Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{-5}\right) +\left(\frac{-3}{9}\right) -\left(\frac{2}{-6}\right)\\= \frac{-4}{5}- \frac{3}{9}+\frac{2}{6}\\=\frac{-4}{5}-\frac{1}{3}+\frac{1}{3}\\=\frac{-12}{15}-\frac{5}{15}+\frac{5}{15}\\=\frac{-12-5+5}{15}\\=\frac{-12}{15}\\=\frac{-4}{5}\)
2. \(-\left(\frac{-6}{-5}\right) +\left(\frac{5}{-4}\right) -\left(\frac{2}{3}\right)\\= \frac{-6}{5}- \frac{5}{4}-\frac{2}{3}\\=\frac{-72}{60}-\frac{75}{60}-\frac{40}{60}\\=\frac{-72-75-40}{60}\\=\frac{-187}{60}\)
3. \(-\left(\frac{9}{7}\right) +\left(\frac{-5}{10}\right) -\left(\frac{7}{-6}\right)\\= \frac{-9}{7}- \frac{5}{10}+\frac{7}{6}\\=\frac{-9}{7}-\frac{1}{2}+\frac{7}{6}\\=\frac{-54}{42}-\frac{21}{42}+\frac{49}{42}\\=\frac{-54-21+49}{42}\\=\frac{-26}{42}\\=\frac{-13}{21}\)
4. \(+\left(\frac{8}{3}\right) -\left(\frac{6}{-9}\right) -\left(\frac{12}{-7}\right)\\= \frac{8}{3}+ \frac{6}{9}+\frac{12}{7}\\=\frac{8}{3}+\frac{2}{3}+\frac{12}{7}\\=\frac{56}{21}+\frac{14}{21}+\frac{36}{21}\\=\frac{56+14+36}{21}\\=\frac{106}{21}\)
5. \(-\left(\frac{-5}{-8}\right) +\left(\frac{8}{2}\right) +\left(\frac{-10}{-8}\right)\\= \frac{-5}{8}+ \frac{8}{2}+\frac{10}{8}\\=\frac{-5}{8}+\frac{4}{1}+\frac{5}{4}\\=\frac{-5+4+5}{8}\\=\frac{4}{8}\\=\frac{1}{2}\)
6. \(+\left(\frac{-5}{2}\right) +\left(\frac{-4}{2}\right) +\left(\frac{-7}{-2}\right)\\= \frac{-5}{2}- \frac{4}{2}+\frac{7}{2}\\=\frac{-5}{2}-\frac{2}{1}+\frac{7}{2}\\=\frac{-5-2+7}{2}\\=\frac{0}{2}\\=\frac{0}{1}\)
7. \(-\left(\frac{-2}{3}\right) -\left(\frac{-5}{7}\right) +\left(\frac{8}{-6}\right)\\= \frac{2}{3}+ \frac{5}{7}-\frac{8}{6}\\=\frac{2}{3}+\frac{5}{7}-\frac{4}{3}\\=\frac{14}{21}+\frac{15}{21}-\frac{28}{21}\\=\frac{14+15-28}{21}\\=\frac{1}{21}\)
8. \(-\left(\frac{7}{8}\right) +\left(\frac{-6}{8}\right) +\left(\frac{-2}{-4}\right)\\= \frac{-7}{8}- \frac{6}{8}+\frac{2}{4}\\=\frac{-7}{8}-\frac{3}{4}+\frac{1}{2}\\=\frac{-7-3+1}{8}\\=\frac{-9}{8}\)
9. \(+\left(\frac{-8}{-9}\right) +\left(\frac{-2}{-4}\right) +\left(\frac{-12}{4}\right)\\= \frac{8}{9}+ \frac{2}{4}-\frac{12}{4}\\=\frac{8}{9}+\frac{1}{2}-\frac{3}{1}\\=\frac{16}{18}+\frac{9}{18}-\frac{54}{18}\\=\frac{16+9-54}{18}\\=\frac{-29}{18}\)
10. \(+\left(\frac{-6}{-7}\right) +\left(\frac{-9}{8}\right) -\left(\frac{2}{-5}\right)\\= \frac{6}{7}- \frac{9}{8}+\frac{2}{5}\\=\frac{240}{280}-\frac{315}{280}+\frac{112}{280}\\=\frac{240-315+112}{280}\\=\frac{37}{280}\)
11. \(-\left(\frac{10}{9}\right) -\left(\frac{-4}{6}\right) -\left(\frac{6}{7}\right)\\= \frac{-10}{9}+ \frac{4}{6}-\frac{6}{7}\\=\frac{-10}{9}+\frac{2}{3}-\frac{6}{7}\\=\frac{-70}{63}+\frac{42}{63}-\frac{54}{63}\\=\frac{-70+42-54}{63}\\=\frac{-82}{63}\)
12. \(-\left(\frac{-3}{4}\right) +\left(\frac{3}{-9}\right) -\left(\frac{-8}{4}\right)\\= \frac{3}{4}- \frac{3}{9}+\frac{8}{4}\\=\frac{3}{4}-\frac{1}{3}+\frac{2}{1}\\=\frac{9}{12}-\frac{4}{12}+\frac{24}{12}\\=\frac{9-4+24}{12}\\=\frac{29}{12}\)