Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{8}\right) +\left(\frac{-8}{6}\right) +\left(\frac{11}{9}\right)\\= \frac{3}{8}- \frac{8}{6}+\frac{11}{9}\\=\frac{3}{8}-\frac{4}{3}+\frac{11}{9}\\=\frac{27}{72}-\frac{96}{72}+\frac{88}{72}\\=\frac{27-96+88}{72}\\=\frac{19}{72}\)
2. \(-\left(\frac{5}{-2}\right) +\left(\frac{-5}{-2}\right) -\left(\frac{-10}{4}\right)\\= \frac{5}{2}+ \frac{5}{2}+\frac{10}{4}\\=\frac{5}{2}+\frac{5}{2}+\frac{5}{2}\\=\frac{5+5+5}{2}\\=\frac{15}{2}\)
3. \(-\left(\frac{-9}{4}\right) -\left(\frac{10}{8}\right) +\left(\frac{-2}{9}\right)\\= \frac{9}{4}- \frac{10}{8}-\frac{2}{9}\\=\frac{9}{4}-\frac{5}{4}-\frac{2}{9}\\=\frac{81}{36}-\frac{45}{36}-\frac{8}{36}\\=\frac{81-45-8}{36}\\=\frac{28}{36}\\=\frac{7}{9}\)
4. \(+\left(\frac{2}{5}\right) -\left(\frac{9}{-4}\right) -\left(\frac{5}{5}\right)\\= \frac{2}{5}+ \frac{9}{4}-\frac{5}{5}\\=\frac{2}{5}+\frac{9}{4}-\frac{1}{1}\\=\frac{8}{20}+\frac{45}{20}-\frac{20}{20}\\=\frac{8+45-20}{20}\\=\frac{33}{20}\)
5. \(+\left(\frac{8}{7}\right) +\left(\frac{-6}{7}\right) -\left(\frac{-9}{11}\right)\\= \frac{8}{7}- \frac{6}{7}+\frac{9}{11}\\=\frac{88}{77}-\frac{66}{77}+\frac{63}{77}\\=\frac{88-66+63}{77}\\=\frac{85}{77}\)
6. \(+\left(\frac{-7}{4}\right) -\left(\frac{5}{-6}\right) -\left(\frac{-4}{5}\right)\\= \frac{-7}{4}+ \frac{5}{6}+\frac{4}{5}\\=\frac{-105}{60}+\frac{50}{60}+\frac{48}{60}\\=\frac{-105+50+48}{60}\\=\frac{-7}{60}\)
7. \(+\left(\frac{-7}{5}\right) +\left(\frac{-7}{4}\right) +\left(\frac{8}{11}\right)\\= \frac{-7}{5}- \frac{7}{4}+\frac{8}{11}\\=\frac{-308}{220}-\frac{385}{220}+\frac{160}{220}\\=\frac{-308-385+160}{220}\\=\frac{-533}{220}\)
8. \(-\left(\frac{6}{5}\right) -\left(\frac{3}{5}\right) -\left(\frac{-7}{-10}\right)\\= \frac{-6}{5}- \frac{3}{5}-\frac{7}{10}\\=\frac{-12}{10}-\frac{6}{10}-\frac{7}{10}\\=\frac{-12-6-7}{10}\\=\frac{-25}{10}\\=\frac{-5}{2}\)
9. \(+\left(\frac{2}{5}\right) -\left(\frac{-9}{-9}\right) +\left(\frac{10}{6}\right)\\= \frac{2}{5}- \frac{9}{9}+\frac{10}{6}\\=\frac{2}{5}-\frac{1}{1}+\frac{5}{3}\\=\frac{6}{15}-\frac{15}{15}+\frac{25}{15}\\=\frac{6-15+25}{15}\\=\frac{16}{15}\)
10. \(+\left(\frac{4}{-5}\right) +\left(\frac{4}{4}\right) +\left(\frac{-6}{11}\right)\\= \frac{-4}{5}+ \frac{4}{4}-\frac{6}{11}\\=\frac{-4}{5}+\frac{1}{1}-\frac{6}{11}\\=\frac{-44}{55}+\frac{55}{55}-\frac{30}{55}\\=\frac{-44+55-30}{55}\\=\frac{-19}{55}\)
11. \(-\left(\frac{-3}{-7}\right) -\left(\frac{-10}{9}\right) -\left(\frac{2}{12}\right)\\= \frac{-3}{7}+ \frac{10}{9}-\frac{2}{12}\\=\frac{-3}{7}+\frac{10}{9}-\frac{1}{6}\\=\frac{-54}{126}+\frac{140}{126}-\frac{21}{126}\\=\frac{-54+140-21}{126}\\=\frac{65}{126}\)
12. \(-\left(\frac{3}{2}\right) -\left(\frac{7}{9}\right) -\left(\frac{12}{2}\right)\\= \frac{-3}{2}- \frac{7}{9}-\frac{12}{2}\\=\frac{-3}{2}-\frac{7}{9}-\frac{6}{1}\\=\frac{-27}{18}-\frac{14}{18}-\frac{108}{18}\\=\frac{-27-14-108}{18}\\=\frac{-149}{18}\)