Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{10}{3}\right) -\left(\frac{-7}{4}\right) -\left(\frac{10}{-5}\right)\\= \frac{10}{3}+ \frac{7}{4}+\frac{10}{5}\\=\frac{10}{3}+\frac{7}{4}+\frac{2}{1}\\=\frac{40}{12}+\frac{21}{12}+\frac{24}{12}\\=\frac{40+21+24}{12}\\=\frac{85}{12}\)
2. \(+\left(\frac{6}{-5}\right) +\left(\frac{7}{-4}\right) +\left(\frac{-2}{3}\right)\\= \frac{-6}{5}- \frac{7}{4}-\frac{2}{3}\\=\frac{-72}{60}-\frac{105}{60}-\frac{40}{60}\\=\frac{-72-105-40}{60}\\=\frac{-217}{60}\)
3. \(-\left(\frac{-10}{9}\right) +\left(\frac{4}{-8}\right) +\left(\frac{-9}{7}\right)\\= \frac{10}{9}- \frac{4}{8}-\frac{9}{7}\\=\frac{10}{9}-\frac{1}{2}-\frac{9}{7}\\=\frac{140}{126}-\frac{63}{126}-\frac{162}{126}\\=\frac{140-63-162}{126}\\=\frac{-85}{126}\)
4. \(-\left(\frac{-3}{7}\right) -\left(\frac{10}{3}\right) -\left(\frac{10}{5}\right)\\= \frac{3}{7}- \frac{10}{3}-\frac{10}{5}\\=\frac{3}{7}-\frac{10}{3}-\frac{2}{1}\\=\frac{9}{21}-\frac{70}{21}-\frac{42}{21}\\=\frac{9-70-42}{21}\\=\frac{-103}{21}\)
5. \(+\left(\frac{-4}{7}\right) +\left(\frac{-8}{-10}\right) -\left(\frac{-8}{-8}\right)\\= \frac{-4}{7}+ \frac{8}{10}-\frac{8}{8}\\=\frac{-4}{7}+\frac{4}{5}-\frac{1}{1}\\=\frac{-20}{35}+\frac{28}{35}-\frac{35}{35}\\=\frac{-20+28-35}{35}\\=\frac{-27}{35}\)
6. \(-\left(\frac{-2}{9}\right) +\left(\frac{4}{-4}\right) -\left(\frac{-7}{5}\right)\\= \frac{2}{9}- \frac{4}{4}+\frac{7}{5}\\=\frac{2}{9}-\frac{1}{1}+\frac{7}{5}\\=\frac{10}{45}-\frac{45}{45}+\frac{63}{45}\\=\frac{10-45+63}{45}\\=\frac{28}{45}\)
7. \(-\left(\frac{3}{10}\right) +\left(\frac{5}{-2}\right) +\left(\frac{9}{10}\right)\\= \frac{-3}{10}- \frac{5}{2}+\frac{9}{10}\\=\frac{-3-5+9}{10}\\=\frac{1}{10}\)
8. \(+\left(\frac{10}{-9}\right) +\left(\frac{8}{4}\right) -\left(\frac{3}{-6}\right)\\= \frac{-10}{9}+ \frac{8}{4}+\frac{3}{6}\\=\frac{-10}{9}+\frac{2}{1}+\frac{1}{2}\\=\frac{-20}{18}+\frac{36}{18}+\frac{9}{18}\\=\frac{-20+36+9}{18}\\=\frac{25}{18}\)
9. \(-\left(\frac{-7}{2}\right) +\left(\frac{-2}{-3}\right) -\left(\frac{-12}{-9}\right)\\= \frac{7}{2}+ \frac{2}{3}-\frac{12}{9}\\=\frac{7}{2}+\frac{2}{3}-\frac{4}{3}\\=\frac{21}{6}+\frac{4}{6}-\frac{8}{6}\\=\frac{21+4-8}{6}\\=\frac{17}{6}\)
10. \(+\left(\frac{2}{-7}\right) -\left(\frac{-7}{4}\right) +\left(\frac{12}{3}\right)\\= \frac{-2}{7}+ \frac{7}{4}+\frac{12}{3}\\=\frac{-2}{7}+\frac{7}{4}+\frac{4}{1}\\=\frac{-8}{28}+\frac{49}{28}+\frac{112}{28}\\=\frac{-8+49+112}{28}\\=\frac{153}{28}\)
11. \(+\left(\frac{-2}{7}\right) +\left(\frac{2}{-10}\right) +\left(\frac{-10}{4}\right)\\= \frac{-2}{7}- \frac{2}{10}-\frac{10}{4}\\=\frac{-2}{7}-\frac{1}{5}-\frac{5}{2}\\=\frac{-20}{70}-\frac{14}{70}-\frac{175}{70}\\=\frac{-20-14-175}{70}\\=\frac{-209}{70}\)
12. \(+\left(\frac{5}{-3}\right) +\left(\frac{-10}{-6}\right) -\left(\frac{-12}{-6}\right)\\= \frac{-5}{3}+ \frac{10}{6}-\frac{12}{6}\\=\frac{-5}{3}+\frac{5}{3}-\frac{2}{1}\\=\frac{-5+5-2}{3}\\=\frac{-2}{3}\)