Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{-3}\right) -\left(\frac{-3}{-6}\right) -\left(\frac{8}{12}\right)\\= \frac{-2}{3}- \frac{3}{6}-\frac{8}{12}\\=\frac{-2}{3}-\frac{1}{2}-\frac{2}{3}\\=\frac{-4}{6}-\frac{3}{6}-\frac{4}{6}\\=\frac{-4-3-4}{6}\\=\frac{-11}{6}\)
2. \(-\left(\frac{4}{5}\right) +\left(\frac{-10}{9}\right) +\left(\frac{11}{4}\right)\\= \frac{-4}{5}- \frac{10}{9}+\frac{11}{4}\\=\frac{-144}{180}-\frac{200}{180}+\frac{495}{180}\\=\frac{-144-200+495}{180}\\=\frac{151}{180}\)
3. \(-\left(\frac{5}{-4}\right) -\left(\frac{9}{-2}\right) +\left(\frac{4}{4}\right)\\= \frac{5}{4}+ \frac{9}{2}+\frac{4}{4}\\=\frac{5}{4}+\frac{9}{2}+\frac{1}{1}\\=\frac{5+9+1}{4}\\=\frac{15}{4}\)
4. \(+\left(\frac{-8}{7}\right) +\left(\frac{6}{-2}\right) +\left(\frac{8}{12}\right)\\= \frac{-8}{7}- \frac{6}{2}+\frac{8}{12}\\=\frac{-8}{7}-\frac{3}{1}+\frac{2}{3}\\=\frac{-24}{21}-\frac{63}{21}+\frac{14}{21}\\=\frac{-24-63+14}{21}\\=\frac{-73}{21}\)
5. \(-\left(\frac{-4}{-5}\right) +\left(\frac{2}{3}\right) -\left(\frac{-12}{11}\right)\\= \frac{-4}{5}+ \frac{2}{3}+\frac{12}{11}\\=\frac{-132}{165}+\frac{110}{165}+\frac{180}{165}\\=\frac{-132+110+180}{165}\\=\frac{158}{165}\)
6. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-2}{-6}\right) +\left(\frac{-6}{-2}\right)\\= \frac{6}{5}- \frac{2}{6}+\frac{6}{2}\\=\frac{6}{5}-\frac{1}{3}+\frac{3}{1}\\=\frac{18}{15}-\frac{5}{15}+\frac{45}{15}\\=\frac{18-5+45}{15}\\=\frac{58}{15}\)
7. \(+\left(\frac{4}{3}\right) +\left(\frac{3}{-10}\right) +\left(\frac{-6}{-7}\right)\\= \frac{4}{3}- \frac{3}{10}+\frac{6}{7}\\=\frac{280}{210}-\frac{63}{210}+\frac{180}{210}\\=\frac{280-63+180}{210}\\=\frac{397}{210}\)
8. \(+\left(\frac{3}{4}\right) +\left(\frac{-9}{-10}\right) +\left(\frac{9}{-5}\right)\\= \frac{3}{4}+ \frac{9}{10}-\frac{9}{5}\\=\frac{15}{20}+\frac{18}{20}-\frac{36}{20}\\=\frac{15+18-36}{20}\\=\frac{-3}{20}\)
9. \(-\left(\frac{10}{3}\right) -\left(\frac{-9}{3}\right) -\left(\frac{7}{-5}\right)\\= \frac{-10}{3}+ \frac{9}{3}+\frac{7}{5}\\=\frac{-10}{3}+\frac{3}{1}+\frac{7}{5}\\=\frac{-50}{15}+\frac{45}{15}+\frac{21}{15}\\=\frac{-50+45+21}{15}\\=\frac{16}{15}\)
10. \(+\left(\frac{-8}{-3}\right) +\left(\frac{9}{-3}\right) -\left(\frac{10}{3}\right)\\= \frac{8}{3}- \frac{9}{3}-\frac{10}{3}\\=\frac{8}{3}-\frac{3}{1}-\frac{10}{3}\\=\frac{8-3-10}{3}\\=\frac{-5}{3}\)
11. \(+\left(\frac{3}{-7}\right) +\left(\frac{-2}{-2}\right) +\left(\frac{9}{-7}\right)\\= \frac{-3}{7}+ \frac{2}{2}-\frac{9}{7}\\=\frac{-3}{7}+\frac{1}{1}-\frac{9}{7}\\=\frac{-3+1-9}{7}\\=\frac{-11}{7}\)
12. \(+\left(\frac{2}{3}\right) -\left(\frac{2}{2}\right) +\left(\frac{12}{-11}\right)\\= \frac{2}{3}- \frac{2}{2}-\frac{12}{11}\\=\frac{2}{3}-\frac{1}{1}-\frac{12}{11}\\=\frac{22}{33}-\frac{33}{33}-\frac{36}{33}\\=\frac{22-33-36}{33}\\=\frac{-47}{33}\)