Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{7}{2}\right) -\left(\frac{4}{-10}\right) -\left(\frac{-12}{-9}\right)\\= \frac{7}{2}+ \frac{4}{10}-\frac{12}{9}\\=\frac{7}{2}+\frac{2}{5}-\frac{4}{3}\\=\frac{105}{30}+\frac{12}{30}-\frac{40}{30}\\=\frac{105+12-40}{30}\\=\frac{77}{30}\)
2. \(+\left(\frac{-8}{-5}\right) +\left(\frac{7}{9}\right) +\left(\frac{-6}{9}\right)\\= \frac{8}{5}+ \frac{7}{9}-\frac{6}{9}\\=\frac{8}{5}+\frac{7}{9}-\frac{2}{3}\\=\frac{72}{45}+\frac{35}{45}-\frac{30}{45}\\=\frac{72+35-30}{45}\\=\frac{77}{45}\)
3. \(-\left(\frac{8}{3}\right) -\left(\frac{10}{-5}\right) -\left(\frac{11}{-3}\right)\\= \frac{-8}{3}+ \frac{10}{5}+\frac{11}{3}\\=\frac{-8}{3}+\frac{2}{1}+\frac{11}{3}\\=\frac{-8+2+11}{3}\\=\frac{5}{3}\)
4. \(-\left(\frac{-7}{-3}\right) +\left(\frac{2}{-6}\right) +\left(\frac{9}{2}\right)\\= \frac{-7}{3}- \frac{2}{6}+\frac{9}{2}\\=\frac{-7}{3}-\frac{1}{3}+\frac{9}{2}\\=\frac{-14}{6}-\frac{2}{6}+\frac{27}{6}\\=\frac{-14-2+27}{6}\\=\frac{11}{6}\)
5. \(-\left(\frac{9}{-7}\right) -\left(\frac{-5}{3}\right) +\left(\frac{-9}{6}\right)\\= \frac{9}{7}+ \frac{5}{3}-\frac{9}{6}\\=\frac{9}{7}+\frac{5}{3}-\frac{3}{2}\\=\frac{54}{42}+\frac{70}{42}-\frac{63}{42}\\=\frac{54+70-63}{42}\\=\frac{61}{42}\)
6. \(+\left(\frac{-6}{-5}\right) +\left(\frac{5}{3}\right) -\left(\frac{-11}{2}\right)\\= \frac{6}{5}+ \frac{5}{3}+\frac{11}{2}\\=\frac{36}{30}+\frac{50}{30}+\frac{165}{30}\\=\frac{36+50+165}{30}\\=\frac{251}{30}\)
7. \(+\left(\frac{-3}{7}\right) -\left(\frac{-2}{7}\right) +\left(\frac{11}{-2}\right)\\= \frac{-3}{7}+ \frac{2}{7}-\frac{11}{2}\\=\frac{-6}{14}+\frac{4}{14}-\frac{77}{14}\\=\frac{-6+4-77}{14}\\=\frac{-79}{14}\)
8. \(+\left(\frac{6}{5}\right) -\left(\frac{-5}{4}\right) -\left(\frac{2}{4}\right)\\= \frac{6}{5}+ \frac{5}{4}-\frac{2}{4}\\=\frac{6}{5}+\frac{5}{4}-\frac{1}{2}\\=\frac{24}{20}+\frac{25}{20}-\frac{10}{20}\\=\frac{24+25-10}{20}\\=\frac{39}{20}\)
9. \(+\left(\frac{5}{8}\right) -\left(\frac{-3}{-10}\right) +\left(\frac{12}{-9}\right)\\= \frac{5}{8}- \frac{3}{10}-\frac{12}{9}\\=\frac{5}{8}-\frac{3}{10}-\frac{4}{3}\\=\frac{75}{120}-\frac{36}{120}-\frac{160}{120}\\=\frac{75-36-160}{120}\\=\frac{-121}{120}\)
10. \(+\left(\frac{-6}{7}\right) -\left(\frac{8}{-8}\right) +\left(\frac{-8}{-6}\right)\\= \frac{-6}{7}+ \frac{8}{8}+\frac{8}{6}\\=\frac{-6}{7}+\frac{1}{1}+\frac{4}{3}\\=\frac{-18}{21}+\frac{21}{21}+\frac{28}{21}\\=\frac{-18+21+28}{21}\\=\frac{31}{21}\)
11. \(-\left(\frac{-8}{-7}\right) -\left(\frac{-9}{6}\right) -\left(\frac{-10}{2}\right)\\= \frac{-8}{7}+ \frac{9}{6}+\frac{10}{2}\\=\frac{-8}{7}+\frac{3}{2}+\frac{5}{1}\\=\frac{-16}{14}+\frac{21}{14}+\frac{70}{14}\\=\frac{-16+21+70}{14}\\=\frac{75}{14}\)
12. \(-\left(\frac{9}{4}\right) +\left(\frac{5}{6}\right) -\left(\frac{4}{6}\right)\\= \frac{-9}{4}+ \frac{5}{6}-\frac{4}{6}\\=\frac{-9}{4}+\frac{5}{6}-\frac{2}{3}\\=\frac{-27}{12}+\frac{10}{12}-\frac{8}{12}\\=\frac{-27+10-8}{12}\\=\frac{-25}{12}\)