Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{7}{2}\right) +\left(\frac{7}{3}\right) -\left(\frac{-5}{-2}\right)\\= \frac{7}{2}+ \frac{7}{3}-\frac{5}{2}\\=\frac{21}{6}+\frac{14}{6}-\frac{15}{6}\\=\frac{21+14-15}{6}\\=\frac{20}{6}\\=\frac{10}{3}\)
2. \(-\left(\frac{-10}{3}\right) +\left(\frac{5}{3}\right) +\left(\frac{-11}{5}\right)\\= \frac{10}{3}+ \frac{5}{3}-\frac{11}{5}\\=\frac{50}{15}+\frac{25}{15}-\frac{33}{15}\\=\frac{50+25-33}{15}\\=\frac{42}{15}\\=\frac{14}{5}\)
3. \(-\left(\frac{6}{7}\right) -\left(\frac{6}{-3}\right) -\left(\frac{-5}{-4}\right)\\= \frac{-6}{7}+ \frac{6}{3}-\frac{5}{4}\\=\frac{-6}{7}+\frac{2}{1}-\frac{5}{4}\\=\frac{-24}{28}+\frac{56}{28}-\frac{35}{28}\\=\frac{-24+56-35}{28}\\=\frac{-3}{28}\)
4. \(-\left(\frac{-9}{-8}\right) -\left(\frac{5}{10}\right) -\left(\frac{10}{6}\right)\\= \frac{-9}{8}- \frac{5}{10}-\frac{10}{6}\\=\frac{-9}{8}-\frac{1}{2}-\frac{5}{3}\\=\frac{-27}{24}-\frac{12}{24}-\frac{40}{24}\\=\frac{-27-12-40}{24}\\=\frac{-79}{24}\)
5. \(+\left(\frac{-3}{7}\right) +\left(\frac{9}{5}\right) -\left(\frac{-10}{10}\right)\\= \frac{-3}{7}+ \frac{9}{5}+\frac{10}{10}\\=\frac{-3}{7}+\frac{9}{5}+\frac{1}{1}\\=\frac{-15}{35}+\frac{63}{35}+\frac{35}{35}\\=\frac{-15+63+35}{35}\\=\frac{83}{35}\)
6. \(+\left(\frac{2}{-3}\right) +\left(\frac{-5}{-9}\right) -\left(\frac{-8}{-12}\right)\\= \frac{-2}{3}+ \frac{5}{9}-\frac{8}{12}\\=\frac{-2}{3}+\frac{5}{9}-\frac{2}{3}\\=\frac{-6}{9}+\frac{5}{9}-\frac{6}{9}\\=\frac{-6+5-6}{9}\\=\frac{-7}{9}\)
7. \(+\left(\frac{-5}{-6}\right) -\left(\frac{7}{6}\right) -\left(\frac{-11}{6}\right)\\= \frac{5}{6}- \frac{7}{6}+\frac{11}{6}\\=\frac{5-7+11}{6}\\=\frac{9}{6}\\=\frac{3}{2}\)
8. \(+\left(\frac{3}{-2}\right) +\left(\frac{-6}{-2}\right) -\left(\frac{-12}{3}\right)\\= \frac{-3}{2}+ \frac{6}{2}+\frac{12}{3}\\=\frac{-3}{2}+\frac{3}{1}+\frac{4}{1}\\=\frac{-3+3+4}{2}\\=\frac{4}{2}\\=\frac{2}{1}\)
9. \(+\left(\frac{5}{-2}\right) -\left(\frac{5}{5}\right) +\left(\frac{-12}{8}\right)\\= \frac{-5}{2}- \frac{5}{5}-\frac{12}{8}\\=\frac{-5}{2}-\frac{1}{1}-\frac{3}{2}\\=\frac{-5-1-3}{2}\\=\frac{-9}{2}\)
10. \(+\left(\frac{-10}{3}\right) +\left(\frac{-5}{8}\right) +\left(\frac{6}{-12}\right)\\= \frac{-10}{3}- \frac{5}{8}-\frac{6}{12}\\=\frac{-10}{3}-\frac{5}{8}-\frac{1}{2}\\=\frac{-80}{24}-\frac{15}{24}-\frac{12}{24}\\=\frac{-80-15-12}{24}\\=\frac{-107}{24}\)
11. \(-\left(\frac{-8}{-9}\right) +\left(\frac{-7}{10}\right) +\left(\frac{-6}{12}\right)\\= \frac{-8}{9}- \frac{7}{10}-\frac{6}{12}\\=\frac{-8}{9}-\frac{7}{10}-\frac{1}{2}\\=\frac{-80}{90}-\frac{63}{90}-\frac{45}{90}\\=\frac{-80-63-45}{90}\\=\frac{-188}{90}\\=\frac{-94}{45}\)
12. \(+\left(\frac{6}{5}\right) +\left(\frac{10}{6}\right) -\left(\frac{3}{7}\right)\\= \frac{6}{5}+ \frac{10}{6}-\frac{3}{7}\\=\frac{6}{5}+\frac{5}{3}-\frac{3}{7}\\=\frac{126}{105}+\frac{175}{105}-\frac{45}{105}\\=\frac{126+175-45}{105}\\=\frac{256}{105}\)