Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{3}{2}\right) +\left(\frac{7}{10}\right) -\left(\frac{-6}{-5}\right)\\= \frac{3}{2}+ \frac{7}{10}-\frac{6}{5}\\=\frac{15}{10}+\frac{7}{10}-\frac{12}{10}\\=\frac{15+7-12}{10}\\=\frac{10}{10}\\=\frac{1}{1}\)
2. \(-\left(\frac{-9}{4}\right) -\left(\frac{4}{-9}\right) -\left(\frac{12}{9}\right)\\= \frac{9}{4}+ \frac{4}{9}-\frac{12}{9}\\=\frac{9}{4}+\frac{4}{9}-\frac{4}{3}\\=\frac{81}{36}+\frac{16}{36}-\frac{48}{36}\\=\frac{81+16-48}{36}\\=\frac{49}{36}\)
3. \(-\left(\frac{10}{3}\right) +\left(\frac{-3}{-5}\right) -\left(\frac{2}{2}\right)\\= \frac{-10}{3}+ \frac{3}{5}-\frac{2}{2}\\=\frac{-10}{3}+\frac{3}{5}-\frac{1}{1}\\=\frac{-50}{15}+\frac{9}{15}-\frac{15}{15}\\=\frac{-50+9-15}{15}\\=\frac{-56}{15}\)
4. \(+\left(\frac{6}{-5}\right) +\left(\frac{9}{4}\right) +\left(\frac{7}{3}\right)\\= \frac{-6}{5}+ \frac{9}{4}+\frac{7}{3}\\=\frac{-72}{60}+\frac{135}{60}+\frac{140}{60}\\=\frac{-72+135+140}{60}\\=\frac{203}{60}\)
5. \(+\left(\frac{-3}{-2}\right) -\left(\frac{5}{-5}\right) +\left(\frac{11}{-4}\right)\\= \frac{3}{2}+ \frac{5}{5}-\frac{11}{4}\\=\frac{3}{2}+\frac{1}{1}-\frac{11}{4}\\=\frac{6}{4}+\frac{4}{4}-\frac{11}{4}\\=\frac{6+4-11}{4}\\=\frac{-1}{4}\)
6. \(+\left(\frac{-8}{3}\right) +\left(\frac{10}{10}\right) -\left(\frac{-6}{-7}\right)\\= \frac{-8}{3}+ \frac{10}{10}-\frac{6}{7}\\=\frac{-8}{3}+\frac{1}{1}-\frac{6}{7}\\=\frac{-56}{21}+\frac{21}{21}-\frac{18}{21}\\=\frac{-56+21-18}{21}\\=\frac{-53}{21}\)
7. \(-\left(\frac{-10}{9}\right) -\left(\frac{-3}{-3}\right) -\left(\frac{-9}{-5}\right)\\= \frac{10}{9}- \frac{3}{3}-\frac{9}{5}\\=\frac{10}{9}-\frac{1}{1}-\frac{9}{5}\\=\frac{50}{45}-\frac{45}{45}-\frac{81}{45}\\=\frac{50-45-81}{45}\\=\frac{-76}{45}\)
8. \(+\left(\frac{-10}{-3}\right) +\left(\frac{-6}{-6}\right) -\left(\frac{2}{8}\right)\\= \frac{10}{3}+ \frac{6}{6}-\frac{2}{8}\\=\frac{10}{3}+\frac{1}{1}-\frac{1}{4}\\=\frac{40}{12}+\frac{12}{12}-\frac{3}{12}\\=\frac{40+12-3}{12}\\=\frac{49}{12}\)
9. \(+\left(\frac{-10}{9}\right) -\left(\frac{2}{-2}\right) -\left(\frac{4}{12}\right)\\= \frac{-10}{9}+ \frac{2}{2}-\frac{4}{12}\\=\frac{-10}{9}+\frac{1}{1}-\frac{1}{3}\\=\frac{-10+1-1}{9}\\=\frac{-10}{9}\)
10. \(-\left(\frac{5}{8}\right) +\left(\frac{3}{-8}\right) -\left(\frac{3}{-11}\right)\\= \frac{-5}{8}- \frac{3}{8}+\frac{3}{11}\\=\frac{-55}{88}-\frac{33}{88}+\frac{24}{88}\\=\frac{-55-33+24}{88}\\=\frac{-64}{88}\\=\frac{-8}{11}\)
11. \(-\left(\frac{4}{-9}\right) +\left(\frac{7}{8}\right) -\left(\frac{-11}{-9}\right)\\= \frac{4}{9}+ \frac{7}{8}-\frac{11}{9}\\=\frac{32}{72}+\frac{63}{72}-\frac{88}{72}\\=\frac{32+63-88}{72}\\=\frac{7}{72}\)
12. \(+\left(\frac{8}{7}\right) +\left(\frac{8}{-9}\right) -\left(\frac{-9}{5}\right)\\= \frac{8}{7}- \frac{8}{9}+\frac{9}{5}\\=\frac{360}{315}-\frac{280}{315}+\frac{567}{315}\\=\frac{360-280+567}{315}\\=\frac{647}{315}\)