Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{-5}\right) +\left(\frac{-3}{-7}\right) +\left(\frac{-2}{10}\right)\\= \frac{9}{5}+ \frac{3}{7}-\frac{2}{10}\\=\frac{9}{5}+\frac{3}{7}-\frac{1}{5}\\=\frac{63}{35}+\frac{15}{35}-\frac{7}{35}\\=\frac{63+15-7}{35}\\=\frac{71}{35}\)
2. \(+\left(\frac{2}{5}\right) +\left(\frac{10}{7}\right) +\left(\frac{-12}{11}\right)\\= \frac{2}{5}+ \frac{10}{7}-\frac{12}{11}\\=\frac{154}{385}+\frac{550}{385}-\frac{420}{385}\\=\frac{154+550-420}{385}\\=\frac{284}{385}\)
3. \(-\left(\frac{2}{7}\right) -\left(\frac{2}{6}\right) -\left(\frac{-6}{-9}\right)\\= \frac{-2}{7}- \frac{2}{6}-\frac{6}{9}\\=\frac{-2}{7}-\frac{1}{3}-\frac{2}{3}\\=\frac{-6}{21}-\frac{7}{21}-\frac{14}{21}\\=\frac{-6-7-14}{21}\\=\frac{-27}{21}\\=\frac{-9}{7}\)
4. \(+\left(\frac{-8}{-5}\right) -\left(\frac{-10}{7}\right) -\left(\frac{6}{5}\right)\\= \frac{8}{5}+ \frac{10}{7}-\frac{6}{5}\\=\frac{56}{35}+\frac{50}{35}-\frac{42}{35}\\=\frac{56+50-42}{35}\\=\frac{64}{35}\)
5. \(-\left(\frac{8}{9}\right) +\left(\frac{-4}{-7}\right) -\left(\frac{12}{9}\right)\\= \frac{-8}{9}+ \frac{4}{7}-\frac{12}{9}\\=\frac{-8}{9}+\frac{4}{7}-\frac{4}{3}\\=\frac{-56}{63}+\frac{36}{63}-\frac{84}{63}\\=\frac{-56+36-84}{63}\\=\frac{-104}{63}\)
6. \(+\left(\frac{-8}{-3}\right) -\left(\frac{-7}{-9}\right) +\left(\frac{-3}{8}\right)\\= \frac{8}{3}- \frac{7}{9}-\frac{3}{8}\\=\frac{192}{72}-\frac{56}{72}-\frac{27}{72}\\=\frac{192-56-27}{72}\\=\frac{109}{72}\)
7. \(+\left(\frac{7}{2}\right) -\left(\frac{6}{5}\right) +\left(\frac{8}{-10}\right)\\= \frac{7}{2}- \frac{6}{5}-\frac{8}{10}\\=\frac{7}{2}-\frac{6}{5}-\frac{4}{5}\\=\frac{35}{10}-\frac{12}{10}-\frac{8}{10}\\=\frac{35-12-8}{10}\\=\frac{15}{10}\\=\frac{3}{2}\)
8. \(-\left(\frac{9}{5}\right) -\left(\frac{-4}{2}\right) +\left(\frac{6}{2}\right)\\= \frac{-9}{5}+ \frac{4}{2}+\frac{6}{2}\\=\frac{-9}{5}+\frac{2}{1}+\frac{3}{1}\\=\frac{-9+2+3}{5}\\=\frac{-4}{5}\)
9. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-10}{-2}\right) +\left(\frac{11}{4}\right)\\= \frac{-6}{5}+ \frac{10}{2}+\frac{11}{4}\\=\frac{-6}{5}+\frac{5}{1}+\frac{11}{4}\\=\frac{-24}{20}+\frac{100}{20}+\frac{55}{20}\\=\frac{-24+100+55}{20}\\=\frac{131}{20}\)
10. \(-\left(\frac{7}{-2}\right) -\left(\frac{7}{-9}\right) -\left(\frac{10}{-11}\right)\\= \frac{7}{2}+ \frac{7}{9}+\frac{10}{11}\\=\frac{693}{198}+\frac{154}{198}+\frac{180}{198}\\=\frac{693+154+180}{198}\\=\frac{1027}{198}\)
11. \(+\left(\frac{4}{3}\right) +\left(\frac{-8}{-10}\right) +\left(\frac{-5}{4}\right)\\= \frac{4}{3}+ \frac{8}{10}-\frac{5}{4}\\=\frac{4}{3}+\frac{4}{5}-\frac{5}{4}\\=\frac{80}{60}+\frac{48}{60}-\frac{75}{60}\\=\frac{80+48-75}{60}\\=\frac{53}{60}\)
12. \(+\left(\frac{-10}{9}\right) +\left(\frac{5}{-9}\right) -\left(\frac{-11}{5}\right)\\= \frac{-10}{9}- \frac{5}{9}+\frac{11}{5}\\=\frac{-50}{45}-\frac{25}{45}+\frac{99}{45}\\=\frac{-50-25+99}{45}\\=\frac{24}{45}\\=\frac{8}{15}\)