Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{-7}\right) -\left(\frac{3}{-9}\right) +\left(\frac{6}{8}\right)\\= \frac{-3}{7}+ \frac{3}{9}+\frac{6}{8}\\=\frac{-3}{7}+\frac{1}{3}+\frac{3}{4}\\=\frac{-36}{84}+\frac{28}{84}+\frac{63}{84}\\=\frac{-36+28+63}{84}\\=\frac{55}{84}\)
2. \(+\left(\frac{-10}{7}\right) -\left(\frac{-7}{9}\right) +\left(\frac{-4}{6}\right)\\= \frac{-10}{7}+ \frac{7}{9}-\frac{4}{6}\\=\frac{-10}{7}+\frac{7}{9}-\frac{2}{3}\\=\frac{-90}{63}+\frac{49}{63}-\frac{42}{63}\\=\frac{-90+49-42}{63}\\=\frac{-83}{63}\)
3. \(-\left(\frac{-3}{5}\right) +\left(\frac{-6}{10}\right) -\left(\frac{10}{9}\right)\\= \frac{3}{5}- \frac{6}{10}-\frac{10}{9}\\=\frac{3}{5}-\frac{3}{5}-\frac{10}{9}\\=\frac{27}{45}-\frac{27}{45}-\frac{50}{45}\\=\frac{27-27-50}{45}\\=\frac{-50}{45}\\=\frac{-10}{9}\)
4. \(+\left(\frac{-6}{5}\right) -\left(\frac{-7}{-4}\right) -\left(\frac{-10}{11}\right)\\= \frac{-6}{5}- \frac{7}{4}+\frac{10}{11}\\=\frac{-264}{220}-\frac{385}{220}+\frac{200}{220}\\=\frac{-264-385+200}{220}\\=\frac{-449}{220}\)
5. \(-\left(\frac{-5}{3}\right) -\left(\frac{-2}{-8}\right) -\left(\frac{11}{5}\right)\\= \frac{5}{3}- \frac{2}{8}-\frac{11}{5}\\=\frac{5}{3}-\frac{1}{4}-\frac{11}{5}\\=\frac{100}{60}-\frac{15}{60}-\frac{132}{60}\\=\frac{100-15-132}{60}\\=\frac{-47}{60}\)
6. \(-\left(\frac{-3}{4}\right) -\left(\frac{9}{-3}\right) +\left(\frac{-9}{8}\right)\\= \frac{3}{4}+ \frac{9}{3}-\frac{9}{8}\\=\frac{3}{4}+\frac{3}{1}-\frac{9}{8}\\=\frac{6}{8}+\frac{24}{8}-\frac{9}{8}\\=\frac{6+24-9}{8}\\=\frac{21}{8}\)
7. \(+\left(\frac{-3}{-7}\right) +\left(\frac{2}{4}\right) -\left(\frac{-2}{-8}\right)\\= \frac{3}{7}+ \frac{2}{4}-\frac{2}{8}\\=\frac{3}{7}+\frac{1}{2}-\frac{1}{4}\\=\frac{12}{28}+\frac{14}{28}-\frac{7}{28}\\=\frac{12+14-7}{28}\\=\frac{19}{28}\)
8. \(+\left(\frac{5}{7}\right) -\left(\frac{-5}{7}\right) +\left(\frac{-5}{-3}\right)\\= \frac{5}{7}+ \frac{5}{7}+\frac{5}{3}\\=\frac{15}{21}+\frac{15}{21}+\frac{35}{21}\\=\frac{15+15+35}{21}\\=\frac{65}{21}\)
9. \(+\left(\frac{9}{-2}\right) -\left(\frac{-3}{-5}\right) +\left(\frac{7}{12}\right)\\= \frac{-9}{2}- \frac{3}{5}+\frac{7}{12}\\=\frac{-270}{60}-\frac{36}{60}+\frac{35}{60}\\=\frac{-270-36+35}{60}\\=\frac{-271}{60}\)
10. \(-\left(\frac{2}{-5}\right) +\left(\frac{7}{10}\right) +\left(\frac{3}{7}\right)\\= \frac{2}{5}+ \frac{7}{10}+\frac{3}{7}\\=\frac{28}{70}+\frac{49}{70}+\frac{30}{70}\\=\frac{28+49+30}{70}\\=\frac{107}{70}\)
11. \(-\left(\frac{-6}{-7}\right) +\left(\frac{7}{7}\right) -\left(\frac{-4}{7}\right)\\= \frac{-6}{7}+ \frac{7}{7}+\frac{4}{7}\\=\frac{-6}{7}+\frac{1}{1}+\frac{4}{7}\\=\frac{-6+1+4}{7}\\=\frac{-1}{7}\)
12. \(-\left(\frac{-7}{-9}\right) +\left(\frac{4}{-8}\right) +\left(\frac{-4}{6}\right)\\= \frac{-7}{9}- \frac{4}{8}-\frac{4}{6}\\=\frac{-7}{9}-\frac{1}{2}-\frac{2}{3}\\=\frac{-14}{18}-\frac{9}{18}-\frac{12}{18}\\=\frac{-14-9-12}{18}\\=\frac{-35}{18}\)