Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{-7}\right) +\left(\frac{-8}{5}\right) -\left(\frac{10}{12}\right)\\= \frac{-3}{7}- \frac{8}{5}-\frac{10}{12}\\=\frac{-3}{7}-\frac{8}{5}-\frac{5}{6}\\=\frac{-90}{210}-\frac{336}{210}-\frac{175}{210}\\=\frac{-90-336-175}{210}\\=\frac{-601}{210}\)
2. \(+\left(\frac{-5}{-8}\right) -\left(\frac{-7}{10}\right) -\left(\frac{3}{10}\right)\\= \frac{5}{8}+ \frac{7}{10}-\frac{3}{10}\\=\frac{25}{40}+\frac{28}{40}-\frac{12}{40}\\=\frac{25+28-12}{40}\\=\frac{41}{40}\)
3. \(+\left(\frac{-4}{-9}\right) +\left(\frac{-10}{-9}\right) -\left(\frac{7}{2}\right)\\= \frac{4}{9}+ \frac{10}{9}-\frac{7}{2}\\=\frac{8}{18}+\frac{20}{18}-\frac{63}{18}\\=\frac{8+20-63}{18}\\=\frac{-35}{18}\)
4. \(+\left(\frac{5}{8}\right) +\left(\frac{4}{6}\right) +\left(\frac{-8}{-12}\right)\\= \frac{5}{8}+ \frac{4}{6}+\frac{8}{12}\\=\frac{5}{8}+\frac{2}{3}+\frac{2}{3}\\=\frac{15}{24}+\frac{16}{24}+\frac{16}{24}\\=\frac{15+16+16}{24}\\=\frac{47}{24}\)
5. \(+\left(\frac{8}{3}\right) -\left(\frac{-3}{5}\right) +\left(\frac{6}{5}\right)\\= \frac{8}{3}+ \frac{3}{5}+\frac{6}{5}\\=\frac{40}{15}+\frac{9}{15}+\frac{18}{15}\\=\frac{40+9+18}{15}\\=\frac{67}{15}\)
6. \(-\left(\frac{-9}{2}\right) +\left(\frac{-3}{-9}\right) -\left(\frac{12}{-2}\right)\\= \frac{9}{2}+ \frac{3}{9}+\frac{12}{2}\\=\frac{9}{2}+\frac{1}{3}+\frac{6}{1}\\=\frac{27}{6}+\frac{2}{6}+\frac{36}{6}\\=\frac{27+2+36}{6}\\=\frac{65}{6}\)
7. \(-\left(\frac{5}{-9}\right) +\left(\frac{-9}{7}\right) -\left(\frac{10}{5}\right)\\= \frac{5}{9}- \frac{9}{7}-\frac{10}{5}\\=\frac{5}{9}-\frac{9}{7}-\frac{2}{1}\\=\frac{35}{63}-\frac{81}{63}-\frac{126}{63}\\=\frac{35-81-126}{63}\\=\frac{-172}{63}\)
8. \(-\left(\frac{-7}{-6}\right) -\left(\frac{4}{-3}\right) -\left(\frac{7}{-11}\right)\\= \frac{-7}{6}+ \frac{4}{3}+\frac{7}{11}\\=\frac{-77}{66}+\frac{88}{66}+\frac{42}{66}\\=\frac{-77+88+42}{66}\\=\frac{53}{66}\)
9. \(-\left(\frac{-6}{5}\right) -\left(\frac{5}{6}\right) +\left(\frac{-3}{8}\right)\\= \frac{6}{5}- \frac{5}{6}-\frac{3}{8}\\=\frac{144}{120}-\frac{100}{120}-\frac{45}{120}\\=\frac{144-100-45}{120}\\=\frac{-1}{120}\)
10. \(+\left(\frac{5}{4}\right) -\left(\frac{-3}{-10}\right) -\left(\frac{-10}{-3}\right)\\= \frac{5}{4}- \frac{3}{10}-\frac{10}{3}\\=\frac{75}{60}-\frac{18}{60}-\frac{200}{60}\\=\frac{75-18-200}{60}\\=\frac{-143}{60}\)
11. \(+\left(\frac{4}{7}\right) +\left(\frac{6}{10}\right) -\left(\frac{-6}{-8}\right)\\= \frac{4}{7}+ \frac{6}{10}-\frac{6}{8}\\=\frac{4}{7}+\frac{3}{5}-\frac{3}{4}\\=\frac{80}{140}+\frac{84}{140}-\frac{105}{140}\\=\frac{80+84-105}{140}\\=\frac{59}{140}\)
12. \(-\left(\frac{9}{2}\right) +\left(\frac{-5}{-2}\right) -\left(\frac{12}{12}\right)\\= \frac{-9}{2}+ \frac{5}{2}-\frac{12}{12}\\=\frac{-9}{2}+\frac{5}{2}-\frac{1}{1}\\=\frac{-9+5-1}{2}\\=\frac{-5}{2}\)