Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{7}{-4}\right) -\left(\frac{6}{-4}\right) -\left(\frac{-12}{-12}\right)\\= \frac{7}{4}+ \frac{6}{4}-\frac{12}{12}\\=\frac{7}{4}+\frac{3}{2}-\frac{1}{1}\\=\frac{7+3-1}{4}\\=\frac{9}{4}\)
2. \(+\left(\frac{3}{-7}\right) +\left(\frac{4}{-7}\right) +\left(\frac{-7}{9}\right)\\= \frac{-3}{7}- \frac{4}{7}-\frac{7}{9}\\=\frac{-27}{63}-\frac{36}{63}-\frac{49}{63}\\=\frac{-27-36-49}{63}\\=\frac{-112}{63}\\=\frac{-16}{9}\)
3. \(+\left(\frac{-2}{7}\right) -\left(\frac{-6}{2}\right) -\left(\frac{4}{9}\right)\\= \frac{-2}{7}+ \frac{6}{2}-\frac{4}{9}\\=\frac{-2}{7}+\frac{3}{1}-\frac{4}{9}\\=\frac{-18}{63}+\frac{189}{63}-\frac{28}{63}\\=\frac{-18+189-28}{63}\\=\frac{143}{63}\)
4. \(-\left(\frac{8}{-9}\right) -\left(\frac{3}{6}\right) -\left(\frac{11}{-4}\right)\\= \frac{8}{9}- \frac{3}{6}+\frac{11}{4}\\=\frac{8}{9}-\frac{1}{2}+\frac{11}{4}\\=\frac{32}{36}-\frac{18}{36}+\frac{99}{36}\\=\frac{32-18+99}{36}\\=\frac{113}{36}\)
5. \(+\left(\frac{-9}{4}\right) +\left(\frac{-9}{3}\right) -\left(\frac{12}{-4}\right)\\= \frac{-9}{4}- \frac{9}{3}+\frac{12}{4}\\=\frac{-9}{4}-\frac{3}{1}+\frac{3}{1}\\=\frac{-9-3+3}{4}\\=\frac{-9}{4}\)
6. \(+\left(\frac{5}{2}\right) -\left(\frac{-7}{-10}\right) +\left(\frac{2}{3}\right)\\= \frac{5}{2}- \frac{7}{10}+\frac{2}{3}\\=\frac{75}{30}-\frac{21}{30}+\frac{20}{30}\\=\frac{75-21+20}{30}\\=\frac{74}{30}\\=\frac{37}{15}\)
7. \(-\left(\frac{-7}{-8}\right) -\left(\frac{2}{5}\right) +\left(\frac{3}{6}\right)\\= \frac{-7}{8}- \frac{2}{5}+\frac{3}{6}\\=\frac{-7}{8}-\frac{2}{5}+\frac{1}{2}\\=\frac{-35}{40}-\frac{16}{40}+\frac{20}{40}\\=\frac{-35-16+20}{40}\\=\frac{-31}{40}\)
8. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-5}{-4}\right) +\left(\frac{3}{12}\right)\\= \frac{6}{5}- \frac{5}{4}+\frac{3}{12}\\=\frac{6}{5}-\frac{5}{4}+\frac{1}{4}\\=\frac{24}{20}-\frac{25}{20}+\frac{5}{20}\\=\frac{24-25+5}{20}\\=\frac{4}{20}\\=\frac{1}{5}\)
9. \(+\left(\frac{6}{-5}\right) -\left(\frac{10}{-2}\right) +\left(\frac{-6}{3}\right)\\= \frac{-6}{5}+ \frac{10}{2}-\frac{6}{3}\\=\frac{-6}{5}+\frac{5}{1}-\frac{2}{1}\\=\frac{-6+5-2}{5}\\=\frac{-3}{5}\)
10. \(-\left(\frac{-10}{7}\right) -\left(\frac{6}{-2}\right) +\left(\frac{-4}{-9}\right)\\= \frac{10}{7}+ \frac{6}{2}+\frac{4}{9}\\=\frac{10}{7}+\frac{3}{1}+\frac{4}{9}\\=\frac{90}{63}+\frac{189}{63}+\frac{28}{63}\\=\frac{90+189+28}{63}\\=\frac{307}{63}\)
11. \(+\left(\frac{3}{4}\right) +\left(\frac{-10}{-6}\right) +\left(\frac{6}{10}\right)\\= \frac{3}{4}+ \frac{10}{6}+\frac{6}{10}\\=\frac{3}{4}+\frac{5}{3}+\frac{3}{5}\\=\frac{45}{60}+\frac{100}{60}+\frac{36}{60}\\=\frac{45+100+36}{60}\\=\frac{181}{60}\)
12. \(-\left(\frac{-8}{7}\right) +\left(\frac{3}{-10}\right) -\left(\frac{2}{-12}\right)\\= \frac{8}{7}- \frac{3}{10}+\frac{2}{12}\\=\frac{8}{7}-\frac{3}{10}+\frac{1}{6}\\=\frac{240}{210}-\frac{63}{210}+\frac{35}{210}\\=\frac{240-63+35}{210}\\=\frac{212}{210}\\=\frac{106}{105}\)