Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{8}\right) -\left(\frac{-10}{8}\right) -\left(\frac{-12}{-4}\right)\\= \frac{9}{8}+ \frac{10}{8}-\frac{12}{4}\\=\frac{9}{8}+\frac{5}{4}-\frac{3}{1}\\=\frac{9+5-3}{8}\\=\frac{11}{8}\)
2. \(+\left(\frac{6}{-5}\right) -\left(\frac{-9}{6}\right) +\left(\frac{-7}{12}\right)\\= \frac{-6}{5}+ \frac{9}{6}-\frac{7}{12}\\=\frac{-6}{5}+\frac{3}{2}-\frac{7}{12}\\=\frac{-72}{60}+\frac{90}{60}-\frac{35}{60}\\=\frac{-72+90-35}{60}\\=\frac{-17}{60}\)
3. \(+\left(\frac{-10}{-9}\right) +\left(\frac{8}{-10}\right) -\left(\frac{7}{-3}\right)\\= \frac{10}{9}- \frac{8}{10}+\frac{7}{3}\\=\frac{10}{9}-\frac{4}{5}+\frac{7}{3}\\=\frac{50}{45}-\frac{36}{45}+\frac{105}{45}\\=\frac{50-36+105}{45}\\=\frac{119}{45}\)
4. \(+\left(\frac{8}{-7}\right) -\left(\frac{3}{-6}\right) +\left(\frac{4}{-5}\right)\\= \frac{-8}{7}+ \frac{3}{6}-\frac{4}{5}\\=\frac{-8}{7}+\frac{1}{2}-\frac{4}{5}\\=\frac{-80}{70}+\frac{35}{70}-\frac{56}{70}\\=\frac{-80+35-56}{70}\\=\frac{-101}{70}\)
5. \(-\left(\frac{-3}{7}\right) -\left(\frac{2}{-3}\right) -\left(\frac{-7}{-5}\right)\\= \frac{3}{7}+ \frac{2}{3}-\frac{7}{5}\\=\frac{45}{105}+\frac{70}{105}-\frac{147}{105}\\=\frac{45+70-147}{105}\\=\frac{-32}{105}\)
6. \(-\left(\frac{-6}{5}\right) +\left(\frac{9}{4}\right) +\left(\frac{-2}{-7}\right)\\= \frac{6}{5}+ \frac{9}{4}+\frac{2}{7}\\=\frac{168}{140}+\frac{315}{140}+\frac{40}{140}\\=\frac{168+315+40}{140}\\=\frac{523}{140}\)
7. \(+\left(\frac{-8}{3}\right) +\left(\frac{-2}{-2}\right) -\left(\frac{5}{7}\right)\\= \frac{-8}{3}+ \frac{2}{2}-\frac{5}{7}\\=\frac{-8}{3}+\frac{1}{1}-\frac{5}{7}\\=\frac{-56}{21}+\frac{21}{21}-\frac{15}{21}\\=\frac{-56+21-15}{21}\\=\frac{-50}{21}\)
8. \(+\left(\frac{8}{5}\right) -\left(\frac{10}{9}\right) +\left(\frac{-9}{-10}\right)\\= \frac{8}{5}- \frac{10}{9}+\frac{9}{10}\\=\frac{144}{90}-\frac{100}{90}+\frac{81}{90}\\=\frac{144-100+81}{90}\\=\frac{125}{90}\\=\frac{25}{18}\)
9. \(-\left(\frac{-2}{-9}\right) -\left(\frac{7}{6}\right) +\left(\frac{10}{-10}\right)\\= \frac{-2}{9}- \frac{7}{6}-\frac{10}{10}\\=\frac{-2}{9}-\frac{7}{6}-\frac{1}{1}\\=\frac{-4}{18}-\frac{21}{18}-\frac{18}{18}\\=\frac{-4-21-18}{18}\\=\frac{-43}{18}\)
10. \(-\left(\frac{9}{-4}\right) -\left(\frac{4}{10}\right) -\left(\frac{-6}{-6}\right)\\= \frac{9}{4}- \frac{4}{10}-\frac{6}{6}\\=\frac{9}{4}-\frac{2}{5}-\frac{1}{1}\\=\frac{45}{20}-\frac{8}{20}-\frac{20}{20}\\=\frac{45-8-20}{20}\\=\frac{17}{20}\)
11. \(+\left(\frac{4}{9}\right) -\left(\frac{-4}{5}\right) +\left(\frac{10}{-6}\right)\\= \frac{4}{9}+ \frac{4}{5}-\frac{10}{6}\\=\frac{4}{9}+\frac{4}{5}-\frac{5}{3}\\=\frac{20}{45}+\frac{36}{45}-\frac{75}{45}\\=\frac{20+36-75}{45}\\=\frac{-19}{45}\)
12. \(+\left(\frac{-2}{7}\right) +\left(\frac{-6}{8}\right) +\left(\frac{9}{-12}\right)\\= \frac{-2}{7}- \frac{6}{8}-\frac{9}{12}\\=\frac{-2}{7}-\frac{3}{4}-\frac{3}{4}\\=\frac{-8}{28}-\frac{21}{28}-\frac{21}{28}\\=\frac{-8-21-21}{28}\\=\frac{-50}{28}\\=\frac{-25}{14}\)