Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{-4}\right) +\left(\frac{3}{2}\right) +\left(\frac{2}{-5}\right)\\= \frac{-9}{4}+ \frac{3}{2}-\frac{2}{5}\\=\frac{-45}{20}+\frac{30}{20}-\frac{8}{20}\\=\frac{-45+30-8}{20}\\=\frac{-23}{20}\)
2. \(+\left(\frac{-3}{-2}\right) -\left(\frac{-5}{2}\right) +\left(\frac{8}{-11}\right)\\= \frac{3}{2}+ \frac{5}{2}-\frac{8}{11}\\=\frac{33}{22}+\frac{55}{22}-\frac{16}{22}\\=\frac{33+55-16}{22}\\=\frac{72}{22}\\=\frac{36}{11}\)
3. \(+\left(\frac{-7}{2}\right) -\left(\frac{-6}{-6}\right) +\left(\frac{-7}{11}\right)\\= \frac{-7}{2}- \frac{6}{6}-\frac{7}{11}\\=\frac{-7}{2}-\frac{1}{1}-\frac{7}{11}\\=\frac{-77}{22}-\frac{22}{22}-\frac{14}{22}\\=\frac{-77-22-14}{22}\\=\frac{-113}{22}\)
4. \(+\left(\frac{5}{-2}\right) -\left(\frac{-6}{8}\right) +\left(\frac{7}{6}\right)\\= \frac{-5}{2}+ \frac{6}{8}+\frac{7}{6}\\=\frac{-5}{2}+\frac{3}{4}+\frac{7}{6}\\=\frac{-30}{12}+\frac{9}{12}+\frac{14}{12}\\=\frac{-30+9+14}{12}\\=\frac{-7}{12}\)
5. \(-\left(\frac{-7}{8}\right) +\left(\frac{-3}{-8}\right) -\left(\frac{9}{-2}\right)\\= \frac{7}{8}+ \frac{3}{8}+\frac{9}{2}\\=\frac{7+3+9}{8}\\=\frac{19}{8}\)
6. \(+\left(\frac{10}{3}\right) -\left(\frac{-8}{5}\right) +\left(\frac{3}{9}\right)\\= \frac{10}{3}+ \frac{8}{5}+\frac{3}{9}\\=\frac{10}{3}+\frac{8}{5}+\frac{1}{3}\\=\frac{50}{15}+\frac{24}{15}+\frac{5}{15}\\=\frac{50+24+5}{15}\\=\frac{79}{15}\)
7. \(-\left(\frac{8}{7}\right) -\left(\frac{6}{-8}\right) +\left(\frac{-2}{-4}\right)\\= \frac{-8}{7}+ \frac{6}{8}+\frac{2}{4}\\=\frac{-8}{7}+\frac{3}{4}+\frac{1}{2}\\=\frac{-32}{28}+\frac{21}{28}+\frac{14}{28}\\=\frac{-32+21+14}{28}\\=\frac{3}{28}\)
8. \(+\left(\frac{-2}{5}\right) -\left(\frac{-10}{8}\right) +\left(\frac{5}{10}\right)\\= \frac{-2}{5}+ \frac{10}{8}+\frac{5}{10}\\=\frac{-2}{5}+\frac{5}{4}+\frac{1}{2}\\=\frac{-8}{20}+\frac{25}{20}+\frac{10}{20}\\=\frac{-8+25+10}{20}\\=\frac{27}{20}\)
9. \(+\left(\frac{-7}{2}\right) +\left(\frac{10}{4}\right) -\left(\frac{-2}{5}\right)\\= \frac{-7}{2}+ \frac{10}{4}+\frac{2}{5}\\=\frac{-7}{2}+\frac{5}{2}+\frac{2}{5}\\=\frac{-35}{10}+\frac{25}{10}+\frac{4}{10}\\=\frac{-35+25+4}{10}\\=\frac{-6}{10}\\=\frac{-3}{5}\)
10. \(-\left(\frac{-3}{-2}\right) -\left(\frac{7}{2}\right) +\left(\frac{5}{-11}\right)\\= \frac{-3}{2}- \frac{7}{2}-\frac{5}{11}\\=\frac{-33}{22}-\frac{77}{22}-\frac{10}{22}\\=\frac{-33-77-10}{22}\\=\frac{-120}{22}\\=\frac{-60}{11}\)
11. \(+\left(\frac{-9}{-5}\right) +\left(\frac{-10}{-8}\right) -\left(\frac{-2}{-12}\right)\\= \frac{9}{5}+ \frac{10}{8}-\frac{2}{12}\\=\frac{9}{5}+\frac{5}{4}-\frac{1}{6}\\=\frac{108}{60}+\frac{75}{60}-\frac{10}{60}\\=\frac{108+75-10}{60}\\=\frac{173}{60}\)
12. \(+\left(\frac{3}{-5}\right) +\left(\frac{-5}{7}\right) +\left(\frac{7}{-11}\right)\\= \frac{-3}{5}- \frac{5}{7}-\frac{7}{11}\\=\frac{-231}{385}-\frac{275}{385}-\frac{245}{385}\\=\frac{-231-275-245}{385}\\=\frac{-751}{385}\)