Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{-4}\right) -\left(\frac{-10}{-2}\right) -\left(\frac{-10}{-2}\right)\\= \frac{3}{4}- \frac{10}{2}-\frac{10}{2}\\=\frac{3}{4}-\frac{5}{1}-\frac{5}{1}\\=\frac{3-5-5}{4}\\=\frac{-7}{4}\)
2. \(+\left(\frac{-8}{-3}\right) +\left(\frac{-3}{-3}\right) +\left(\frac{7}{7}\right)\\= \frac{8}{3}+ \frac{3}{3}+\frac{7}{7}\\=\frac{8}{3}+\frac{1}{1}+\frac{1}{1}\\=\frac{8+1+1}{3}\\=\frac{10}{3}\)
3. \(+\left(\frac{10}{-7}\right) -\left(\frac{-9}{-6}\right) +\left(\frac{-12}{6}\right)\\= \frac{-10}{7}- \frac{9}{6}-\frac{12}{6}\\=\frac{-10}{7}-\frac{3}{2}-\frac{2}{1}\\=\frac{-20}{14}-\frac{21}{14}-\frac{28}{14}\\=\frac{-20-21-28}{14}\\=\frac{-69}{14}\)
4. \(-\left(\frac{-5}{-3}\right) +\left(\frac{10}{6}\right) -\left(\frac{-6}{2}\right)\\= \frac{-5}{3}+ \frac{10}{6}+\frac{6}{2}\\=\frac{-5}{3}+\frac{5}{3}+\frac{3}{1}\\=\frac{-5+5+3}{3}\\=\frac{3}{3}\\=\frac{1}{1}\)
5. \(+\left(\frac{8}{-9}\right) -\left(\frac{-3}{-8}\right) +\left(\frac{2}{4}\right)\\= \frac{-8}{9}- \frac{3}{8}+\frac{2}{4}\\=\frac{-8}{9}-\frac{3}{8}+\frac{1}{2}\\=\frac{-64}{72}-\frac{27}{72}+\frac{36}{72}\\=\frac{-64-27+36}{72}\\=\frac{-55}{72}\)
6. \(-\left(\frac{-6}{7}\right) -\left(\frac{8}{-10}\right) +\left(\frac{-2}{-12}\right)\\= \frac{6}{7}+ \frac{8}{10}+\frac{2}{12}\\=\frac{6}{7}+\frac{4}{5}+\frac{1}{6}\\=\frac{180}{210}+\frac{168}{210}+\frac{35}{210}\\=\frac{180+168+35}{210}\\=\frac{383}{210}\)
7. \(+\left(\frac{-6}{5}\right) -\left(\frac{-6}{5}\right) +\left(\frac{5}{4}\right)\\= \frac{-6}{5}+ \frac{6}{5}+\frac{5}{4}\\=\frac{-24}{20}+\frac{24}{20}+\frac{25}{20}\\=\frac{-24+24+25}{20}\\=\frac{25}{20}\\=\frac{5}{4}\)
8. \(+\left(\frac{3}{2}\right) +\left(\frac{6}{4}\right) -\left(\frac{10}{-10}\right)\\= \frac{3}{2}+ \frac{6}{4}+\frac{10}{10}\\=\frac{3}{2}+\frac{3}{2}+\frac{1}{1}\\=\frac{3+3+1}{2}\\=\frac{7}{2}\)
9. \(+\left(\frac{-6}{5}\right) -\left(\frac{2}{3}\right) -\left(\frac{2}{4}\right)\\= \frac{-6}{5}- \frac{2}{3}-\frac{2}{4}\\=\frac{-6}{5}-\frac{2}{3}-\frac{1}{2}\\=\frac{-36}{30}-\frac{20}{30}-\frac{15}{30}\\=\frac{-36-20-15}{30}\\=\frac{-71}{30}\)
10. \(-\left(\frac{8}{-7}\right) +\left(\frac{8}{3}\right) +\left(\frac{-10}{4}\right)\\= \frac{8}{7}+ \frac{8}{3}-\frac{10}{4}\\=\frac{8}{7}+\frac{8}{3}-\frac{5}{2}\\=\frac{48}{42}+\frac{112}{42}-\frac{105}{42}\\=\frac{48+112-105}{42}\\=\frac{55}{42}\)
11. \(-\left(\frac{-9}{2}\right) +\left(\frac{8}{-6}\right) +\left(\frac{-3}{-4}\right)\\= \frac{9}{2}- \frac{8}{6}+\frac{3}{4}\\=\frac{9}{2}-\frac{4}{3}+\frac{3}{4}\\=\frac{54}{12}-\frac{16}{12}+\frac{9}{12}\\=\frac{54-16+9}{12}\\=\frac{47}{12}\)
12. \(+\left(\frac{-5}{8}\right) -\left(\frac{5}{-6}\right) -\left(\frac{-2}{12}\right)\\= \frac{-5}{8}+ \frac{5}{6}+\frac{2}{12}\\=\frac{-5}{8}+\frac{5}{6}+\frac{1}{6}\\=\frac{-15}{24}+\frac{20}{24}+\frac{4}{24}\\=\frac{-15+20+4}{24}\\=\frac{9}{24}\\=\frac{3}{8}\)