Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{2}\right) +\left(\frac{-2}{9}\right) -\left(\frac{12}{-11}\right)\\= \frac{-5}{2}- \frac{2}{9}+\frac{12}{11}\\=\frac{-495}{198}-\frac{44}{198}+\frac{216}{198}\\=\frac{-495-44+216}{198}\\=\frac{-323}{198}\)
2. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-5}{-5}\right) -\left(\frac{-2}{2}\right)\\= \frac{6}{5}- \frac{5}{5}+\frac{2}{2}\\=\frac{6}{5}-\frac{1}{1}+\frac{1}{1}\\=\frac{6-1+1}{5}\\=\frac{6}{5}\)
3. \(-\left(\frac{-2}{-3}\right) +\left(\frac{-6}{7}\right) -\left(\frac{2}{11}\right)\\= \frac{-2}{3}- \frac{6}{7}-\frac{2}{11}\\=\frac{-154}{231}-\frac{198}{231}-\frac{42}{231}\\=\frac{-154-198-42}{231}\\=\frac{-394}{231}\)
4. \(-\left(\frac{7}{-5}\right) +\left(\frac{-2}{4}\right) -\left(\frac{7}{10}\right)\\= \frac{7}{5}- \frac{2}{4}-\frac{7}{10}\\=\frac{7}{5}-\frac{1}{2}-\frac{7}{10}\\=\frac{14}{10}-\frac{5}{10}-\frac{7}{10}\\=\frac{14-5-7}{10}\\=\frac{2}{10}\\=\frac{1}{5}\)
5. \(+\left(\frac{-5}{-4}\right) -\left(\frac{5}{-10}\right) +\left(\frac{-4}{11}\right)\\= \frac{5}{4}+ \frac{5}{10}-\frac{4}{11}\\=\frac{5}{4}+\frac{1}{2}-\frac{4}{11}\\=\frac{55}{44}+\frac{22}{44}-\frac{16}{44}\\=\frac{55+22-16}{44}\\=\frac{61}{44}\)
6. \(+\left(\frac{-3}{-5}\right) +\left(\frac{-9}{-3}\right) -\left(\frac{-9}{10}\right)\\= \frac{3}{5}+ \frac{9}{3}+\frac{9}{10}\\=\frac{3}{5}+\frac{3}{1}+\frac{9}{10}\\=\frac{6}{10}+\frac{30}{10}+\frac{9}{10}\\=\frac{6+30+9}{10}\\=\frac{45}{10}\\=\frac{9}{2}\)
7. \(+\left(\frac{-3}{4}\right) +\left(\frac{-8}{6}\right) +\left(\frac{-8}{12}\right)\\= \frac{-3}{4}- \frac{8}{6}-\frac{8}{12}\\=\frac{-3}{4}-\frac{4}{3}-\frac{2}{3}\\=\frac{-9}{12}-\frac{16}{12}-\frac{8}{12}\\=\frac{-9-16-8}{12}\\=\frac{-33}{12}\\=\frac{-11}{4}\)
8. \(-\left(\frac{4}{-5}\right) -\left(\frac{7}{6}\right) +\left(\frac{-9}{-4}\right)\\= \frac{4}{5}- \frac{7}{6}+\frac{9}{4}\\=\frac{48}{60}-\frac{70}{60}+\frac{135}{60}\\=\frac{48-70+135}{60}\\=\frac{113}{60}\)
9. \(+\left(\frac{-10}{-7}\right) +\left(\frac{-4}{-10}\right) -\left(\frac{-5}{6}\right)\\= \frac{10}{7}+ \frac{4}{10}+\frac{5}{6}\\=\frac{10}{7}+\frac{2}{5}+\frac{5}{6}\\=\frac{300}{210}+\frac{84}{210}+\frac{175}{210}\\=\frac{300+84+175}{210}\\=\frac{559}{210}\)
10. \(+\left(\frac{-4}{9}\right) +\left(\frac{-2}{6}\right) +\left(\frac{-11}{-4}\right)\\= \frac{-4}{9}- \frac{2}{6}+\frac{11}{4}\\=\frac{-4}{9}-\frac{1}{3}+\frac{11}{4}\\=\frac{-16}{36}-\frac{12}{36}+\frac{99}{36}\\=\frac{-16-12+99}{36}\\=\frac{71}{36}\)
11. \(-\left(\frac{10}{9}\right) +\left(\frac{-8}{-3}\right) -\left(\frac{6}{-7}\right)\\= \frac{-10}{9}+ \frac{8}{3}+\frac{6}{7}\\=\frac{-70}{63}+\frac{168}{63}+\frac{54}{63}\\=\frac{-70+168+54}{63}\\=\frac{152}{63}\)
12. \(-\left(\frac{9}{-4}\right) +\left(\frac{-6}{-9}\right) -\left(\frac{-3}{4}\right)\\= \frac{9}{4}+ \frac{6}{9}+\frac{3}{4}\\=\frac{9}{4}+\frac{2}{3}+\frac{3}{4}\\=\frac{27}{12}+\frac{8}{12}+\frac{9}{12}\\=\frac{27+8+9}{12}\\=\frac{44}{12}\\=\frac{11}{3}\)