Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{5}{4}\right) +\left(\frac{-4}{-3}\right) +\left(\frac{-9}{11}\right)\\= \frac{5}{4}+ \frac{4}{3}-\frac{9}{11}\\=\frac{165}{132}+\frac{176}{132}-\frac{108}{132}\\=\frac{165+176-108}{132}\\=\frac{233}{132}\)
2. \(+\left(\frac{-4}{-3}\right) -\left(\frac{-9}{3}\right) -\left(\frac{-2}{-9}\right)\\= \frac{4}{3}+ \frac{9}{3}-\frac{2}{9}\\=\frac{4}{3}+\frac{3}{1}-\frac{2}{9}\\=\frac{12}{9}+\frac{27}{9}-\frac{2}{9}\\=\frac{12+27-2}{9}\\=\frac{37}{9}\)
3. \(+\left(\frac{5}{-6}\right) +\left(\frac{-5}{-10}\right) -\left(\frac{-5}{-9}\right)\\= \frac{-5}{6}+ \frac{5}{10}-\frac{5}{9}\\=\frac{-5}{6}+\frac{1}{2}-\frac{5}{9}\\=\frac{-15}{18}+\frac{9}{18}-\frac{10}{18}\\=\frac{-15+9-10}{18}\\=\frac{-16}{18}\\=\frac{-8}{9}\)
4. \(+\left(\frac{-10}{-7}\right) -\left(\frac{-5}{-2}\right) +\left(\frac{-12}{-11}\right)\\= \frac{10}{7}- \frac{5}{2}+\frac{12}{11}\\=\frac{220}{154}-\frac{385}{154}+\frac{168}{154}\\=\frac{220-385+168}{154}\\=\frac{3}{154}\)
5. \(+\left(\frac{-3}{5}\right) -\left(\frac{6}{2}\right) -\left(\frac{12}{-9}\right)\\= \frac{-3}{5}- \frac{6}{2}+\frac{12}{9}\\=\frac{-3}{5}-\frac{3}{1}+\frac{4}{3}\\=\frac{-9}{15}-\frac{45}{15}+\frac{20}{15}\\=\frac{-9-45+20}{15}\\=\frac{-34}{15}\)
6. \(-\left(\frac{-9}{-8}\right) +\left(\frac{6}{5}\right) +\left(\frac{-10}{4}\right)\\= \frac{-9}{8}+ \frac{6}{5}-\frac{10}{4}\\=\frac{-9}{8}+\frac{6}{5}-\frac{5}{2}\\=\frac{-45}{40}+\frac{48}{40}-\frac{100}{40}\\=\frac{-45+48-100}{40}\\=\frac{-97}{40}\)
7. \(-\left(\frac{2}{9}\right) +\left(\frac{2}{-10}\right) -\left(\frac{3}{9}\right)\\= \frac{-2}{9}- \frac{2}{10}-\frac{3}{9}\\=\frac{-2}{9}-\frac{1}{5}-\frac{1}{3}\\=\frac{-10}{45}-\frac{9}{45}-\frac{15}{45}\\=\frac{-10-9-15}{45}\\=\frac{-34}{45}\)
8. \(-\left(\frac{-6}{5}\right) -\left(\frac{-5}{-2}\right) +\left(\frac{-4}{-11}\right)\\= \frac{6}{5}- \frac{5}{2}+\frac{4}{11}\\=\frac{132}{110}-\frac{275}{110}+\frac{40}{110}\\=\frac{132-275+40}{110}\\=\frac{-103}{110}\)
9. \(-\left(\frac{-7}{-5}\right) -\left(\frac{-9}{-10}\right) -\left(\frac{12}{12}\right)\\= \frac{-7}{5}- \frac{9}{10}-\frac{12}{12}\\=\frac{-7}{5}-\frac{9}{10}-\frac{1}{1}\\=\frac{-14}{10}-\frac{9}{10}-\frac{10}{10}\\=\frac{-14-9-10}{10}\\=\frac{-33}{10}\)
10. \(+\left(\frac{8}{-5}\right) +\left(\frac{-10}{-2}\right) -\left(\frac{-6}{4}\right)\\= \frac{-8}{5}+ \frac{10}{2}+\frac{6}{4}\\=\frac{-8}{5}+\frac{5}{1}+\frac{3}{2}\\=\frac{-16}{10}+\frac{50}{10}+\frac{15}{10}\\=\frac{-16+50+15}{10}\\=\frac{49}{10}\)
11. \(+\left(\frac{4}{3}\right) -\left(\frac{-7}{-9}\right) -\left(\frac{8}{3}\right)\\= \frac{4}{3}- \frac{7}{9}-\frac{8}{3}\\=\frac{12}{9}-\frac{7}{9}-\frac{24}{9}\\=\frac{12-7-24}{9}\\=\frac{-19}{9}\)
12. \(+\left(\frac{-8}{3}\right) +\left(\frac{-2}{-4}\right) +\left(\frac{-5}{4}\right)\\= \frac{-8}{3}+ \frac{2}{4}-\frac{5}{4}\\=\frac{-8}{3}+\frac{1}{2}-\frac{5}{4}\\=\frac{-32}{12}+\frac{6}{12}-\frac{15}{12}\\=\frac{-32+6-15}{12}\\=\frac{-41}{12}\)