Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{7}{5}\right) +\left(\frac{-10}{7}\right) +\left(\frac{-10}{5}\right)\\= \frac{7}{5}- \frac{10}{7}-\frac{10}{5}\\=\frac{7}{5}-\frac{10}{7}-\frac{2}{1}\\=\frac{49}{35}-\frac{50}{35}-\frac{70}{35}\\=\frac{49-50-70}{35}\\=\frac{-71}{35}\)
2. \(+\left(\frac{-2}{-3}\right) +\left(\frac{2}{10}\right) +\left(\frac{11}{7}\right)\\= \frac{2}{3}+ \frac{2}{10}+\frac{11}{7}\\=\frac{2}{3}+\frac{1}{5}+\frac{11}{7}\\=\frac{70}{105}+\frac{21}{105}+\frac{165}{105}\\=\frac{70+21+165}{105}\\=\frac{256}{105}\)
3. \(+\left(\frac{-2}{-7}\right) +\left(\frac{2}{-9}\right) +\left(\frac{-8}{12}\right)\\= \frac{2}{7}- \frac{2}{9}-\frac{8}{12}\\=\frac{2}{7}-\frac{2}{9}-\frac{2}{3}\\=\frac{18}{63}-\frac{14}{63}-\frac{42}{63}\\=\frac{18-14-42}{63}\\=\frac{-38}{63}\)
4. \(+\left(\frac{10}{3}\right) -\left(\frac{-10}{-4}\right) -\left(\frac{-4}{-4}\right)\\= \frac{10}{3}- \frac{10}{4}-\frac{4}{4}\\=\frac{10}{3}-\frac{5}{2}-\frac{1}{1}\\=\frac{20}{6}-\frac{15}{6}-\frac{6}{6}\\=\frac{20-15-6}{6}\\=\frac{-1}{6}\)
5. \(+\left(\frac{-5}{6}\right) +\left(\frac{8}{-6}\right) -\left(\frac{-11}{-3}\right)\\= \frac{-5}{6}- \frac{8}{6}-\frac{11}{3}\\=\frac{-5}{6}-\frac{4}{3}-\frac{11}{3}\\=\frac{-5-4-11}{6}\\=\frac{-20}{6}\\=\frac{-10}{3}\)
6. \(+\left(\frac{-10}{-9}\right) +\left(\frac{4}{2}\right) -\left(\frac{8}{-3}\right)\\= \frac{10}{9}+ \frac{4}{2}+\frac{8}{3}\\=\frac{10}{9}+\frac{2}{1}+\frac{8}{3}\\=\frac{10+2+8}{9}\\=\frac{20}{9}\)
7. \(+\left(\frac{-10}{9}\right) -\left(\frac{3}{10}\right) -\left(\frac{-8}{3}\right)\\= \frac{-10}{9}- \frac{3}{10}+\frac{8}{3}\\=\frac{-100}{90}-\frac{27}{90}+\frac{240}{90}\\=\frac{-100-27+240}{90}\\=\frac{113}{90}\)
8. \(-\left(\frac{-3}{7}\right) +\left(\frac{-5}{-7}\right) +\left(\frac{4}{5}\right)\\= \frac{3}{7}+ \frac{5}{7}+\frac{4}{5}\\=\frac{15}{35}+\frac{25}{35}+\frac{28}{35}\\=\frac{15+25+28}{35}\\=\frac{68}{35}\)
9. \(+\left(\frac{4}{-9}\right) -\left(\frac{-4}{3}\right) -\left(\frac{8}{-2}\right)\\= \frac{-4}{9}+ \frac{4}{3}+\frac{8}{2}\\=\frac{-4}{9}+\frac{4}{3}+\frac{4}{1}\\=\frac{-4+4+4}{9}\\=\frac{4}{9}\)
10. \(+\left(\frac{10}{3}\right) +\left(\frac{8}{-10}\right) +\left(\frac{3}{4}\right)\\= \frac{10}{3}- \frac{8}{10}+\frac{3}{4}\\=\frac{10}{3}-\frac{4}{5}+\frac{3}{4}\\=\frac{200}{60}-\frac{48}{60}+\frac{45}{60}\\=\frac{200-48+45}{60}\\=\frac{197}{60}\)
11. \(+\left(\frac{3}{7}\right) +\left(\frac{-6}{-6}\right) -\left(\frac{-2}{6}\right)\\= \frac{3}{7}+ \frac{6}{6}+\frac{2}{6}\\=\frac{3}{7}+\frac{1}{1}+\frac{1}{3}\\=\frac{9}{21}+\frac{21}{21}+\frac{7}{21}\\=\frac{9+21+7}{21}\\=\frac{37}{21}\)
12. \(-\left(\frac{-4}{-9}\right) +\left(\frac{4}{6}\right) -\left(\frac{6}{6}\right)\\= \frac{-4}{9}+ \frac{4}{6}-\frac{6}{6}\\=\frac{-4}{9}+\frac{2}{3}-\frac{1}{1}\\=\frac{-4+2-1}{9}\\=\frac{-3}{9}\\=\frac{-1}{3}\)