Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{10}{-7}\right) +\left(\frac{9}{-2}\right) -\left(\frac{5}{7}\right)\\= \frac{-10}{7}- \frac{9}{2}-\frac{5}{7}\\=\frac{-20}{14}-\frac{63}{14}-\frac{10}{14}\\=\frac{-20-63-10}{14}\\=\frac{-93}{14}\)
2. \(-\left(\frac{5}{4}\right) -\left(\frac{-3}{5}\right) +\left(\frac{11}{12}\right)\\= \frac{-5}{4}+ \frac{3}{5}+\frac{11}{12}\\=\frac{-75}{60}+\frac{36}{60}+\frac{55}{60}\\=\frac{-75+36+55}{60}\\=\frac{16}{60}\\=\frac{4}{15}\)
3. \(+\left(\frac{-9}{4}\right) +\left(\frac{-8}{5}\right) +\left(\frac{2}{-10}\right)\\= \frac{-9}{4}- \frac{8}{5}-\frac{2}{10}\\=\frac{-9}{4}-\frac{8}{5}-\frac{1}{5}\\=\frac{-45}{20}-\frac{32}{20}-\frac{4}{20}\\=\frac{-45-32-4}{20}\\=\frac{-81}{20}\)
4. \(+\left(\frac{9}{-2}\right) -\left(\frac{8}{4}\right) +\left(\frac{9}{3}\right)\\= \frac{-9}{2}- \frac{8}{4}+\frac{9}{3}\\=\frac{-9}{2}-\frac{2}{1}+\frac{3}{1}\\=\frac{-9-2+3}{2}\\=\frac{-8}{2}\\=\frac{-4}{1}\)
5. \(-\left(\frac{7}{8}\right) +\left(\frac{-6}{-9}\right) -\left(\frac{-3}{-5}\right)\\= \frac{-7}{8}+ \frac{6}{9}-\frac{3}{5}\\=\frac{-7}{8}+\frac{2}{3}-\frac{3}{5}\\=\frac{-105}{120}+\frac{80}{120}-\frac{72}{120}\\=\frac{-105+80-72}{120}\\=\frac{-97}{120}\)
6. \(-\left(\frac{-10}{9}\right) +\left(\frac{5}{7}\right) +\left(\frac{-6}{-2}\right)\\= \frac{10}{9}+ \frac{5}{7}+\frac{6}{2}\\=\frac{10}{9}+\frac{5}{7}+\frac{3}{1}\\=\frac{70}{63}+\frac{45}{63}+\frac{189}{63}\\=\frac{70+45+189}{63}\\=\frac{304}{63}\)
7. \(-\left(\frac{4}{9}\right) +\left(\frac{-10}{-10}\right) +\left(\frac{-11}{4}\right)\\= \frac{-4}{9}+ \frac{10}{10}-\frac{11}{4}\\=\frac{-4}{9}+\frac{1}{1}-\frac{11}{4}\\=\frac{-16}{36}+\frac{36}{36}-\frac{99}{36}\\=\frac{-16+36-99}{36}\\=\frac{-79}{36}\)
8. \(-\left(\frac{2}{3}\right) -\left(\frac{9}{-4}\right) +\left(\frac{10}{5}\right)\\= \frac{-2}{3}+ \frac{9}{4}+\frac{10}{5}\\=\frac{-2}{3}+\frac{9}{4}+\frac{2}{1}\\=\frac{-8}{12}+\frac{27}{12}+\frac{24}{12}\\=\frac{-8+27+24}{12}\\=\frac{43}{12}\)
9. \(+\left(\frac{7}{-2}\right) +\left(\frac{-9}{3}\right) -\left(\frac{-6}{6}\right)\\= \frac{-7}{2}- \frac{9}{3}+\frac{6}{6}\\=\frac{-7}{2}-\frac{3}{1}+\frac{1}{1}\\=\frac{-7-3+1}{2}\\=\frac{-9}{2}\)
10. \(-\left(\frac{-7}{2}\right) +\left(\frac{-9}{-6}\right) -\left(\frac{-12}{-11}\right)\\= \frac{7}{2}+ \frac{9}{6}-\frac{12}{11}\\=\frac{7}{2}+\frac{3}{2}-\frac{12}{11}\\=\frac{77}{22}+\frac{33}{22}-\frac{24}{22}\\=\frac{77+33-24}{22}\\=\frac{86}{22}\\=\frac{43}{11}\)
11. \(-\left(\frac{-7}{-2}\right) -\left(\frac{-9}{-9}\right) -\left(\frac{-11}{-6}\right)\\= \frac{-7}{2}- \frac{9}{9}-\frac{11}{6}\\=\frac{-7}{2}-\frac{1}{1}-\frac{11}{6}\\=\frac{-21}{6}-\frac{6}{6}-\frac{11}{6}\\=\frac{-21-6-11}{6}\\=\frac{-38}{6}\\=\frac{-19}{3}\)
12. \(-\left(\frac{-7}{2}\right) -\left(\frac{-6}{4}\right) +\left(\frac{-6}{-5}\right)\\= \frac{7}{2}+ \frac{6}{4}+\frac{6}{5}\\=\frac{7}{2}+\frac{3}{2}+\frac{6}{5}\\=\frac{35}{10}+\frac{15}{10}+\frac{12}{10}\\=\frac{35+15+12}{10}\\=\frac{62}{10}\\=\frac{31}{5}\)