Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{-4}\right) -\left(\frac{10}{-3}\right) -\left(\frac{10}{-8}\right)\\= \frac{5}{4}+ \frac{10}{3}+\frac{10}{8}\\=\frac{5}{4}+\frac{10}{3}+\frac{5}{4}\\=\frac{15}{12}+\frac{40}{12}+\frac{15}{12}\\=\frac{15+40+15}{12}\\=\frac{70}{12}\\=\frac{35}{6}\)
2. \(+\left(\frac{9}{-7}\right) -\left(\frac{2}{6}\right) +\left(\frac{-4}{4}\right)\\= \frac{-9}{7}- \frac{2}{6}-\frac{4}{4}\\=\frac{-9}{7}-\frac{1}{3}-\frac{1}{1}\\=\frac{-27}{21}-\frac{7}{21}-\frac{21}{21}\\=\frac{-27-7-21}{21}\\=\frac{-55}{21}\)
3. \(-\left(\frac{-10}{-9}\right) +\left(\frac{7}{-10}\right) -\left(\frac{-4}{10}\right)\\= \frac{-10}{9}- \frac{7}{10}+\frac{4}{10}\\=\frac{-10}{9}-\frac{7}{10}+\frac{2}{5}\\=\frac{-100}{90}-\frac{63}{90}+\frac{36}{90}\\=\frac{-100-63+36}{90}\\=\frac{-127}{90}\)
4. \(+\left(\frac{3}{-7}\right) -\left(\frac{-6}{3}\right) +\left(\frac{-5}{9}\right)\\= \frac{-3}{7}+ \frac{6}{3}-\frac{5}{9}\\=\frac{-3}{7}+\frac{2}{1}-\frac{5}{9}\\=\frac{-27}{63}+\frac{126}{63}-\frac{35}{63}\\=\frac{-27+126-35}{63}\\=\frac{64}{63}\)
5. \(+\left(\frac{-4}{5}\right) +\left(\frac{-5}{4}\right) +\left(\frac{-11}{-4}\right)\\= \frac{-4}{5}- \frac{5}{4}+\frac{11}{4}\\=\frac{-16}{20}-\frac{25}{20}+\frac{55}{20}\\=\frac{-16-25+55}{20}\\=\frac{14}{20}\\=\frac{7}{10}\)
6. \(-\left(\frac{-5}{4}\right) +\left(\frac{-5}{3}\right) +\left(\frac{8}{12}\right)\\= \frac{5}{4}- \frac{5}{3}+\frac{8}{12}\\=\frac{5}{4}-\frac{5}{3}+\frac{2}{3}\\=\frac{15}{12}-\frac{20}{12}+\frac{8}{12}\\=\frac{15-20+8}{12}\\=\frac{3}{12}\\=\frac{1}{4}\)
7. \(+\left(\frac{-8}{5}\right) -\left(\frac{-10}{-8}\right) +\left(\frac{4}{-9}\right)\\= \frac{-8}{5}- \frac{10}{8}-\frac{4}{9}\\=\frac{-8}{5}-\frac{5}{4}-\frac{4}{9}\\=\frac{-288}{180}-\frac{225}{180}-\frac{80}{180}\\=\frac{-288-225-80}{180}\\=\frac{-593}{180}\)
8. \(-\left(\frac{6}{-5}\right) -\left(\frac{9}{3}\right) -\left(\frac{12}{-3}\right)\\= \frac{6}{5}- \frac{9}{3}+\frac{12}{3}\\=\frac{6}{5}-\frac{3}{1}+\frac{4}{1}\\=\frac{6-3+4}{5}\\=\frac{7}{5}\)
9. \(+\left(\frac{6}{-5}\right) +\left(\frac{-9}{8}\right) +\left(\frac{-7}{6}\right)\\= \frac{-6}{5}- \frac{9}{8}-\frac{7}{6}\\=\frac{-144}{120}-\frac{135}{120}-\frac{140}{120}\\=\frac{-144-135-140}{120}\\=\frac{-419}{120}\)
10. \(+\left(\frac{6}{5}\right) +\left(\frac{4}{-6}\right) -\left(\frac{2}{-6}\right)\\= \frac{6}{5}- \frac{4}{6}+\frac{2}{6}\\=\frac{6}{5}-\frac{2}{3}+\frac{1}{3}\\=\frac{18}{15}-\frac{10}{15}+\frac{5}{15}\\=\frac{18-10+5}{15}\\=\frac{13}{15}\)
11. \(-\left(\frac{-10}{-9}\right) -\left(\frac{7}{3}\right) -\left(\frac{-7}{12}\right)\\= \frac{-10}{9}- \frac{7}{3}+\frac{7}{12}\\=\frac{-40}{36}-\frac{84}{36}+\frac{21}{36}\\=\frac{-40-84+21}{36}\\=\frac{-103}{36}\)
12. \(-\left(\frac{-9}{7}\right) -\left(\frac{-6}{-9}\right) -\left(\frac{5}{-7}\right)\\= \frac{9}{7}- \frac{6}{9}+\frac{5}{7}\\=\frac{9}{7}-\frac{2}{3}+\frac{5}{7}\\=\frac{27}{21}-\frac{14}{21}+\frac{15}{21}\\=\frac{27-14+15}{21}\\=\frac{28}{21}\\=\frac{4}{3}\)