Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{3}\right) -\left(\frac{-6}{3}\right) -\left(\frac{4}{5}\right)\\= \frac{-2}{3}+ \frac{6}{3}-\frac{4}{5}\\=\frac{-2}{3}+\frac{2}{1}-\frac{4}{5}\\=\frac{-10}{15}+\frac{30}{15}-\frac{12}{15}\\=\frac{-10+30-12}{15}\\=\frac{8}{15}\)
2. \(-\left(\frac{6}{-5}\right) +\left(\frac{7}{-3}\right) +\left(\frac{5}{2}\right)\\= \frac{6}{5}- \frac{7}{3}+\frac{5}{2}\\=\frac{36}{30}-\frac{70}{30}+\frac{75}{30}\\=\frac{36-70+75}{30}\\=\frac{41}{30}\)
3. \(-\left(\frac{-8}{-9}\right) +\left(\frac{-10}{-3}\right) +\left(\frac{-9}{6}\right)\\= \frac{-8}{9}+ \frac{10}{3}-\frac{9}{6}\\=\frac{-8}{9}+\frac{10}{3}-\frac{3}{2}\\=\frac{-16}{18}+\frac{60}{18}-\frac{27}{18}\\=\frac{-16+60-27}{18}\\=\frac{17}{18}\)
4. \(+\left(\frac{9}{-2}\right) -\left(\frac{4}{5}\right) +\left(\frac{6}{-6}\right)\\= \frac{-9}{2}- \frac{4}{5}-\frac{6}{6}\\=\frac{-9}{2}-\frac{4}{5}-\frac{1}{1}\\=\frac{-45}{10}-\frac{8}{10}-\frac{10}{10}\\=\frac{-45-8-10}{10}\\=\frac{-63}{10}\)
5. \(-\left(\frac{-3}{-8}\right) +\left(\frac{-8}{-8}\right) -\left(\frac{-10}{10}\right)\\= \frac{-3}{8}+ \frac{8}{8}+\frac{10}{10}\\=\frac{-3}{8}+\frac{1}{1}+\frac{1}{1}\\=\frac{-3+1+1}{8}\\=\frac{-1}{8}\)
6. \(+\left(\frac{2}{-3}\right) -\left(\frac{9}{6}\right) +\left(\frac{-7}{-7}\right)\\= \frac{-2}{3}- \frac{9}{6}+\frac{7}{7}\\=\frac{-2}{3}-\frac{3}{2}+\frac{1}{1}\\=\frac{-4}{6}-\frac{9}{6}+\frac{6}{6}\\=\frac{-4-9+6}{6}\\=\frac{-7}{6}\)
7. \(-\left(\frac{-2}{-3}\right) +\left(\frac{10}{6}\right) -\left(\frac{-10}{-11}\right)\\= \frac{-2}{3}+ \frac{10}{6}-\frac{10}{11}\\=\frac{-2}{3}+\frac{5}{3}-\frac{10}{11}\\=\frac{-22}{33}+\frac{55}{33}-\frac{30}{33}\\=\frac{-22+55-30}{33}\\=\frac{3}{33}\\=\frac{1}{11}\)
8. \(-\left(\frac{-6}{5}\right) +\left(\frac{-4}{2}\right) -\left(\frac{-6}{-6}\right)\\= \frac{6}{5}- \frac{4}{2}-\frac{6}{6}\\=\frac{6}{5}-\frac{2}{1}-\frac{1}{1}\\=\frac{6-2-1}{5}\\=\frac{3}{5}\)
9. \(-\left(\frac{9}{-7}\right) +\left(\frac{6}{7}\right) +\left(\frac{3}{-12}\right)\\= \frac{9}{7}+ \frac{6}{7}-\frac{3}{12}\\=\frac{9}{7}+\frac{6}{7}-\frac{1}{4}\\=\frac{36}{28}+\frac{24}{28}-\frac{7}{28}\\=\frac{36+24-7}{28}\\=\frac{53}{28}\)
10. \(-\left(\frac{-9}{-8}\right) +\left(\frac{-9}{7}\right) +\left(\frac{-12}{10}\right)\\= \frac{-9}{8}- \frac{9}{7}-\frac{12}{10}\\=\frac{-9}{8}-\frac{9}{7}-\frac{6}{5}\\=\frac{-315}{280}-\frac{360}{280}-\frac{336}{280}\\=\frac{-315-360-336}{280}\\=\frac{-1011}{280}\)
11. \(-\left(\frac{10}{9}\right) +\left(\frac{-2}{-9}\right) +\left(\frac{-2}{-4}\right)\\= \frac{-10}{9}+ \frac{2}{9}+\frac{2}{4}\\=\frac{-10}{9}+\frac{2}{9}+\frac{1}{2}\\=\frac{-20}{18}+\frac{4}{18}+\frac{9}{18}\\=\frac{-20+4+9}{18}\\=\frac{-7}{18}\)
12. \(+\left(\frac{-6}{5}\right) +\left(\frac{5}{2}\right) -\left(\frac{10}{-2}\right)\\= \frac{-6}{5}+ \frac{5}{2}+\frac{10}{2}\\=\frac{-6}{5}+\frac{5}{2}+\frac{5}{1}\\=\frac{-12}{10}+\frac{25}{10}+\frac{50}{10}\\=\frac{-12+25+50}{10}\\=\frac{63}{10}\)