Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{-9}\right) +\left(\frac{7}{-10}\right) -\left(\frac{4}{-10}\right)\\= \frac{7}{9}- \frac{7}{10}+\frac{4}{10}\\=\frac{7}{9}-\frac{7}{10}+\frac{2}{5}\\=\frac{70}{90}-\frac{63}{90}+\frac{36}{90}\\=\frac{70-63+36}{90}\\=\frac{43}{90}\)
2. \(+\left(\frac{3}{8}\right) -\left(\frac{5}{8}\right) -\left(\frac{-10}{-5}\right)\\= \frac{3}{8}- \frac{5}{8}-\frac{10}{5}\\=\frac{3}{8}-\frac{5}{8}-\frac{2}{1}\\=\frac{3-5-2}{8}\\=\frac{-4}{8}\\=\frac{-1}{2}\)
3. \(-\left(\frac{-9}{-7}\right) -\left(\frac{8}{9}\right) -\left(\frac{4}{-2}\right)\\= \frac{-9}{7}- \frac{8}{9}+\frac{4}{2}\\=\frac{-9}{7}-\frac{8}{9}+\frac{2}{1}\\=\frac{-81}{63}-\frac{56}{63}+\frac{126}{63}\\=\frac{-81-56+126}{63}\\=\frac{-11}{63}\)
4. \(-\left(\frac{3}{5}\right) +\left(\frac{-5}{9}\right) +\left(\frac{-10}{-4}\right)\\= \frac{-3}{5}- \frac{5}{9}+\frac{10}{4}\\=\frac{-3}{5}-\frac{5}{9}+\frac{5}{2}\\=\frac{-54}{90}-\frac{50}{90}+\frac{225}{90}\\=\frac{-54-50+225}{90}\\=\frac{121}{90}\)
5. \(-\left(\frac{5}{2}\right) +\left(\frac{6}{5}\right) -\left(\frac{3}{-2}\right)\\= \frac{-5}{2}+ \frac{6}{5}+\frac{3}{2}\\=\frac{-25}{10}+\frac{12}{10}+\frac{15}{10}\\=\frac{-25+12+15}{10}\\=\frac{2}{10}\\=\frac{1}{5}\)
6. \(-\left(\frac{-4}{-3}\right) +\left(\frac{2}{3}\right) +\left(\frac{-12}{10}\right)\\= \frac{-4}{3}+ \frac{2}{3}-\frac{12}{10}\\=\frac{-4}{3}+\frac{2}{3}-\frac{6}{5}\\=\frac{-20}{15}+\frac{10}{15}-\frac{18}{15}\\=\frac{-20+10-18}{15}\\=\frac{-28}{15}\)
7. \(+\left(\frac{-5}{9}\right) -\left(\frac{-7}{3}\right) -\left(\frac{10}{-8}\right)\\= \frac{-5}{9}+ \frac{7}{3}+\frac{10}{8}\\=\frac{-5}{9}+\frac{7}{3}+\frac{5}{4}\\=\frac{-20}{36}+\frac{84}{36}+\frac{45}{36}\\=\frac{-20+84+45}{36}\\=\frac{109}{36}\)
8. \(+\left(\frac{-9}{-7}\right) +\left(\frac{-3}{-2}\right) +\left(\frac{10}{12}\right)\\= \frac{9}{7}+ \frac{3}{2}+\frac{10}{12}\\=\frac{9}{7}+\frac{3}{2}+\frac{5}{6}\\=\frac{54}{42}+\frac{63}{42}+\frac{35}{42}\\=\frac{54+63+35}{42}\\=\frac{152}{42}\\=\frac{76}{21}\)
9. \(-\left(\frac{8}{-7}\right) -\left(\frac{-3}{6}\right) -\left(\frac{8}{-2}\right)\\= \frac{8}{7}+ \frac{3}{6}+\frac{8}{2}\\=\frac{8}{7}+\frac{1}{2}+\frac{4}{1}\\=\frac{16}{14}+\frac{7}{14}+\frac{56}{14}\\=\frac{16+7+56}{14}\\=\frac{79}{14}\)
10. \(+\left(\frac{-8}{3}\right) +\left(\frac{5}{-4}\right) +\left(\frac{-8}{-4}\right)\\= \frac{-8}{3}- \frac{5}{4}+\frac{8}{4}\\=\frac{-8}{3}-\frac{5}{4}+\frac{2}{1}\\=\frac{-32}{12}-\frac{15}{12}+\frac{24}{12}\\=\frac{-32-15+24}{12}\\=\frac{-23}{12}\)
11. \(-\left(\frac{-3}{-7}\right) -\left(\frac{-6}{-8}\right) -\left(\frac{3}{-9}\right)\\= \frac{-3}{7}- \frac{6}{8}+\frac{3}{9}\\=\frac{-3}{7}-\frac{3}{4}+\frac{1}{3}\\=\frac{-36}{84}-\frac{63}{84}+\frac{28}{84}\\=\frac{-36-63+28}{84}\\=\frac{-71}{84}\)
12. \(-\left(\frac{6}{5}\right) -\left(\frac{-9}{4}\right) +\left(\frac{-2}{9}\right)\\= \frac{-6}{5}+ \frac{9}{4}-\frac{2}{9}\\=\frac{-216}{180}+\frac{405}{180}-\frac{40}{180}\\=\frac{-216+405-40}{180}\\=\frac{149}{180}\)