Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{-3}\right) -\left(\frac{8}{-6}\right) -\left(\frac{8}{7}\right)\\= \frac{-10}{3}+ \frac{8}{6}-\frac{8}{7}\\=\frac{-10}{3}+\frac{4}{3}-\frac{8}{7}\\=\frac{-70}{21}+\frac{28}{21}-\frac{24}{21}\\=\frac{-70+28-24}{21}\\=\frac{-66}{21}\\=\frac{-22}{7}\)
2. \(-\left(\frac{-8}{5}\right) +\left(\frac{-8}{9}\right) +\left(\frac{-5}{-9}\right)\\= \frac{8}{5}- \frac{8}{9}+\frac{5}{9}\\=\frac{72}{45}-\frac{40}{45}+\frac{25}{45}\\=\frac{72-40+25}{45}\\=\frac{57}{45}\\=\frac{19}{15}\)
3. \(-\left(\frac{5}{8}\right) +\left(\frac{-3}{-5}\right) -\left(\frac{-6}{12}\right)\\= \frac{-5}{8}+ \frac{3}{5}+\frac{6}{12}\\=\frac{-5}{8}+\frac{3}{5}+\frac{1}{2}\\=\frac{-25}{40}+\frac{24}{40}+\frac{20}{40}\\=\frac{-25+24+20}{40}\\=\frac{19}{40}\)
4. \(-\left(\frac{6}{5}\right) +\left(\frac{8}{4}\right) +\left(\frac{-4}{-11}\right)\\= \frac{-6}{5}+ \frac{8}{4}+\frac{4}{11}\\=\frac{-6}{5}+\frac{2}{1}+\frac{4}{11}\\=\frac{-66}{55}+\frac{110}{55}+\frac{20}{55}\\=\frac{-66+110+20}{55}\\=\frac{64}{55}\)
5. \(+\left(\frac{8}{-9}\right) +\left(\frac{9}{-6}\right) +\left(\frac{11}{4}\right)\\= \frac{-8}{9}- \frac{9}{6}+\frac{11}{4}\\=\frac{-8}{9}-\frac{3}{2}+\frac{11}{4}\\=\frac{-32}{36}-\frac{54}{36}+\frac{99}{36}\\=\frac{-32-54+99}{36}\\=\frac{13}{36}\)
6. \(+\left(\frac{6}{5}\right) +\left(\frac{5}{-4}\right) -\left(\frac{-4}{9}\right)\\= \frac{6}{5}- \frac{5}{4}+\frac{4}{9}\\=\frac{216}{180}-\frac{225}{180}+\frac{80}{180}\\=\frac{216-225+80}{180}\\=\frac{71}{180}\)
7. \(+\left(\frac{3}{2}\right) -\left(\frac{-7}{3}\right) +\left(\frac{-10}{-11}\right)\\= \frac{3}{2}+ \frac{7}{3}+\frac{10}{11}\\=\frac{99}{66}+\frac{154}{66}+\frac{60}{66}\\=\frac{99+154+60}{66}\\=\frac{313}{66}\)
8. \(+\left(\frac{-7}{-6}\right) -\left(\frac{8}{2}\right) -\left(\frac{-5}{-9}\right)\\= \frac{7}{6}- \frac{8}{2}-\frac{5}{9}\\=\frac{7}{6}-\frac{4}{1}-\frac{5}{9}\\=\frac{21}{18}-\frac{72}{18}-\frac{10}{18}\\=\frac{21-72-10}{18}\\=\frac{-61}{18}\)
9. \(-\left(\frac{8}{-3}\right) -\left(\frac{-4}{-2}\right) +\left(\frac{-7}{-2}\right)\\= \frac{8}{3}- \frac{4}{2}+\frac{7}{2}\\=\frac{8}{3}-\frac{2}{1}+\frac{7}{2}\\=\frac{16}{6}-\frac{12}{6}+\frac{21}{6}\\=\frac{16-12+21}{6}\\=\frac{25}{6}\)
10. \(-\left(\frac{3}{2}\right) +\left(\frac{-4}{3}\right) -\left(\frac{-3}{-4}\right)\\= \frac{-3}{2}- \frac{4}{3}-\frac{3}{4}\\=\frac{-18}{12}-\frac{16}{12}-\frac{9}{12}\\=\frac{-18-16-9}{12}\\=\frac{-43}{12}\)
11. \(-\left(\frac{-6}{7}\right) -\left(\frac{9}{3}\right) +\left(\frac{-8}{-5}\right)\\= \frac{6}{7}- \frac{9}{3}+\frac{8}{5}\\=\frac{6}{7}-\frac{3}{1}+\frac{8}{5}\\=\frac{30}{35}-\frac{105}{35}+\frac{56}{35}\\=\frac{30-105+56}{35}\\=\frac{-19}{35}\)
12. \(+\left(\frac{-6}{-5}\right) +\left(\frac{10}{4}\right) -\left(\frac{8}{-4}\right)\\= \frac{6}{5}+ \frac{10}{4}+\frac{8}{4}\\=\frac{6}{5}+\frac{5}{2}+\frac{2}{1}\\=\frac{12}{10}+\frac{25}{10}+\frac{20}{10}\\=\frac{12+25+20}{10}\\=\frac{57}{10}\)