Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{-4}\right) -\left(\frac{-7}{-5}\right) +\left(\frac{-7}{9}\right)\\= \frac{3}{4}- \frac{7}{5}-\frac{7}{9}\\=\frac{135}{180}-\frac{252}{180}-\frac{140}{180}\\=\frac{135-252-140}{180}\\=\frac{-257}{180}\)
2. \(+\left(\frac{3}{-5}\right) +\left(\frac{6}{-8}\right) +\left(\frac{2}{-7}\right)\\= \frac{-3}{5}- \frac{6}{8}-\frac{2}{7}\\=\frac{-3}{5}-\frac{3}{4}-\frac{2}{7}\\=\frac{-84}{140}-\frac{105}{140}-\frac{40}{140}\\=\frac{-84-105-40}{140}\\=\frac{-229}{140}\)
3. \(-\left(\frac{6}{5}\right) +\left(\frac{-2}{7}\right) +\left(\frac{-2}{9}\right)\\= \frac{-6}{5}- \frac{2}{7}-\frac{2}{9}\\=\frac{-378}{315}-\frac{90}{315}-\frac{70}{315}\\=\frac{-378-90-70}{315}\\=\frac{-538}{315}\)
4. \(+\left(\frac{4}{-3}\right) +\left(\frac{5}{4}\right) +\left(\frac{3}{10}\right)\\= \frac{-4}{3}+ \frac{5}{4}+\frac{3}{10}\\=\frac{-80}{60}+\frac{75}{60}+\frac{18}{60}\\=\frac{-80+75+18}{60}\\=\frac{13}{60}\)
5. \(-\left(\frac{3}{4}\right) -\left(\frac{7}{8}\right) +\left(\frac{4}{6}\right)\\= \frac{-3}{4}- \frac{7}{8}+\frac{4}{6}\\=\frac{-3}{4}-\frac{7}{8}+\frac{2}{3}\\=\frac{-18}{24}-\frac{21}{24}+\frac{16}{24}\\=\frac{-18-21+16}{24}\\=\frac{-23}{24}\)
6. \(+\left(\frac{-7}{8}\right) +\left(\frac{-6}{-4}\right) -\left(\frac{-7}{-9}\right)\\= \frac{-7}{8}+ \frac{6}{4}-\frac{7}{9}\\=\frac{-7}{8}+\frac{3}{2}-\frac{7}{9}\\=\frac{-63}{72}+\frac{108}{72}-\frac{56}{72}\\=\frac{-63+108-56}{72}\\=\frac{-11}{72}\)
7. \(+\left(\frac{5}{-6}\right) +\left(\frac{-4}{2}\right) +\left(\frac{-2}{11}\right)\\= \frac{-5}{6}- \frac{4}{2}-\frac{2}{11}\\=\frac{-5}{6}-\frac{2}{1}-\frac{2}{11}\\=\frac{-55}{66}-\frac{132}{66}-\frac{12}{66}\\=\frac{-55-132-12}{66}\\=\frac{-199}{66}\)
8. \(-\left(\frac{9}{-2}\right) -\left(\frac{9}{-7}\right) -\left(\frac{-10}{2}\right)\\= \frac{9}{2}+ \frac{9}{7}+\frac{10}{2}\\=\frac{9}{2}+\frac{9}{7}+\frac{5}{1}\\=\frac{63}{14}+\frac{18}{14}+\frac{70}{14}\\=\frac{63+18+70}{14}\\=\frac{151}{14}\)
9. \(+\left(\frac{-3}{-2}\right) -\left(\frac{-5}{4}\right) -\left(\frac{-3}{12}\right)\\= \frac{3}{2}+ \frac{5}{4}+\frac{3}{12}\\=\frac{3}{2}+\frac{5}{4}+\frac{1}{4}\\=\frac{6}{4}+\frac{5}{4}+\frac{1}{4}\\=\frac{6+5+1}{4}\\=\frac{12}{4}\\=\frac{3}{1}\)
10. \(+\left(\frac{9}{4}\right) +\left(\frac{-2}{-5}\right) -\left(\frac{2}{-6}\right)\\= \frac{9}{4}+ \frac{2}{5}+\frac{2}{6}\\=\frac{9}{4}+\frac{2}{5}+\frac{1}{3}\\=\frac{135}{60}+\frac{24}{60}+\frac{20}{60}\\=\frac{135+24+20}{60}\\=\frac{179}{60}\)
11. \(-\left(\frac{-2}{-7}\right) +\left(\frac{-6}{-5}\right) -\left(\frac{-4}{5}\right)\\= \frac{-2}{7}+ \frac{6}{5}+\frac{4}{5}\\=\frac{-10}{35}+\frac{42}{35}+\frac{28}{35}\\=\frac{-10+42+28}{35}\\=\frac{60}{35}\\=\frac{12}{7}\)
12. \(+\left(\frac{-6}{-7}\right) +\left(\frac{-6}{-9}\right) -\left(\frac{12}{12}\right)\\= \frac{6}{7}+ \frac{6}{9}-\frac{12}{12}\\=\frac{6}{7}+\frac{2}{3}-\frac{1}{1}\\=\frac{18}{21}+\frac{14}{21}-\frac{21}{21}\\=\frac{18+14-21}{21}\\=\frac{11}{21}\)