Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{-4}{-3}\right) +\left(\frac{-5}{-10}\right) +\left(\frac{-4}{-4}\right)\\= \frac{4}{3}+ \frac{5}{10}+\frac{4}{4}\\=\frac{4}{3}+\frac{1}{2}+\frac{1}{1}\\=\frac{8}{6}+\frac{3}{6}+\frac{6}{6}\\=\frac{8+3+6}{6}\\=\frac{17}{6}\)
2. \(-\left(\frac{9}{4}\right) +\left(\frac{-3}{-4}\right) -\left(\frac{-3}{5}\right)\\= \frac{-9}{4}+ \frac{3}{4}+\frac{3}{5}\\=\frac{-45}{20}+\frac{15}{20}+\frac{12}{20}\\=\frac{-45+15+12}{20}\\=\frac{-18}{20}\\=\frac{-9}{10}\)
3. \(+\left(\frac{4}{9}\right) +\left(\frac{5}{-4}\right) -\left(\frac{6}{-11}\right)\\= \frac{4}{9}- \frac{5}{4}+\frac{6}{11}\\=\frac{176}{396}-\frac{495}{396}+\frac{216}{396}\\=\frac{176-495+216}{396}\\=\frac{-103}{396}\)
4. \(-\left(\frac{7}{4}\right) +\left(\frac{-9}{-10}\right) -\left(\frac{-10}{-8}\right)\\= \frac{-7}{4}+ \frac{9}{10}-\frac{10}{8}\\=\frac{-7}{4}+\frac{9}{10}-\frac{5}{4}\\=\frac{-35}{20}+\frac{18}{20}-\frac{25}{20}\\=\frac{-35+18-25}{20}\\=\frac{-42}{20}\\=\frac{-21}{10}\)
5. \(-\left(\frac{-9}{-2}\right) +\left(\frac{-9}{-7}\right) -\left(\frac{4}{9}\right)\\= \frac{-9}{2}+ \frac{9}{7}-\frac{4}{9}\\=\frac{-567}{126}+\frac{162}{126}-\frac{56}{126}\\=\frac{-567+162-56}{126}\\=\frac{-461}{126}\)
6. \(-\left(\frac{8}{-9}\right) +\left(\frac{-2}{-6}\right) -\left(\frac{11}{-7}\right)\\= \frac{8}{9}+ \frac{2}{6}+\frac{11}{7}\\=\frac{8}{9}+\frac{1}{3}+\frac{11}{7}\\=\frac{56}{63}+\frac{21}{63}+\frac{99}{63}\\=\frac{56+21+99}{63}\\=\frac{176}{63}\)
7. \(-\left(\frac{-3}{-2}\right) -\left(\frac{2}{-2}\right) -\left(\frac{12}{12}\right)\\= \frac{-3}{2}+ \frac{2}{2}-\frac{12}{12}\\=\frac{-3}{2}+\frac{1}{1}-\frac{1}{1}\\=\frac{-3+1-1}{2}\\=\frac{-3}{2}\)
8. \(-\left(\frac{-9}{-2}\right) -\left(\frac{10}{-9}\right) -\left(\frac{8}{-5}\right)\\= \frac{-9}{2}+ \frac{10}{9}+\frac{8}{5}\\=\frac{-405}{90}+\frac{100}{90}+\frac{144}{90}\\=\frac{-405+100+144}{90}\\=\frac{-161}{90}\)
9. \(-\left(\frac{6}{-7}\right) -\left(\frac{10}{-10}\right) +\left(\frac{-12}{9}\right)\\= \frac{6}{7}+ \frac{10}{10}-\frac{12}{9}\\=\frac{6}{7}+\frac{1}{1}-\frac{4}{3}\\=\frac{18}{21}+\frac{21}{21}-\frac{28}{21}\\=\frac{18+21-28}{21}\\=\frac{11}{21}\)
10. \(-\left(\frac{-4}{3}\right) -\left(\frac{-2}{3}\right) +\left(\frac{-10}{-8}\right)\\= \frac{4}{3}+ \frac{2}{3}+\frac{10}{8}\\=\frac{4}{3}+\frac{2}{3}+\frac{5}{4}\\=\frac{16}{12}+\frac{8}{12}+\frac{15}{12}\\=\frac{16+8+15}{12}\\=\frac{39}{12}\\=\frac{13}{4}\)
11. \(+\left(\frac{-2}{5}\right) +\left(\frac{5}{-5}\right) +\left(\frac{5}{6}\right)\\= \frac{-2}{5}- \frac{5}{5}+\frac{5}{6}\\=\frac{-2}{5}-\frac{1}{1}+\frac{5}{6}\\=\frac{-12}{30}-\frac{30}{30}+\frac{25}{30}\\=\frac{-12-30+25}{30}\\=\frac{-17}{30}\)
12. \(-\left(\frac{5}{4}\right) -\left(\frac{-6}{-5}\right) +\left(\frac{9}{-4}\right)\\= \frac{-5}{4}- \frac{6}{5}-\frac{9}{4}\\=\frac{-25}{20}-\frac{24}{20}-\frac{45}{20}\\=\frac{-25-24-45}{20}\\=\frac{-94}{20}\\=\frac{-47}{10}\)