Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{-8}\right) +\left(\frac{-9}{2}\right) +\left(\frac{4}{10}\right)\\= \frac{7}{8}- \frac{9}{2}+\frac{4}{10}\\=\frac{7}{8}-\frac{9}{2}+\frac{2}{5}\\=\frac{35}{40}-\frac{180}{40}+\frac{16}{40}\\=\frac{35-180+16}{40}\\=\frac{-129}{40}\)
2. \(+\left(\frac{10}{-3}\right) -\left(\frac{3}{-9}\right) -\left(\frac{9}{8}\right)\\= \frac{-10}{3}+ \frac{3}{9}-\frac{9}{8}\\=\frac{-10}{3}+\frac{1}{3}-\frac{9}{8}\\=\frac{-80}{24}+\frac{8}{24}-\frac{27}{24}\\=\frac{-80+8-27}{24}\\=\frac{-99}{24}\\=\frac{-33}{8}\)
3. \(+\left(\frac{-8}{-5}\right) +\left(\frac{-6}{9}\right) -\left(\frac{12}{-2}\right)\\= \frac{8}{5}- \frac{6}{9}+\frac{12}{2}\\=\frac{8}{5}-\frac{2}{3}+\frac{6}{1}\\=\frac{24}{15}-\frac{10}{15}+\frac{90}{15}\\=\frac{24-10+90}{15}\\=\frac{104}{15}\)
4. \(-\left(\frac{-5}{2}\right) +\left(\frac{-4}{-8}\right) -\left(\frac{-7}{4}\right)\\= \frac{5}{2}+ \frac{4}{8}+\frac{7}{4}\\=\frac{5}{2}+\frac{1}{2}+\frac{7}{4}\\=\frac{10}{4}+\frac{2}{4}+\frac{7}{4}\\=\frac{10+2+7}{4}\\=\frac{19}{4}\)
5. \(+\left(\frac{-5}{7}\right) -\left(\frac{-10}{4}\right) +\left(\frac{-2}{8}\right)\\= \frac{-5}{7}+ \frac{10}{4}-\frac{2}{8}\\=\frac{-5}{7}+\frac{5}{2}-\frac{1}{4}\\=\frac{-20}{28}+\frac{70}{28}-\frac{7}{28}\\=\frac{-20+70-7}{28}\\=\frac{43}{28}\)
6. \(-\left(\frac{7}{5}\right) +\left(\frac{10}{9}\right) +\left(\frac{-6}{6}\right)\\= \frac{-7}{5}+ \frac{10}{9}-\frac{6}{6}\\=\frac{-7}{5}+\frac{10}{9}-\frac{1}{1}\\=\frac{-63}{45}+\frac{50}{45}-\frac{45}{45}\\=\frac{-63+50-45}{45}\\=\frac{-58}{45}\)
7. \(+\left(\frac{-10}{9}\right) +\left(\frac{-4}{-6}\right) -\left(\frac{10}{3}\right)\\= \frac{-10}{9}+ \frac{4}{6}-\frac{10}{3}\\=\frac{-10}{9}+\frac{2}{3}-\frac{10}{3}\\=\frac{-10+2-10}{9}\\=\frac{-18}{9}\\=\frac{-2}{1}\)
8. \(-\left(\frac{-5}{6}\right) +\left(\frac{-2}{8}\right) -\left(\frac{-11}{-12}\right)\\= \frac{5}{6}- \frac{2}{8}-\frac{11}{12}\\=\frac{5}{6}-\frac{1}{4}-\frac{11}{12}\\=\frac{10}{12}-\frac{3}{12}-\frac{11}{12}\\=\frac{10-3-11}{12}\\=\frac{-4}{12}\\=\frac{-1}{3}\)
9. \(-\left(\frac{9}{2}\right) -\left(\frac{4}{-10}\right) +\left(\frac{6}{-3}\right)\\= \frac{-9}{2}+ \frac{4}{10}-\frac{6}{3}\\=\frac{-9}{2}+\frac{2}{5}-\frac{2}{1}\\=\frac{-45}{10}+\frac{4}{10}-\frac{20}{10}\\=\frac{-45+4-20}{10}\\=\frac{-61}{10}\)
10. \(-\left(\frac{5}{-6}\right) -\left(\frac{7}{-5}\right) -\left(\frac{-9}{-2}\right)\\= \frac{5}{6}+ \frac{7}{5}-\frac{9}{2}\\=\frac{25}{30}+\frac{42}{30}-\frac{135}{30}\\=\frac{25+42-135}{30}\\=\frac{-68}{30}\\=\frac{-34}{15}\)
11. \(+\left(\frac{5}{-6}\right) -\left(\frac{9}{-4}\right) -\left(\frac{-2}{-3}\right)\\= \frac{-5}{6}+ \frac{9}{4}-\frac{2}{3}\\=\frac{-10}{12}+\frac{27}{12}-\frac{8}{12}\\=\frac{-10+27-8}{12}\\=\frac{9}{12}\\=\frac{3}{4}\)
12. \(+\left(\frac{5}{6}\right) +\left(\frac{4}{6}\right) -\left(\frac{3}{11}\right)\\= \frac{5}{6}+ \frac{4}{6}-\frac{3}{11}\\=\frac{5}{6}+\frac{2}{3}-\frac{3}{11}\\=\frac{55}{66}+\frac{44}{66}-\frac{18}{66}\\=\frac{55+44-18}{66}\\=\frac{81}{66}\\=\frac{27}{22}\)