+\left(\frac{5}{-7}\right) -\left(\frac{-10}{-5}\right) +\left(\frac{4}{-8}\right)\\= \frac{-5}{7}- \frac{10}{5}-\frac{4}{8}\\=\frac{-5}{7}-\frac{2}{1}-\frac{1}{2}\\=\frac{-10}{14}-\frac{28}{14}-\frac{7}{14}\\=\frac{-10-28-7}{14}\\=\frac{-45}{14}\)
12. \(+\left(\frac{6}{5}\right) -\left(\frac{6}{-7}\right) +\left(\frac{-9}{4}\right)\\= \frac{6}{5}+ \frac{6}{7}-\frac{9}{4}\\=\frac{168}{140}+\frac{120}{140}-\frac{315}{140}\\=\frac{168+120-315}{140}\\=\frac{-27}{140}\)