Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{4}\right) -\left(\frac{8}{6}\right) -\left(\frac{-7}{-5}\right)\\= \frac{5}{4}- \frac{8}{6}-\frac{7}{5}\\=\frac{5}{4}-\frac{4}{3}-\frac{7}{5}\\=\frac{75}{60}-\frac{80}{60}-\frac{84}{60}\\=\frac{75-80-84}{60}\\=\frac{-89}{60}\)
2. \(-\left(\frac{-3}{8}\right) +\left(\frac{3}{9}\right) +\left(\frac{-12}{5}\right)\\= \frac{3}{8}+ \frac{3}{9}-\frac{12}{5}\\=\frac{3}{8}+\frac{1}{3}-\frac{12}{5}\\=\frac{45}{120}+\frac{40}{120}-\frac{288}{120}\\=\frac{45+40-288}{120}\\=\frac{-203}{120}\)
3. \(+\left(\frac{7}{10}\right) -\left(\frac{-2}{-5}\right) +\left(\frac{3}{-6}\right)\\= \frac{7}{10}- \frac{2}{5}-\frac{3}{6}\\=\frac{7}{10}-\frac{2}{5}-\frac{1}{2}\\=\frac{7-2-1}{10}\\=\frac{4}{10}\\=\frac{2}{5}\)
4. \(+\left(\frac{-2}{-7}\right) +\left(\frac{2}{4}\right) +\left(\frac{-10}{-12}\right)\\= \frac{2}{7}+ \frac{2}{4}+\frac{10}{12}\\=\frac{2}{7}+\frac{1}{2}+\frac{5}{6}\\=\frac{12}{42}+\frac{21}{42}+\frac{35}{42}\\=\frac{12+21+35}{42}\\=\frac{68}{42}\\=\frac{34}{21}\)
5. \(-\left(\frac{-3}{-10}\right) -\left(\frac{-4}{-2}\right) -\left(\frac{-12}{9}\right)\\= \frac{-3}{10}- \frac{4}{2}+\frac{12}{9}\\=\frac{-3}{10}-\frac{2}{1}+\frac{4}{3}\\=\frac{-9}{30}-\frac{60}{30}+\frac{40}{30}\\=\frac{-9-60+40}{30}\\=\frac{-29}{30}\)
6. \(+\left(\frac{8}{7}\right) +\left(\frac{-7}{6}\right) -\left(\frac{-6}{3}\right)\\= \frac{8}{7}- \frac{7}{6}+\frac{6}{3}\\=\frac{8}{7}-\frac{7}{6}+\frac{2}{1}\\=\frac{48}{42}-\frac{49}{42}+\frac{84}{42}\\=\frac{48-49+84}{42}\\=\frac{83}{42}\)
7. \(-\left(\frac{9}{-8}\right) +\left(\frac{10}{10}\right) -\left(\frac{-4}{12}\right)\\= \frac{9}{8}+ \frac{10}{10}+\frac{4}{12}\\=\frac{9}{8}+\frac{1}{1}+\frac{1}{3}\\=\frac{27}{24}+\frac{24}{24}+\frac{8}{24}\\=\frac{27+24+8}{24}\\=\frac{59}{24}\)
8. \(-\left(\frac{-9}{5}\right) +\left(\frac{4}{10}\right) +\left(\frac{9}{4}\right)\\= \frac{9}{5}+ \frac{4}{10}+\frac{9}{4}\\=\frac{9}{5}+\frac{2}{5}+\frac{9}{4}\\=\frac{36}{20}+\frac{8}{20}+\frac{45}{20}\\=\frac{36+8+45}{20}\\=\frac{89}{20}\)
9. \(+\left(\frac{-8}{5}\right) +\left(\frac{-9}{-6}\right) -\left(\frac{7}{-12}\right)\\= \frac{-8}{5}+ \frac{9}{6}+\frac{7}{12}\\=\frac{-8}{5}+\frac{3}{2}+\frac{7}{12}\\=\frac{-96}{60}+\frac{90}{60}+\frac{35}{60}\\=\frac{-96+90+35}{60}\\=\frac{29}{60}\)
10. \(+\left(\frac{4}{3}\right) +\left(\frac{-9}{-8}\right) -\left(\frac{-8}{9}\right)\\= \frac{4}{3}+ \frac{9}{8}+\frac{8}{9}\\=\frac{96}{72}+\frac{81}{72}+\frac{64}{72}\\=\frac{96+81+64}{72}\\=\frac{241}{72}\)
11. \(-\left(\frac{-9}{2}\right) +\left(\frac{3}{10}\right) -\left(\frac{6}{11}\right)\\= \frac{9}{2}+ \frac{3}{10}-\frac{6}{11}\\=\frac{495}{110}+\frac{33}{110}-\frac{60}{110}\\=\frac{495+33-60}{110}\\=\frac{468}{110}\\=\frac{234}{55}\)
12. \(+\left(\frac{-4}{-5}\right) -\left(\frac{-6}{-2}\right) -\left(\frac{7}{9}\right)\\= \frac{4}{5}- \frac{6}{2}-\frac{7}{9}\\=\frac{4}{5}-\frac{3}{1}-\frac{7}{9}\\=\frac{36}{45}-\frac{135}{45}-\frac{35}{45}\\=\frac{36-135-35}{45}\\=\frac{-134}{45}\)