Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{-5}\right) -\left(\frac{-9}{9}\right) -\left(\frac{-5}{2}\right)\\= \frac{-2}{5}+ \frac{9}{9}+\frac{5}{2}\\=\frac{-2}{5}+\frac{1}{1}+\frac{5}{2}\\=\frac{-4}{10}+\frac{10}{10}+\frac{25}{10}\\=\frac{-4+10+25}{10}\\=\frac{31}{10}\)
2. \(+\left(\frac{-9}{2}\right) +\left(\frac{7}{5}\right) -\left(\frac{3}{-4}\right)\\= \frac{-9}{2}+ \frac{7}{5}+\frac{3}{4}\\=\frac{-90}{20}+\frac{28}{20}+\frac{15}{20}\\=\frac{-90+28+15}{20}\\=\frac{-47}{20}\)
3. \(+\left(\frac{6}{7}\right) +\left(\frac{-3}{10}\right) -\left(\frac{12}{-4}\right)\\= \frac{6}{7}- \frac{3}{10}+\frac{12}{4}\\=\frac{6}{7}-\frac{3}{10}+\frac{3}{1}\\=\frac{60}{70}-\frac{21}{70}+\frac{210}{70}\\=\frac{60-21+210}{70}\\=\frac{249}{70}\)
4. \(+\left(\frac{8}{-3}\right) +\left(\frac{-3}{-3}\right) -\left(\frac{8}{-10}\right)\\= \frac{-8}{3}+ \frac{3}{3}+\frac{8}{10}\\=\frac{-8}{3}+\frac{1}{1}+\frac{4}{5}\\=\frac{-40}{15}+\frac{15}{15}+\frac{12}{15}\\=\frac{-40+15+12}{15}\\=\frac{-13}{15}\)
5. \(+\left(\frac{-9}{-2}\right) -\left(\frac{-7}{-3}\right) -\left(\frac{-9}{-10}\right)\\= \frac{9}{2}- \frac{7}{3}-\frac{9}{10}\\=\frac{135}{30}-\frac{70}{30}-\frac{27}{30}\\=\frac{135-70-27}{30}\\=\frac{38}{30}\\=\frac{19}{15}\)
6. \(+\left(\frac{4}{-9}\right) -\left(\frac{-5}{-6}\right) +\left(\frac{-3}{-11}\right)\\= \frac{-4}{9}- \frac{5}{6}+\frac{3}{11}\\=\frac{-88}{198}-\frac{165}{198}+\frac{54}{198}\\=\frac{-88-165+54}{198}\\=\frac{-199}{198}\)
7. \(-\left(\frac{-4}{5}\right) +\left(\frac{6}{-7}\right) -\left(\frac{10}{-12}\right)\\= \frac{4}{5}- \frac{6}{7}+\frac{10}{12}\\=\frac{4}{5}-\frac{6}{7}+\frac{5}{6}\\=\frac{168}{210}-\frac{180}{210}+\frac{175}{210}\\=\frac{168-180+175}{210}\\=\frac{163}{210}\)
8. \(+\left(\frac{9}{2}\right) +\left(\frac{9}{-3}\right) +\left(\frac{-7}{8}\right)\\= \frac{9}{2}- \frac{9}{3}-\frac{7}{8}\\=\frac{9}{2}-\frac{3}{1}-\frac{7}{8}\\=\frac{36}{8}-\frac{24}{8}-\frac{7}{8}\\=\frac{36-24-7}{8}\\=\frac{5}{8}\)
9. \(-\left(\frac{-5}{9}\right) +\left(\frac{-3}{3}\right) -\left(\frac{4}{-4}\right)\\= \frac{5}{9}- \frac{3}{3}+\frac{4}{4}\\=\frac{5}{9}-\frac{1}{1}+\frac{1}{1}\\=\frac{5-1+1}{9}\\=\frac{5}{9}\)
10. \(-\left(\frac{-2}{-5}\right) -\left(\frac{6}{6}\right) +\left(\frac{6}{-7}\right)\\= \frac{-2}{5}- \frac{6}{6}-\frac{6}{7}\\=\frac{-2}{5}-\frac{1}{1}-\frac{6}{7}\\=\frac{-14}{35}-\frac{35}{35}-\frac{30}{35}\\=\frac{-14-35-30}{35}\\=\frac{-79}{35}\)
11. \(+\left(\frac{7}{2}\right) -\left(\frac{-4}{4}\right) -\left(\frac{-10}{-10}\right)\\= \frac{7}{2}+ \frac{4}{4}-\frac{10}{10}\\=\frac{7}{2}+\frac{1}{1}-\frac{1}{1}\\=\frac{7+1-1}{2}\\=\frac{7}{2}\)
12. \(-\left(\frac{-5}{6}\right) +\left(\frac{-6}{-5}\right) -\left(\frac{11}{-8}\right)\\= \frac{5}{6}+ \frac{6}{5}+\frac{11}{8}\\=\frac{100}{120}+\frac{144}{120}+\frac{165}{120}\\=\frac{100+144+165}{120}\\=\frac{409}{120}\)