Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{-5}\right) -\left(\frac{-10}{-9}\right) +\left(\frac{3}{-6}\right)\\= \frac{-3}{5}- \frac{10}{9}-\frac{3}{6}\\=\frac{-3}{5}-\frac{10}{9}-\frac{1}{2}\\=\frac{-54}{90}-\frac{100}{90}-\frac{45}{90}\\=\frac{-54-100-45}{90}\\=\frac{-199}{90}\)
2. \(+\left(\frac{9}{-7}\right) +\left(\frac{-6}{-10}\right) +\left(\frac{-10}{-8}\right)\\= \frac{-9}{7}+ \frac{6}{10}+\frac{10}{8}\\=\frac{-9}{7}+\frac{3}{5}+\frac{5}{4}\\=\frac{-180}{140}+\frac{84}{140}+\frac{175}{140}\\=\frac{-180+84+175}{140}\\=\frac{79}{140}\)
3. \(+\left(\frac{7}{-9}\right) +\left(\frac{-9}{-3}\right) -\left(\frac{-4}{-4}\right)\\= \frac{-7}{9}+ \frac{9}{3}-\frac{4}{4}\\=\frac{-7}{9}+\frac{3}{1}-\frac{1}{1}\\=\frac{-7+3-1}{9}\\=\frac{-5}{9}\)
4. \(-\left(\frac{-7}{-2}\right) +\left(\frac{2}{-7}\right) -\left(\frac{2}{-7}\right)\\= \frac{-7}{2}- \frac{2}{7}+\frac{2}{7}\\=\frac{-49}{14}-\frac{4}{14}+\frac{4}{14}\\=\frac{-49-4+4}{14}\\=\frac{-49}{14}\\=\frac{-7}{2}\)
5. \(+\left(\frac{4}{-3}\right) -\left(\frac{10}{-6}\right) -\left(\frac{2}{-4}\right)\\= \frac{-4}{3}+ \frac{10}{6}+\frac{2}{4}\\=\frac{-4}{3}+\frac{5}{3}+\frac{1}{2}\\=\frac{-8}{6}+\frac{10}{6}+\frac{3}{6}\\=\frac{-8+10+3}{6}\\=\frac{5}{6}\)
6. \(+\left(\frac{5}{6}\right) -\left(\frac{-4}{-5}\right) -\left(\frac{-5}{9}\right)\\= \frac{5}{6}- \frac{4}{5}+\frac{5}{9}\\=\frac{75}{90}-\frac{72}{90}+\frac{50}{90}\\=\frac{75-72+50}{90}\\=\frac{53}{90}\)
7. \(+\left(\frac{8}{3}\right) -\left(\frac{-7}{5}\right) +\left(\frac{3}{-8}\right)\\= \frac{8}{3}+ \frac{7}{5}-\frac{3}{8}\\=\frac{320}{120}+\frac{168}{120}-\frac{45}{120}\\=\frac{320+168-45}{120}\\=\frac{443}{120}\)
8. \(-\left(\frac{-5}{-9}\right) -\left(\frac{8}{4}\right) -\left(\frac{12}{-11}\right)\\= \frac{-5}{9}- \frac{8}{4}+\frac{12}{11}\\=\frac{-5}{9}-\frac{2}{1}+\frac{12}{11}\\=\frac{-55}{99}-\frac{198}{99}+\frac{108}{99}\\=\frac{-55-198+108}{99}\\=\frac{-145}{99}\)
9. \(+\left(\frac{8}{9}\right) +\left(\frac{7}{-4}\right) -\left(\frac{-10}{-12}\right)\\= \frac{8}{9}- \frac{7}{4}-\frac{10}{12}\\=\frac{8}{9}-\frac{7}{4}-\frac{5}{6}\\=\frac{32}{36}-\frac{63}{36}-\frac{30}{36}\\=\frac{32-63-30}{36}\\=\frac{-61}{36}\)
10. \(-\left(\frac{-6}{5}\right) -\left(\frac{9}{7}\right) -\left(\frac{4}{-4}\right)\\= \frac{6}{5}- \frac{9}{7}+\frac{4}{4}\\=\frac{6}{5}-\frac{9}{7}+\frac{1}{1}\\=\frac{42}{35}-\frac{45}{35}+\frac{35}{35}\\=\frac{42-45+35}{35}\\=\frac{32}{35}\)
11. \(+\left(\frac{2}{-3}\right) +\left(\frac{-3}{-9}\right) -\left(\frac{5}{4}\right)\\= \frac{-2}{3}+ \frac{3}{9}-\frac{5}{4}\\=\frac{-2}{3}+\frac{1}{3}-\frac{5}{4}\\=\frac{-8}{12}+\frac{4}{12}-\frac{15}{12}\\=\frac{-8+4-15}{12}\\=\frac{-19}{12}\)
12. \(+\left(\frac{8}{3}\right) -\left(\frac{10}{-2}\right) +\left(\frac{9}{-9}\right)\\= \frac{8}{3}+ \frac{10}{2}-\frac{9}{9}\\=\frac{8}{3}+\frac{5}{1}-\frac{1}{1}\\=\frac{8+5-1}{3}\\=\frac{12}{3}\\=\frac{4}{1}\)