Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{-2}\right) -\left(\frac{-7}{-3}\right) -\left(\frac{-8}{9}\right)\\= \frac{9}{2}- \frac{7}{3}+\frac{8}{9}\\=\frac{81}{18}-\frac{42}{18}+\frac{16}{18}\\=\frac{81-42+16}{18}\\=\frac{55}{18}\)
2. \(-\left(\frac{5}{7}\right) -\left(\frac{8}{-9}\right) -\left(\frac{10}{5}\right)\\= \frac{-5}{7}+ \frac{8}{9}-\frac{10}{5}\\=\frac{-5}{7}+\frac{8}{9}-\frac{2}{1}\\=\frac{-45}{63}+\frac{56}{63}-\frac{126}{63}\\=\frac{-45+56-126}{63}\\=\frac{-115}{63}\)
3. \(+\left(\frac{4}{-3}\right) -\left(\frac{-6}{-6}\right) +\left(\frac{-5}{-7}\right)\\= \frac{-4}{3}- \frac{6}{6}+\frac{5}{7}\\=\frac{-4}{3}-\frac{1}{1}+\frac{5}{7}\\=\frac{-28}{21}-\frac{21}{21}+\frac{15}{21}\\=\frac{-28-21+15}{21}\\=\frac{-34}{21}\)
4. \(-\left(\frac{-3}{4}\right) +\left(\frac{10}{-3}\right) +\left(\frac{-10}{-3}\right)\\= \frac{3}{4}- \frac{10}{3}+\frac{10}{3}\\=\frac{9}{12}-\frac{40}{12}+\frac{40}{12}\\=\frac{9-40+40}{12}\\=\frac{9}{12}\\=\frac{3}{4}\)
5. \(-\left(\frac{-10}{7}\right) -\left(\frac{-4}{3}\right) +\left(\frac{-5}{6}\right)\\= \frac{10}{7}+ \frac{4}{3}-\frac{5}{6}\\=\frac{60}{42}+\frac{56}{42}-\frac{35}{42}\\=\frac{60+56-35}{42}\\=\frac{81}{42}\\=\frac{27}{14}\)
6. \(-\left(\frac{4}{-7}\right) +\left(\frac{-2}{8}\right) -\left(\frac{-8}{-5}\right)\\= \frac{4}{7}- \frac{2}{8}-\frac{8}{5}\\=\frac{4}{7}-\frac{1}{4}-\frac{8}{5}\\=\frac{80}{140}-\frac{35}{140}-\frac{224}{140}\\=\frac{80-35-224}{140}\\=\frac{-179}{140}\)
7. \(-\left(\frac{-2}{5}\right) -\left(\frac{6}{3}\right) +\left(\frac{-2}{-11}\right)\\= \frac{2}{5}- \frac{6}{3}+\frac{2}{11}\\=\frac{2}{5}-\frac{2}{1}+\frac{2}{11}\\=\frac{22}{55}-\frac{110}{55}+\frac{10}{55}\\=\frac{22-110+10}{55}\\=\frac{-78}{55}\)
8. \(+\left(\frac{3}{2}\right) -\left(\frac{-4}{3}\right) -\left(\frac{10}{12}\right)\\= \frac{3}{2}+ \frac{4}{3}-\frac{10}{12}\\=\frac{3}{2}+\frac{4}{3}-\frac{5}{6}\\=\frac{9}{6}+\frac{8}{6}-\frac{5}{6}\\=\frac{9+8-5}{6}\\=\frac{12}{6}\\=\frac{2}{1}\)
9. \(-\left(\frac{-6}{-7}\right) +\left(\frac{10}{7}\right) +\left(\frac{12}{-5}\right)\\= \frac{-6}{7}+ \frac{10}{7}-\frac{12}{5}\\=\frac{-30}{35}+\frac{50}{35}-\frac{84}{35}\\=\frac{-30+50-84}{35}\\=\frac{-64}{35}\)
10. \(-\left(\frac{3}{-8}\right) -\left(\frac{-3}{-6}\right) -\left(\frac{5}{-7}\right)\\= \frac{3}{8}- \frac{3}{6}+\frac{5}{7}\\=\frac{3}{8}-\frac{1}{2}+\frac{5}{7}\\=\frac{21}{56}-\frac{28}{56}+\frac{40}{56}\\=\frac{21-28+40}{56}\\=\frac{33}{56}\)
11. \(+\left(\frac{-2}{9}\right) +\left(\frac{5}{5}\right) +\left(\frac{-5}{-12}\right)\\= \frac{-2}{9}+ \frac{5}{5}+\frac{5}{12}\\=\frac{-2}{9}+\frac{1}{1}+\frac{5}{12}\\=\frac{-8}{36}+\frac{36}{36}+\frac{15}{36}\\=\frac{-8+36+15}{36}\\=\frac{43}{36}\)
12. \(-\left(\frac{8}{9}\right) +\left(\frac{5}{3}\right) -\left(\frac{10}{2}\right)\\= \frac{-8}{9}+ \frac{5}{3}-\frac{10}{2}\\=\frac{-8}{9}+\frac{5}{3}-\frac{5}{1}\\=\frac{-8+5-5}{9}\\=\frac{-8}{9}\)