Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{6}{7}\right) +\left(\frac{7}{-9}\right) -\left(\frac{7}{7}\right)\\= \frac{-6}{7}- \frac{7}{9}-\frac{7}{7}\\=\frac{-6}{7}-\frac{7}{9}-\frac{1}{1}\\=\frac{-54}{63}-\frac{49}{63}-\frac{63}{63}\\=\frac{-54-49-63}{63}\\=\frac{-166}{63}\)
2. \(+\left(\frac{8}{-7}\right) +\left(\frac{-10}{-7}\right) +\left(\frac{-4}{10}\right)\\= \frac{-8}{7}+ \frac{10}{7}-\frac{4}{10}\\=\frac{-8}{7}+\frac{10}{7}-\frac{2}{5}\\=\frac{-40}{35}+\frac{50}{35}-\frac{14}{35}\\=\frac{-40+50-14}{35}\\=\frac{-4}{35}\)
3. \(+\left(\frac{-8}{-7}\right) -\left(\frac{10}{-2}\right) -\left(\frac{4}{8}\right)\\= \frac{8}{7}+ \frac{10}{2}-\frac{4}{8}\\=\frac{8}{7}+\frac{5}{1}-\frac{1}{2}\\=\frac{16}{14}+\frac{70}{14}-\frac{7}{14}\\=\frac{16+70-7}{14}\\=\frac{79}{14}\)
4. \(-\left(\frac{-10}{7}\right) -\left(\frac{-10}{-5}\right) +\left(\frac{-2}{-6}\right)\\= \frac{10}{7}- \frac{10}{5}+\frac{2}{6}\\=\frac{10}{7}-\frac{2}{1}+\frac{1}{3}\\=\frac{30}{21}-\frac{42}{21}+\frac{7}{21}\\=\frac{30-42+7}{21}\\=\frac{-5}{21}\)
5. \(-\left(\frac{8}{5}\right) +\left(\frac{-4}{3}\right) -\left(\frac{-10}{-11}\right)\\= \frac{-8}{5}- \frac{4}{3}-\frac{10}{11}\\=\frac{-264}{165}-\frac{220}{165}-\frac{150}{165}\\=\frac{-264-220-150}{165}\\=\frac{-634}{165}\)
6. \(+\left(\frac{3}{7}\right) +\left(\frac{-9}{4}\right) +\left(\frac{-10}{9}\right)\\= \frac{3}{7}- \frac{9}{4}-\frac{10}{9}\\=\frac{108}{252}-\frac{567}{252}-\frac{280}{252}\\=\frac{108-567-280}{252}\\=\frac{-739}{252}\)
7. \(+\left(\frac{6}{5}\right) -\left(\frac{10}{9}\right) +\left(\frac{-10}{-12}\right)\\= \frac{6}{5}- \frac{10}{9}+\frac{10}{12}\\=\frac{6}{5}-\frac{10}{9}+\frac{5}{6}\\=\frac{108}{90}-\frac{100}{90}+\frac{75}{90}\\=\frac{108-100+75}{90}\\=\frac{83}{90}\)
8. \(+\left(\frac{4}{-7}\right) -\left(\frac{5}{2}\right) -\left(\frac{12}{5}\right)\\= \frac{-4}{7}- \frac{5}{2}-\frac{12}{5}\\=\frac{-40}{70}-\frac{175}{70}-\frac{168}{70}\\=\frac{-40-175-168}{70}\\=\frac{-383}{70}\)
9. \(-\left(\frac{-5}{2}\right) -\left(\frac{3}{-5}\right) -\left(\frac{-7}{-7}\right)\\= \frac{5}{2}+ \frac{3}{5}-\frac{7}{7}\\=\frac{5}{2}+\frac{3}{5}-\frac{1}{1}\\=\frac{25}{10}+\frac{6}{10}-\frac{10}{10}\\=\frac{25+6-10}{10}\\=\frac{21}{10}\)
10. \(-\left(\frac{-5}{8}\right) -\left(\frac{-3}{7}\right) -\left(\frac{3}{-2}\right)\\= \frac{5}{8}+ \frac{3}{7}+\frac{3}{2}\\=\frac{35}{56}+\frac{24}{56}+\frac{84}{56}\\=\frac{35+24+84}{56}\\=\frac{143}{56}\)
11. \(+\left(\frac{-10}{-3}\right) -\left(\frac{5}{-9}\right) -\left(\frac{11}{9}\right)\\= \frac{10}{3}+ \frac{5}{9}-\frac{11}{9}\\=\frac{30}{9}+\frac{5}{9}-\frac{11}{9}\\=\frac{30+5-11}{9}\\=\frac{24}{9}\\=\frac{8}{3}\)
12. \(+\left(\frac{-8}{-9}\right) -\left(\frac{9}{-9}\right) -\left(\frac{-10}{2}\right)\\= \frac{8}{9}+ \frac{9}{9}+\frac{10}{2}\\=\frac{8}{9}+\frac{1}{1}+\frac{5}{1}\\=\frac{8+1+5}{9}\\=\frac{14}{9}\)