Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{7}\right) -\left(\frac{6}{6}\right) +\left(\frac{-7}{-2}\right)\\= \frac{-10}{7}- \frac{6}{6}+\frac{7}{2}\\=\frac{-10}{7}-\frac{1}{1}+\frac{7}{2}\\=\frac{-20}{14}-\frac{14}{14}+\frac{49}{14}\\=\frac{-20-14+49}{14}\\=\frac{15}{14}\)
2. \(-\left(\frac{2}{5}\right) +\left(\frac{7}{9}\right) +\left(\frac{-9}{5}\right)\\= \frac{-2}{5}+ \frac{7}{9}-\frac{9}{5}\\=\frac{-18}{45}+\frac{35}{45}-\frac{81}{45}\\=\frac{-18+35-81}{45}\\=\frac{-64}{45}\)
3. \(+\left(\frac{-5}{8}\right) +\left(\frac{-9}{-6}\right) +\left(\frac{-9}{-8}\right)\\= \frac{-5}{8}+ \frac{9}{6}+\frac{9}{8}\\=\frac{-5}{8}+\frac{3}{2}+\frac{9}{8}\\=\frac{-5+3+9}{8}\\=\frac{7}{8}\)
4. \(+\left(\frac{-8}{-5}\right) +\left(\frac{-7}{-10}\right) +\left(\frac{5}{4}\right)\\= \frac{8}{5}+ \frac{7}{10}+\frac{5}{4}\\=\frac{32}{20}+\frac{14}{20}+\frac{25}{20}\\=\frac{32+14+25}{20}\\=\frac{71}{20}\)
5. \(-\left(\frac{10}{7}\right) -\left(\frac{8}{5}\right) +\left(\frac{7}{-2}\right)\\= \frac{-10}{7}- \frac{8}{5}-\frac{7}{2}\\=\frac{-100}{70}-\frac{112}{70}-\frac{245}{70}\\=\frac{-100-112-245}{70}\\=\frac{-457}{70}\)
6. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-2}{3}\right) +\left(\frac{6}{-9}\right)\\= \frac{-6}{5}- \frac{2}{3}-\frac{6}{9}\\=\frac{-6}{5}-\frac{2}{3}-\frac{2}{3}\\=\frac{-18}{15}-\frac{10}{15}-\frac{10}{15}\\=\frac{-18-10-10}{15}\\=\frac{-38}{15}\)
7. \(+\left(\frac{-7}{-4}\right) +\left(\frac{-2}{-8}\right) -\left(\frac{2}{-7}\right)\\= \frac{7}{4}+ \frac{2}{8}+\frac{2}{7}\\=\frac{7}{4}+\frac{1}{4}+\frac{2}{7}\\=\frac{49}{28}+\frac{7}{28}+\frac{8}{28}\\=\frac{49+7+8}{28}\\=\frac{64}{28}\\=\frac{16}{7}\)
8. \(-\left(\frac{8}{-3}\right) -\left(\frac{9}{2}\right) -\left(\frac{4}{-3}\right)\\= \frac{8}{3}- \frac{9}{2}+\frac{4}{3}\\=\frac{16}{6}-\frac{27}{6}+\frac{8}{6}\\=\frac{16-27+8}{6}\\=\frac{-3}{6}\\=\frac{-1}{2}\)
9. \(+\left(\frac{2}{-3}\right) -\left(\frac{3}{10}\right) +\left(\frac{4}{-6}\right)\\= \frac{-2}{3}- \frac{3}{10}-\frac{4}{6}\\=\frac{-2}{3}-\frac{3}{10}-\frac{2}{3}\\=\frac{-20}{30}-\frac{9}{30}-\frac{20}{30}\\=\frac{-20-9-20}{30}\\=\frac{-49}{30}\)
10. \(-\left(\frac{-3}{4}\right) -\left(\frac{-10}{3}\right) -\left(\frac{-11}{-9}\right)\\= \frac{3}{4}+ \frac{10}{3}-\frac{11}{9}\\=\frac{27}{36}+\frac{120}{36}-\frac{44}{36}\\=\frac{27+120-44}{36}\\=\frac{103}{36}\)
11. \(+\left(\frac{7}{-6}\right) +\left(\frac{-5}{-4}\right) +\left(\frac{-7}{-4}\right)\\= \frac{-7}{6}+ \frac{5}{4}+\frac{7}{4}\\=\frac{-14}{12}+\frac{15}{12}+\frac{21}{12}\\=\frac{-14+15+21}{12}\\=\frac{22}{12}\\=\frac{11}{6}\)
12. \(+\left(\frac{-10}{-7}\right) +\left(\frac{-7}{-2}\right) +\left(\frac{-8}{8}\right)\\= \frac{10}{7}+ \frac{7}{2}-\frac{8}{8}\\=\frac{10}{7}+\frac{7}{2}-\frac{1}{1}\\=\frac{20}{14}+\frac{49}{14}-\frac{14}{14}\\=\frac{20+49-14}{14}\\=\frac{55}{14}\)