Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{-7}\right) -\left(\frac{-10}{4}\right) -\left(\frac{-11}{12}\right)\\= \frac{3}{7}+ \frac{10}{4}+\frac{11}{12}\\=\frac{3}{7}+\frac{5}{2}+\frac{11}{12}\\=\frac{36}{84}+\frac{210}{84}+\frac{77}{84}\\=\frac{36+210+77}{84}\\=\frac{323}{84}\)
2. \(-\left(\frac{-6}{-5}\right) +\left(\frac{6}{-2}\right) +\left(\frac{-12}{4}\right)\\= \frac{-6}{5}- \frac{6}{2}-\frac{12}{4}\\=\frac{-6}{5}-\frac{3}{1}-\frac{3}{1}\\=\frac{-6-3-3}{5}\\=\frac{-12}{5}\)
3. \(+\left(\frac{-7}{8}\right) -\left(\frac{-8}{-10}\right) -\left(\frac{-8}{-7}\right)\\= \frac{-7}{8}- \frac{8}{10}-\frac{8}{7}\\=\frac{-7}{8}-\frac{4}{5}-\frac{8}{7}\\=\frac{-245}{280}-\frac{224}{280}-\frac{320}{280}\\=\frac{-245-224-320}{280}\\=\frac{-789}{280}\)
4. \(-\left(\frac{3}{2}\right) -\left(\frac{-5}{-4}\right) -\left(\frac{-2}{12}\right)\\= \frac{-3}{2}- \frac{5}{4}+\frac{2}{12}\\=\frac{-3}{2}-\frac{5}{4}+\frac{1}{6}\\=\frac{-18}{12}-\frac{15}{12}+\frac{2}{12}\\=\frac{-18-15+2}{12}\\=\frac{-31}{12}\)
5. \(-\left(\frac{7}{-9}\right) +\left(\frac{-6}{-2}\right) -\left(\frac{-12}{-10}\right)\\= \frac{7}{9}+ \frac{6}{2}-\frac{12}{10}\\=\frac{7}{9}+\frac{3}{1}-\frac{6}{5}\\=\frac{35}{45}+\frac{135}{45}-\frac{54}{45}\\=\frac{35+135-54}{45}\\=\frac{116}{45}\)
6. \(-\left(\frac{-4}{-5}\right) +\left(\frac{-9}{3}\right) -\left(\frac{-12}{-7}\right)\\= \frac{-4}{5}- \frac{9}{3}-\frac{12}{7}\\=\frac{-4}{5}-\frac{3}{1}-\frac{12}{7}\\=\frac{-28}{35}-\frac{105}{35}-\frac{60}{35}\\=\frac{-28-105-60}{35}\\=\frac{-193}{35}\)
7. \(-\left(\frac{-6}{-7}\right) -\left(\frac{8}{7}\right) -\left(\frac{9}{-12}\right)\\= \frac{-6}{7}- \frac{8}{7}+\frac{9}{12}\\=\frac{-6}{7}-\frac{8}{7}+\frac{3}{4}\\=\frac{-24}{28}-\frac{32}{28}+\frac{21}{28}\\=\frac{-24-32+21}{28}\\=\frac{-35}{28}\\=\frac{-5}{4}\)
8. \(+\left(\frac{5}{-8}\right) +\left(\frac{-2}{-4}\right) +\left(\frac{-8}{-9}\right)\\= \frac{-5}{8}+ \frac{2}{4}+\frac{8}{9}\\=\frac{-5}{8}+\frac{1}{2}+\frac{8}{9}\\=\frac{-45}{72}+\frac{36}{72}+\frac{64}{72}\\=\frac{-45+36+64}{72}\\=\frac{55}{72}\)
9. \(+\left(\frac{8}{9}\right) +\left(\frac{8}{2}\right) +\left(\frac{-3}{4}\right)\\= \frac{8}{9}+ \frac{8}{2}-\frac{3}{4}\\=\frac{8}{9}+\frac{4}{1}-\frac{3}{4}\\=\frac{32}{36}+\frac{144}{36}-\frac{27}{36}\\=\frac{32+144-27}{36}\\=\frac{149}{36}\)
10. \(+\left(\frac{3}{-8}\right) -\left(\frac{7}{-7}\right) -\left(\frac{-9}{3}\right)\\= \frac{-3}{8}+ \frac{7}{7}+\frac{9}{3}\\=\frac{-3}{8}+\frac{1}{1}+\frac{3}{1}\\=\frac{-3+1+3}{8}\\=\frac{1}{8}\)
11. \(-\left(\frac{-5}{9}\right) +\left(\frac{-6}{10}\right) -\left(\frac{-4}{-9}\right)\\= \frac{5}{9}- \frac{6}{10}-\frac{4}{9}\\=\frac{5}{9}-\frac{3}{5}-\frac{4}{9}\\=\frac{25}{45}-\frac{27}{45}-\frac{20}{45}\\=\frac{25-27-20}{45}\\=\frac{-22}{45}\)
12. \(+\left(\frac{3}{2}\right) -\left(\frac{9}{-6}\right) +\left(\frac{-7}{-2}\right)\\= \frac{3}{2}+ \frac{9}{6}+\frac{7}{2}\\=\frac{3}{2}+\frac{3}{2}+\frac{7}{2}\\=\frac{3+3+7}{2}\\=\frac{13}{2}\)