Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{-3}\right) -\left(\frac{-2}{-4}\right) +\left(\frac{3}{8}\right)\\= \frac{2}{3}- \frac{2}{4}+\frac{3}{8}\\=\frac{2}{3}-\frac{1}{2}+\frac{3}{8}\\=\frac{16}{24}-\frac{12}{24}+\frac{9}{24}\\=\frac{16-12+9}{24}\\=\frac{13}{24}\)
2. \(-\left(\frac{-7}{-6}\right) -\left(\frac{10}{2}\right) -\left(\frac{-8}{7}\right)\\= \frac{-7}{6}- \frac{10}{2}+\frac{8}{7}\\=\frac{-7}{6}-\frac{5}{1}+\frac{8}{7}\\=\frac{-49}{42}-\frac{210}{42}+\frac{48}{42}\\=\frac{-49-210+48}{42}\\=\frac{-211}{42}\)
3. \(+\left(\frac{6}{-5}\right) -\left(\frac{-4}{-8}\right) +\left(\frac{-12}{-8}\right)\\= \frac{-6}{5}- \frac{4}{8}+\frac{12}{8}\\=\frac{-6}{5}-\frac{1}{2}+\frac{3}{2}\\=\frac{-12}{10}-\frac{5}{10}+\frac{15}{10}\\=\frac{-12-5+15}{10}\\=\frac{-2}{10}\\=\frac{-1}{5}\)
4. \(-\left(\frac{-8}{-7}\right) -\left(\frac{7}{-5}\right) +\left(\frac{-5}{-10}\right)\\= \frac{-8}{7}+ \frac{7}{5}+\frac{5}{10}\\=\frac{-8}{7}+\frac{7}{5}+\frac{1}{2}\\=\frac{-80}{70}+\frac{98}{70}+\frac{35}{70}\\=\frac{-80+98+35}{70}\\=\frac{53}{70}\)
5. \(+\left(\frac{-7}{-9}\right) -\left(\frac{7}{-8}\right) -\left(\frac{5}{7}\right)\\= \frac{7}{9}+ \frac{7}{8}-\frac{5}{7}\\=\frac{392}{504}+\frac{441}{504}-\frac{360}{504}\\=\frac{392+441-360}{504}\\=\frac{473}{504}\)
6. \(+\left(\frac{5}{3}\right) -\left(\frac{3}{7}\right) -\left(\frac{9}{5}\right)\\= \frac{5}{3}- \frac{3}{7}-\frac{9}{5}\\=\frac{175}{105}-\frac{45}{105}-\frac{189}{105}\\=\frac{175-45-189}{105}\\=\frac{-59}{105}\)
7. \(-\left(\frac{-9}{-4}\right) -\left(\frac{-7}{9}\right) -\left(\frac{8}{10}\right)\\= \frac{-9}{4}+ \frac{7}{9}-\frac{8}{10}\\=\frac{-9}{4}+\frac{7}{9}-\frac{4}{5}\\=\frac{-405}{180}+\frac{140}{180}-\frac{144}{180}\\=\frac{-405+140-144}{180}\\=\frac{-409}{180}\)
8. \(+\left(\frac{-10}{-7}\right) -\left(\frac{9}{-2}\right) +\left(\frac{-4}{8}\right)\\= \frac{10}{7}+ \frac{9}{2}-\frac{4}{8}\\=\frac{10}{7}+\frac{9}{2}-\frac{1}{2}\\=\frac{20}{14}+\frac{63}{14}-\frac{7}{14}\\=\frac{20+63-7}{14}\\=\frac{76}{14}\\=\frac{38}{7}\)
9. \(+\left(\frac{-4}{3}\right) +\left(\frac{-3}{-5}\right) +\left(\frac{8}{11}\right)\\= \frac{-4}{3}+ \frac{3}{5}+\frac{8}{11}\\=\frac{-220}{165}+\frac{99}{165}+\frac{120}{165}\\=\frac{-220+99+120}{165}\\=\frac{-1}{165}\)
10. \(+\left(\frac{7}{9}\right) +\left(\frac{-9}{4}\right) +\left(\frac{4}{7}\right)\\= \frac{7}{9}- \frac{9}{4}+\frac{4}{7}\\=\frac{196}{252}-\frac{567}{252}+\frac{144}{252}\\=\frac{196-567+144}{252}\\=\frac{-227}{252}\)
11. \(+\left(\frac{-8}{-5}\right) +\left(\frac{6}{-10}\right) -\left(\frac{4}{6}\right)\\= \frac{8}{5}- \frac{6}{10}-\frac{4}{6}\\=\frac{8}{5}-\frac{3}{5}-\frac{2}{3}\\=\frac{24}{15}-\frac{9}{15}-\frac{10}{15}\\=\frac{24-9-10}{15}\\=\frac{5}{15}\\=\frac{1}{3}\)
12. \(-\left(\frac{-2}{9}\right) -\left(\frac{4}{-2}\right) +\left(\frac{-4}{8}\right)\\= \frac{2}{9}+ \frac{4}{2}-\frac{4}{8}\\=\frac{2}{9}+\frac{2}{1}-\frac{1}{2}\\=\frac{4}{18}+\frac{36}{18}-\frac{9}{18}\\=\frac{4+36-9}{18}\\=\frac{31}{18}\)