Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{7}\right) -\left(\frac{-9}{10}\right) +\left(\frac{3}{-6}\right)\\= \frac{9}{7}+ \frac{9}{10}-\frac{3}{6}\\=\frac{9}{7}+\frac{9}{10}-\frac{1}{2}\\=\frac{90}{70}+\frac{63}{70}-\frac{35}{70}\\=\frac{90+63-35}{70}\\=\frac{118}{70}\\=\frac{59}{35}\)
2. \(+\left(\frac{7}{2}\right) -\left(\frac{-7}{-10}\right) -\left(\frac{-4}{3}\right)\\= \frac{7}{2}- \frac{7}{10}+\frac{4}{3}\\=\frac{105}{30}-\frac{21}{30}+\frac{40}{30}\\=\frac{105-21+40}{30}\\=\frac{124}{30}\\=\frac{62}{15}\)
3. \(-\left(\frac{-5}{-6}\right) +\left(\frac{7}{6}\right) -\left(\frac{-9}{7}\right)\\= \frac{-5}{6}+ \frac{7}{6}+\frac{9}{7}\\=\frac{-35}{42}+\frac{49}{42}+\frac{54}{42}\\=\frac{-35+49+54}{42}\\=\frac{68}{42}\\=\frac{34}{21}\)
4. \(-\left(\frac{5}{7}\right) -\left(\frac{5}{6}\right) -\left(\frac{-12}{-3}\right)\\= \frac{-5}{7}- \frac{5}{6}-\frac{12}{3}\\=\frac{-5}{7}-\frac{5}{6}-\frac{4}{1}\\=\frac{-30}{42}-\frac{35}{42}-\frac{168}{42}\\=\frac{-30-35-168}{42}\\=\frac{-233}{42}\)
5. \(+\left(\frac{3}{5}\right) -\left(\frac{9}{6}\right) -\left(\frac{-7}{-7}\right)\\= \frac{3}{5}- \frac{9}{6}-\frac{7}{7}\\=\frac{3}{5}-\frac{3}{2}-\frac{1}{1}\\=\frac{6}{10}-\frac{15}{10}-\frac{10}{10}\\=\frac{6-15-10}{10}\\=\frac{-19}{10}\)
6. \(+\left(\frac{10}{-3}\right) +\left(\frac{-5}{-9}\right) -\left(\frac{-12}{-8}\right)\\= \frac{-10}{3}+ \frac{5}{9}-\frac{12}{8}\\=\frac{-10}{3}+\frac{5}{9}-\frac{3}{2}\\=\frac{-60}{18}+\frac{10}{18}-\frac{27}{18}\\=\frac{-60+10-27}{18}\\=\frac{-77}{18}\)
7. \(+\left(\frac{-2}{5}\right) +\left(\frac{-2}{-7}\right) +\left(\frac{7}{11}\right)\\= \frac{-2}{5}+ \frac{2}{7}+\frac{7}{11}\\=\frac{-154}{385}+\frac{110}{385}+\frac{245}{385}\\=\frac{-154+110+245}{385}\\=\frac{201}{385}\)
8. \(+\left(\frac{-6}{5}\right) -\left(\frac{7}{5}\right) +\left(\frac{-8}{-12}\right)\\= \frac{-6}{5}- \frac{7}{5}+\frac{8}{12}\\=\frac{-6}{5}-\frac{7}{5}+\frac{2}{3}\\=\frac{-18}{15}-\frac{21}{15}+\frac{10}{15}\\=\frac{-18-21+10}{15}\\=\frac{-29}{15}\)
9. \(+\left(\frac{-2}{-9}\right) +\left(\frac{10}{-9}\right) +\left(\frac{-9}{5}\right)\\= \frac{2}{9}- \frac{10}{9}-\frac{9}{5}\\=\frac{10}{45}-\frac{50}{45}-\frac{81}{45}\\=\frac{10-50-81}{45}\\=\frac{-121}{45}\)
10. \(+\left(\frac{-3}{7}\right) +\left(\frac{2}{7}\right) -\left(\frac{8}{-2}\right)\\= \frac{-3}{7}+ \frac{2}{7}+\frac{8}{2}\\=\frac{-3}{7}+\frac{2}{7}+\frac{4}{1}\\=\frac{-3+2+4}{7}\\=\frac{3}{7}\)
11. \(-\left(\frac{-8}{-7}\right) -\left(\frac{7}{9}\right) -\left(\frac{4}{7}\right)\\= \frac{-8}{7}- \frac{7}{9}-\frac{4}{7}\\=\frac{-72}{63}-\frac{49}{63}-\frac{36}{63}\\=\frac{-72-49-36}{63}\\=\frac{-157}{63}\)
12. \(-\left(\frac{-3}{7}\right) -\left(\frac{4}{-5}\right) -\left(\frac{-9}{7}\right)\\= \frac{3}{7}+ \frac{4}{5}+\frac{9}{7}\\=\frac{15}{35}+\frac{28}{35}+\frac{45}{35}\\=\frac{15+28+45}{35}\\=\frac{88}{35}\)