Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{10}{7}\right) -\left(\frac{7}{-3}\right) -\left(\frac{-12}{6}\right)\\= \frac{10}{7}+ \frac{7}{3}+\frac{12}{6}\\=\frac{10}{7}+\frac{7}{3}+\frac{2}{1}\\=\frac{30}{21}+\frac{49}{21}+\frac{42}{21}\\=\frac{30+49+42}{21}\\=\frac{121}{21}\)
2. \(+\left(\frac{6}{-5}\right) -\left(\frac{4}{7}\right) -\left(\frac{11}{6}\right)\\= \frac{-6}{5}- \frac{4}{7}-\frac{11}{6}\\=\frac{-252}{210}-\frac{120}{210}-\frac{385}{210}\\=\frac{-252-120-385}{210}\\=\frac{-757}{210}\)
3. \(-\left(\frac{8}{-7}\right) -\left(\frac{9}{-10}\right) +\left(\frac{5}{10}\right)\\= \frac{8}{7}+ \frac{9}{10}+\frac{5}{10}\\=\frac{8}{7}+\frac{9}{10}+\frac{1}{2}\\=\frac{80}{70}+\frac{63}{70}+\frac{35}{70}\\=\frac{80+63+35}{70}\\=\frac{178}{70}\\=\frac{89}{35}\)
4. \(-\left(\frac{10}{-7}\right) +\left(\frac{-4}{8}\right) -\left(\frac{11}{3}\right)\\= \frac{10}{7}- \frac{4}{8}-\frac{11}{3}\\=\frac{10}{7}-\frac{1}{2}-\frac{11}{3}\\=\frac{60}{42}-\frac{21}{42}-\frac{154}{42}\\=\frac{60-21-154}{42}\\=\frac{-115}{42}\)
5. \(+\left(\frac{2}{-5}\right) +\left(\frac{8}{10}\right) -\left(\frac{4}{-7}\right)\\= \frac{-2}{5}+ \frac{8}{10}+\frac{4}{7}\\=\frac{-2}{5}+\frac{4}{5}+\frac{4}{7}\\=\frac{-14}{35}+\frac{28}{35}+\frac{20}{35}\\=\frac{-14+28+20}{35}\\=\frac{34}{35}\)
6. \(-\left(\frac{9}{-2}\right) -\left(\frac{-10}{4}\right) -\left(\frac{-6}{-11}\right)\\= \frac{9}{2}+ \frac{10}{4}-\frac{6}{11}\\=\frac{9}{2}+\frac{5}{2}-\frac{6}{11}\\=\frac{99}{22}+\frac{55}{22}-\frac{12}{22}\\=\frac{99+55-12}{22}\\=\frac{142}{22}\\=\frac{71}{11}\)
7. \(-\left(\frac{9}{-2}\right) -\left(\frac{-5}{4}\right) +\left(\frac{6}{-11}\right)\\= \frac{9}{2}+ \frac{5}{4}-\frac{6}{11}\\=\frac{198}{44}+\frac{55}{44}-\frac{24}{44}\\=\frac{198+55-24}{44}\\=\frac{229}{44}\)
8. \(-\left(\frac{10}{-3}\right) -\left(\frac{-7}{-4}\right) -\left(\frac{8}{-9}\right)\\= \frac{10}{3}- \frac{7}{4}+\frac{8}{9}\\=\frac{120}{36}-\frac{63}{36}+\frac{32}{36}\\=\frac{120-63+32}{36}\\=\frac{89}{36}\)
9. \(-\left(\frac{-9}{-7}\right) +\left(\frac{-6}{2}\right) -\left(\frac{9}{5}\right)\\= \frac{-9}{7}- \frac{6}{2}-\frac{9}{5}\\=\frac{-9}{7}-\frac{3}{1}-\frac{9}{5}\\=\frac{-45}{35}-\frac{105}{35}-\frac{63}{35}\\=\frac{-45-105-63}{35}\\=\frac{-213}{35}\)
10. \(+\left(\frac{8}{-5}\right) -\left(\frac{6}{-6}\right) -\left(\frac{-9}{3}\right)\\= \frac{-8}{5}+ \frac{6}{6}+\frac{9}{3}\\=\frac{-8}{5}+\frac{1}{1}+\frac{3}{1}\\=\frac{-8+1+3}{5}\\=\frac{-4}{5}\)
11. \(-\left(\frac{-3}{-5}\right) -\left(\frac{8}{6}\right) -\left(\frac{-12}{6}\right)\\= \frac{-3}{5}- \frac{8}{6}+\frac{12}{6}\\=\frac{-3}{5}-\frac{4}{3}+\frac{2}{1}\\=\frac{-9}{15}-\frac{20}{15}+\frac{30}{15}\\=\frac{-9-20+30}{15}\\=\frac{1}{15}\)
12. \(+\left(\frac{10}{-7}\right) +\left(\frac{4}{-7}\right) -\left(\frac{-8}{-9}\right)\\= \frac{-10}{7}- \frac{4}{7}-\frac{8}{9}\\=\frac{-90}{63}-\frac{36}{63}-\frac{56}{63}\\=\frac{-90-36-56}{63}\\=\frac{-182}{63}\\=\frac{-26}{9}\)