Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{4}\right) +\left(\frac{4}{3}\right) +\left(\frac{-11}{-2}\right)\\= \frac{-9}{4}+ \frac{4}{3}+\frac{11}{2}\\=\frac{-27}{12}+\frac{16}{12}+\frac{66}{12}\\=\frac{-27+16+66}{12}\\=\frac{55}{12}\)
2. \(+\left(\frac{9}{5}\right) -\left(\frac{6}{-2}\right) -\left(\frac{-3}{-12}\right)\\= \frac{9}{5}+ \frac{6}{2}-\frac{3}{12}\\=\frac{9}{5}+\frac{3}{1}-\frac{1}{4}\\=\frac{36}{20}+\frac{60}{20}-\frac{5}{20}\\=\frac{36+60-5}{20}\\=\frac{91}{20}\)
3. \(+\left(\frac{3}{4}\right) -\left(\frac{3}{-7}\right) +\left(\frac{-3}{12}\right)\\= \frac{3}{4}+ \frac{3}{7}-\frac{3}{12}\\=\frac{3}{4}+\frac{3}{7}-\frac{1}{4}\\=\frac{21}{28}+\frac{12}{28}-\frac{7}{28}\\=\frac{21+12-7}{28}\\=\frac{26}{28}\\=\frac{13}{14}\)
4. \(+\left(\frac{-6}{-7}\right) +\left(\frac{7}{-7}\right) +\left(\frac{-4}{7}\right)\\= \frac{6}{7}- \frac{7}{7}-\frac{4}{7}\\=\frac{6}{7}-\frac{1}{1}-\frac{4}{7}\\=\frac{6-1-4}{7}\\=\frac{1}{7}\)
5. \(+\left(\frac{9}{7}\right) -\left(\frac{-2}{3}\right) +\left(\frac{8}{-5}\right)\\= \frac{9}{7}+ \frac{2}{3}-\frac{8}{5}\\=\frac{135}{105}+\frac{70}{105}-\frac{168}{105}\\=\frac{135+70-168}{105}\\=\frac{37}{105}\)
6. \(+\left(\frac{4}{-7}\right) -\left(\frac{-5}{-7}\right) +\left(\frac{10}{-10}\right)\\= \frac{-4}{7}- \frac{5}{7}-\frac{10}{10}\\=\frac{-4}{7}-\frac{5}{7}-\frac{1}{1}\\=\frac{-4-5-1}{7}\\=\frac{-10}{7}\)
7. \(+\left(\frac{2}{-5}\right) +\left(\frac{4}{-9}\right) -\left(\frac{-12}{-5}\right)\\= \frac{-2}{5}- \frac{4}{9}-\frac{12}{5}\\=\frac{-18}{45}-\frac{20}{45}-\frac{108}{45}\\=\frac{-18-20-108}{45}\\=\frac{-146}{45}\)
8. \(+\left(\frac{-7}{4}\right) +\left(\frac{-4}{4}\right) +\left(\frac{9}{-11}\right)\\= \frac{-7}{4}- \frac{4}{4}-\frac{9}{11}\\=\frac{-7}{4}-\frac{1}{1}-\frac{9}{11}\\=\frac{-77}{44}-\frac{44}{44}-\frac{36}{44}\\=\frac{-77-44-36}{44}\\=\frac{-157}{44}\)
9. \(+\left(\frac{-2}{-5}\right) +\left(\frac{9}{9}\right) +\left(\frac{5}{6}\right)\\= \frac{2}{5}+ \frac{9}{9}+\frac{5}{6}\\=\frac{2}{5}+\frac{1}{1}+\frac{5}{6}\\=\frac{12}{30}+\frac{30}{30}+\frac{25}{30}\\=\frac{12+30+25}{30}\\=\frac{67}{30}\)
10. \(-\left(\frac{5}{4}\right) +\left(\frac{7}{-9}\right) -\left(\frac{-10}{8}\right)\\= \frac{-5}{4}- \frac{7}{9}+\frac{10}{8}\\=\frac{-5}{4}-\frac{7}{9}+\frac{5}{4}\\=\frac{-45}{36}-\frac{28}{36}+\frac{45}{36}\\=\frac{-45-28+45}{36}\\=\frac{-28}{36}\\=\frac{-7}{9}\)
11. \(+\left(\frac{-10}{3}\right) +\left(\frac{3}{9}\right) +\left(\frac{2}{-11}\right)\\= \frac{-10}{3}+ \frac{3}{9}-\frac{2}{11}\\=\frac{-10}{3}+\frac{1}{3}-\frac{2}{11}\\=\frac{-110}{33}+\frac{11}{33}-\frac{6}{33}\\=\frac{-110+11-6}{33}\\=\frac{-105}{33}\\=\frac{-35}{11}\)
12. \(-\left(\frac{-7}{-2}\right) +\left(\frac{2}{6}\right) -\left(\frac{8}{-2}\right)\\= \frac{-7}{2}+ \frac{2}{6}+\frac{8}{2}\\=\frac{-7}{2}+\frac{1}{3}+\frac{4}{1}\\=\frac{-21}{6}+\frac{2}{6}+\frac{24}{6}\\=\frac{-21+2+24}{6}\\=\frac{5}{6}\)