Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{7}\right) -\left(\frac{5}{2}\right) +\left(\frac{-10}{-11}\right)\\= \frac{-6}{7}- \frac{5}{2}+\frac{10}{11}\\=\frac{-132}{154}-\frac{385}{154}+\frac{140}{154}\\=\frac{-132-385+140}{154}\\=\frac{-377}{154}\)
2. \(+\left(\frac{5}{-6}\right) -\left(\frac{10}{9}\right) -\left(\frac{-5}{8}\right)\\= \frac{-5}{6}- \frac{10}{9}+\frac{5}{8}\\=\frac{-60}{72}-\frac{80}{72}+\frac{45}{72}\\=\frac{-60-80+45}{72}\\=\frac{-95}{72}\)
3. \(+\left(\frac{6}{-5}\right) -\left(\frac{3}{-4}\right) +\left(\frac{-2}{-12}\right)\\= \frac{-6}{5}+ \frac{3}{4}+\frac{2}{12}\\=\frac{-6}{5}+\frac{3}{4}+\frac{1}{6}\\=\frac{-72}{60}+\frac{45}{60}+\frac{10}{60}\\=\frac{-72+45+10}{60}\\=\frac{-17}{60}\)
4. \(+\left(\frac{-2}{3}\right) +\left(\frac{8}{8}\right) +\left(\frac{7}{-5}\right)\\= \frac{-2}{3}+ \frac{8}{8}-\frac{7}{5}\\=\frac{-2}{3}+\frac{1}{1}-\frac{7}{5}\\=\frac{-10}{15}+\frac{15}{15}-\frac{21}{15}\\=\frac{-10+15-21}{15}\\=\frac{-16}{15}\)
5. \(-\left(\frac{-9}{2}\right) +\left(\frac{2}{-5}\right) -\left(\frac{-9}{5}\right)\\= \frac{9}{2}- \frac{2}{5}+\frac{9}{5}\\=\frac{45}{10}-\frac{4}{10}+\frac{18}{10}\\=\frac{45-4+18}{10}\\=\frac{59}{10}\)
6. \(-\left(\frac{9}{-4}\right) +\left(\frac{-8}{5}\right) +\left(\frac{9}{-7}\right)\\= \frac{9}{4}- \frac{8}{5}-\frac{9}{7}\\=\frac{315}{140}-\frac{224}{140}-\frac{180}{140}\\=\frac{315-224-180}{140}\\=\frac{-89}{140}\)
7. \(-\left(\frac{-7}{5}\right) +\left(\frac{8}{-7}\right) -\left(\frac{-4}{-2}\right)\\= \frac{7}{5}- \frac{8}{7}-\frac{4}{2}\\=\frac{7}{5}-\frac{8}{7}-\frac{2}{1}\\=\frac{49}{35}-\frac{40}{35}-\frac{70}{35}\\=\frac{49-40-70}{35}\\=\frac{-61}{35}\)
8. \(+\left(\frac{5}{-2}\right) +\left(\frac{6}{-7}\right) +\left(\frac{7}{-3}\right)\\= \frac{-5}{2}- \frac{6}{7}-\frac{7}{3}\\=\frac{-105}{42}-\frac{36}{42}-\frac{98}{42}\\=\frac{-105-36-98}{42}\\=\frac{-239}{42}\)
9. \(+\left(\frac{-9}{7}\right) +\left(\frac{2}{-4}\right) +\left(\frac{11}{-3}\right)\\= \frac{-9}{7}- \frac{2}{4}-\frac{11}{3}\\=\frac{-9}{7}-\frac{1}{2}-\frac{11}{3}\\=\frac{-54}{42}-\frac{21}{42}-\frac{154}{42}\\=\frac{-54-21-154}{42}\\=\frac{-229}{42}\)
10. \(-\left(\frac{-7}{8}\right) -\left(\frac{10}{-9}\right) -\left(\frac{-7}{10}\right)\\= \frac{7}{8}+ \frac{10}{9}+\frac{7}{10}\\=\frac{315}{360}+\frac{400}{360}+\frac{252}{360}\\=\frac{315+400+252}{360}\\=\frac{967}{360}\)
11. \(+\left(\frac{7}{5}\right) -\left(\frac{5}{4}\right) +\left(\frac{-12}{-3}\right)\\= \frac{7}{5}- \frac{5}{4}+\frac{12}{3}\\=\frac{7}{5}-\frac{5}{4}+\frac{4}{1}\\=\frac{28}{20}-\frac{25}{20}+\frac{80}{20}\\=\frac{28-25+80}{20}\\=\frac{83}{20}\)
12. \(+\left(\frac{-3}{-2}\right) -\left(\frac{9}{5}\right) -\left(\frac{12}{7}\right)\\= \frac{3}{2}- \frac{9}{5}-\frac{12}{7}\\=\frac{105}{70}-\frac{126}{70}-\frac{120}{70}\\=\frac{105-126-120}{70}\\=\frac{-141}{70}\)