Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{-7}\right) -\left(\frac{3}{-6}\right) -\left(\frac{2}{9}\right)\\= \frac{-6}{7}+ \frac{3}{6}-\frac{2}{9}\\=\frac{-6}{7}+\frac{1}{2}-\frac{2}{9}\\=\frac{-108}{126}+\frac{63}{126}-\frac{28}{126}\\=\frac{-108+63-28}{126}\\=\frac{-73}{126}\)
2. \(-\left(\frac{7}{3}\right) +\left(\frac{-10}{10}\right) +\left(\frac{-12}{12}\right)\\= \frac{-7}{3}- \frac{10}{10}-\frac{12}{12}\\=\frac{-7}{3}-\frac{1}{1}-\frac{1}{1}\\=\frac{-7-1-1}{3}\\=\frac{-9}{3}\\=\frac{-3}{1}\)
3. \(+\left(\frac{9}{7}\right) +\left(\frac{-7}{7}\right) +\left(\frac{8}{-7}\right)\\= \frac{9}{7}- \frac{7}{7}-\frac{8}{7}\\=\frac{9}{7}-\frac{1}{1}-\frac{8}{7}\\=\frac{9-1-8}{7}\\=\frac{0}{7}\\=\frac{0}{1}\)
4. \(+\left(\frac{8}{-3}\right) +\left(\frac{-8}{5}\right) -\left(\frac{-3}{7}\right)\\= \frac{-8}{3}- \frac{8}{5}+\frac{3}{7}\\=\frac{-280}{105}-\frac{168}{105}+\frac{45}{105}\\=\frac{-280-168+45}{105}\\=\frac{-403}{105}\)
5. \(+\left(\frac{-2}{-3}\right) -\left(\frac{10}{-7}\right) -\left(\frac{3}{3}\right)\\= \frac{2}{3}+ \frac{10}{7}-\frac{3}{3}\\=\frac{2}{3}+\frac{10}{7}-\frac{1}{1}\\=\frac{14}{21}+\frac{30}{21}-\frac{21}{21}\\=\frac{14+30-21}{21}\\=\frac{23}{21}\)
6. \(-\left(\frac{9}{-7}\right) -\left(\frac{-9}{2}\right) +\left(\frac{7}{3}\right)\\= \frac{9}{7}+ \frac{9}{2}+\frac{7}{3}\\=\frac{54}{42}+\frac{189}{42}+\frac{98}{42}\\=\frac{54+189+98}{42}\\=\frac{341}{42}\)
7. \(+\left(\frac{9}{-7}\right) +\left(\frac{-2}{-8}\right) -\left(\frac{-4}{-2}\right)\\= \frac{-9}{7}+ \frac{2}{8}-\frac{4}{2}\\=\frac{-9}{7}+\frac{1}{4}-\frac{2}{1}\\=\frac{-36}{28}+\frac{7}{28}-\frac{56}{28}\\=\frac{-36+7-56}{28}\\=\frac{-85}{28}\)
8. \(+\left(\frac{5}{-4}\right) +\left(\frac{-5}{-4}\right) -\left(\frac{-9}{-5}\right)\\= \frac{-5}{4}+ \frac{5}{4}-\frac{9}{5}\\=\frac{-25}{20}+\frac{25}{20}-\frac{36}{20}\\=\frac{-25+25-36}{20}\\=\frac{-36}{20}\\=\frac{-9}{5}\)
9. \(+\left(\frac{-10}{7}\right) +\left(\frac{-4}{-7}\right) +\left(\frac{11}{3}\right)\\= \frac{-10}{7}+ \frac{4}{7}+\frac{11}{3}\\=\frac{-30}{21}+\frac{12}{21}+\frac{77}{21}\\=\frac{-30+12+77}{21}\\=\frac{59}{21}\)
10. \(-\left(\frac{7}{-8}\right) -\left(\frac{-10}{-3}\right) +\left(\frac{2}{-9}\right)\\= \frac{7}{8}- \frac{10}{3}-\frac{2}{9}\\=\frac{63}{72}-\frac{240}{72}-\frac{16}{72}\\=\frac{63-240-16}{72}\\=\frac{-193}{72}\)
11. \(-\left(\frac{3}{-7}\right) +\left(\frac{-8}{-3}\right) +\left(\frac{8}{-5}\right)\\= \frac{3}{7}+ \frac{8}{3}-\frac{8}{5}\\=\frac{45}{105}+\frac{280}{105}-\frac{168}{105}\\=\frac{45+280-168}{105}\\=\frac{157}{105}\)
12. \(-\left(\frac{10}{7}\right) -\left(\frac{-5}{-7}\right) +\left(\frac{12}{-7}\right)\\= \frac{-10}{7}- \frac{5}{7}-\frac{12}{7}\\=\frac{-10-5-12}{7}\\=\frac{-27}{7}\)