Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{5}\right) +\left(\frac{-8}{3}\right) +\left(\frac{11}{10}\right)\\= \frac{3}{5}- \frac{8}{3}+\frac{11}{10}\\=\frac{18}{30}-\frac{80}{30}+\frac{33}{30}\\=\frac{18-80+33}{30}\\=\frac{-29}{30}\)
2. \(+\left(\frac{9}{5}\right) -\left(\frac{9}{3}\right) -\left(\frac{-8}{2}\right)\\= \frac{9}{5}- \frac{9}{3}+\frac{8}{2}\\=\frac{9}{5}-\frac{3}{1}+\frac{4}{1}\\=\frac{9-3+4}{5}\\=\frac{10}{5}\\=\frac{2}{1}\)
3. \(-\left(\frac{10}{3}\right) -\left(\frac{-2}{-7}\right) +\left(\frac{10}{8}\right)\\= \frac{-10}{3}- \frac{2}{7}+\frac{10}{8}\\=\frac{-10}{3}-\frac{2}{7}+\frac{5}{4}\\=\frac{-280}{84}-\frac{24}{84}+\frac{105}{84}\\=\frac{-280-24+105}{84}\\=\frac{-199}{84}\)
4. \(-\left(\frac{3}{7}\right) +\left(\frac{-7}{-5}\right) +\left(\frac{-4}{2}\right)\\= \frac{-3}{7}+ \frac{7}{5}-\frac{4}{2}\\=\frac{-3}{7}+\frac{7}{5}-\frac{2}{1}\\=\frac{-15}{35}+\frac{49}{35}-\frac{70}{35}\\=\frac{-15+49-70}{35}\\=\frac{-36}{35}\)
5. \(-\left(\frac{9}{7}\right) +\left(\frac{-2}{-8}\right) -\left(\frac{-2}{5}\right)\\= \frac{-9}{7}+ \frac{2}{8}+\frac{2}{5}\\=\frac{-9}{7}+\frac{1}{4}+\frac{2}{5}\\=\frac{-180}{140}+\frac{35}{140}+\frac{56}{140}\\=\frac{-180+35+56}{140}\\=\frac{-89}{140}\)
6. \(-\left(\frac{-9}{-4}\right) +\left(\frac{-2}{4}\right) +\left(\frac{-12}{11}\right)\\= \frac{-9}{4}- \frac{2}{4}-\frac{12}{11}\\=\frac{-9}{4}-\frac{1}{2}-\frac{12}{11}\\=\frac{-99}{44}-\frac{22}{44}-\frac{48}{44}\\=\frac{-99-22-48}{44}\\=\frac{-169}{44}\)
7. \(+\left(\frac{-4}{3}\right) -\left(\frac{4}{5}\right) +\left(\frac{-2}{8}\right)\\= \frac{-4}{3}- \frac{4}{5}-\frac{2}{8}\\=\frac{-4}{3}-\frac{4}{5}-\frac{1}{4}\\=\frac{-80}{60}-\frac{48}{60}-\frac{15}{60}\\=\frac{-80-48-15}{60}\\=\frac{-143}{60}\)
8. \(-\left(\frac{7}{-6}\right) -\left(\frac{5}{6}\right) +\left(\frac{-6}{10}\right)\\= \frac{7}{6}- \frac{5}{6}-\frac{6}{10}\\=\frac{7}{6}-\frac{5}{6}-\frac{3}{5}\\=\frac{35}{30}-\frac{25}{30}-\frac{18}{30}\\=\frac{35-25-18}{30}\\=\frac{-8}{30}\\=\frac{-4}{15}\)
9. \(-\left(\frac{7}{-4}\right) +\left(\frac{6}{7}\right) -\left(\frac{-11}{-10}\right)\\= \frac{7}{4}+ \frac{6}{7}-\frac{11}{10}\\=\frac{245}{140}+\frac{120}{140}-\frac{154}{140}\\=\frac{245+120-154}{140}\\=\frac{211}{140}\)
10. \(-\left(\frac{-9}{-5}\right) -\left(\frac{5}{8}\right) +\left(\frac{-4}{-2}\right)\\= \frac{-9}{5}- \frac{5}{8}+\frac{4}{2}\\=\frac{-9}{5}-\frac{5}{8}+\frac{2}{1}\\=\frac{-72}{40}-\frac{25}{40}+\frac{80}{40}\\=\frac{-72-25+80}{40}\\=\frac{-17}{40}\)
11. \(-\left(\frac{9}{-2}\right) -\left(\frac{-9}{9}\right) -\left(\frac{-9}{8}\right)\\= \frac{9}{2}+ \frac{9}{9}+\frac{9}{8}\\=\frac{9}{2}+\frac{1}{1}+\frac{9}{8}\\=\frac{36}{8}+\frac{8}{8}+\frac{9}{8}\\=\frac{36+8+9}{8}\\=\frac{53}{8}\)
12. \(+\left(\frac{2}{5}\right) +\left(\frac{-2}{-6}\right) +\left(\frac{-6}{-5}\right)\\= \frac{2}{5}+ \frac{2}{6}+\frac{6}{5}\\=\frac{2}{5}+\frac{1}{3}+\frac{6}{5}\\=\frac{6}{15}+\frac{5}{15}+\frac{18}{15}\\=\frac{6+5+18}{15}\\=\frac{29}{15}\)