Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{6}{-5}\right) +\left(\frac{-9}{-8}\right) +\left(\frac{4}{-9}\right)\\= \frac{-6}{5}+ \frac{9}{8}-\frac{4}{9}\\=\frac{-432}{360}+\frac{405}{360}-\frac{160}{360}\\=\frac{-432+405-160}{360}\\=\frac{-187}{360}\)
2. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-2}{3}\right) -\left(\frac{11}{7}\right)\\= \frac{6}{5}+ \frac{2}{3}-\frac{11}{7}\\=\frac{126}{105}+\frac{70}{105}-\frac{165}{105}\\=\frac{126+70-165}{105}\\=\frac{31}{105}\)
3. \(-\left(\frac{-10}{9}\right) +\left(\frac{5}{8}\right) -\left(\frac{10}{-10}\right)\\= \frac{10}{9}+ \frac{5}{8}+\frac{10}{10}\\=\frac{10}{9}+\frac{5}{8}+\frac{1}{1}\\=\frac{80}{72}+\frac{45}{72}+\frac{72}{72}\\=\frac{80+45+72}{72}\\=\frac{197}{72}\)
4. \(+\left(\frac{10}{-9}\right) +\left(\frac{-3}{10}\right) +\left(\frac{-5}{-12}\right)\\= \frac{-10}{9}- \frac{3}{10}+\frac{5}{12}\\=\frac{-200}{180}-\frac{54}{180}+\frac{75}{180}\\=\frac{-200-54+75}{180}\\=\frac{-179}{180}\)
5. \(+\left(\frac{-3}{-7}\right) -\left(\frac{-6}{-6}\right) +\left(\frac{9}{-6}\right)\\= \frac{3}{7}- \frac{6}{6}-\frac{9}{6}\\=\frac{3}{7}-\frac{1}{1}-\frac{3}{2}\\=\frac{6}{14}-\frac{14}{14}-\frac{21}{14}\\=\frac{6-14-21}{14}\\=\frac{-29}{14}\)
6. \(-\left(\frac{2}{-3}\right) +\left(\frac{-5}{2}\right) +\left(\frac{-11}{11}\right)\\= \frac{2}{3}- \frac{5}{2}-\frac{11}{11}\\=\frac{2}{3}-\frac{5}{2}-\frac{1}{1}\\=\frac{4}{6}-\frac{15}{6}-\frac{6}{6}\\=\frac{4-15-6}{6}\\=\frac{-17}{6}\)
7. \(+\left(\frac{8}{3}\right) +\left(\frac{9}{9}\right) +\left(\frac{-7}{-5}\right)\\= \frac{8}{3}+ \frac{9}{9}+\frac{7}{5}\\=\frac{8}{3}+\frac{1}{1}+\frac{7}{5}\\=\frac{40}{15}+\frac{15}{15}+\frac{21}{15}\\=\frac{40+15+21}{15}\\=\frac{76}{15}\)
8. \(+\left(\frac{10}{7}\right) +\left(\frac{-7}{6}\right) -\left(\frac{-2}{-10}\right)\\= \frac{10}{7}- \frac{7}{6}-\frac{2}{10}\\=\frac{10}{7}-\frac{7}{6}-\frac{1}{5}\\=\frac{300}{210}-\frac{245}{210}-\frac{42}{210}\\=\frac{300-245-42}{210}\\=\frac{13}{210}\)
9. \(+\left(\frac{-8}{-7}\right) +\left(\frac{2}{-10}\right) -\left(\frac{-10}{12}\right)\\= \frac{8}{7}- \frac{2}{10}+\frac{10}{12}\\=\frac{8}{7}-\frac{1}{5}+\frac{5}{6}\\=\frac{240}{210}-\frac{42}{210}+\frac{175}{210}\\=\frac{240-42+175}{210}\\=\frac{373}{210}\)
10. \(-\left(\frac{-2}{-5}\right) +\left(\frac{-6}{9}\right) +\left(\frac{-4}{-6}\right)\\= \frac{-2}{5}- \frac{6}{9}+\frac{4}{6}\\=\frac{-2}{5}-\frac{2}{3}+\frac{2}{3}\\=\frac{-6}{15}-\frac{10}{15}+\frac{10}{15}\\=\frac{-6-10+10}{15}\\=\frac{-6}{15}\\=\frac{-2}{5}\)
11. \(+\left(\frac{9}{-4}\right) +\left(\frac{-6}{-5}\right) -\left(\frac{7}{4}\right)\\= \frac{-9}{4}+ \frac{6}{5}-\frac{7}{4}\\=\frac{-45}{20}+\frac{24}{20}-\frac{35}{20}\\=\frac{-45+24-35}{20}\\=\frac{-56}{20}\\=\frac{-14}{5}\)
12. \(-\left(\frac{-7}{4}\right) -\left(\frac{4}{4}\right) +\left(\frac{2}{-4}\right)\\= \frac{7}{4}- \frac{4}{4}-\frac{2}{4}\\=\frac{7}{4}-\frac{1}{1}-\frac{1}{2}\\=\frac{7-1-1}{4}\\=\frac{5}{4}\)