Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{-4}\right) +\left(\frac{4}{9}\right) -\left(\frac{-2}{-11}\right)\\= \frac{7}{4}+ \frac{4}{9}-\frac{2}{11}\\=\frac{693}{396}+\frac{176}{396}-\frac{72}{396}\\=\frac{693+176-72}{396}\\=\frac{797}{396}\)
2. \(+\left(\frac{2}{-7}\right) +\left(\frac{-7}{4}\right) +\left(\frac{4}{8}\right)\\= \frac{-2}{7}- \frac{7}{4}+\frac{4}{8}\\=\frac{-2}{7}-\frac{7}{4}+\frac{1}{2}\\=\frac{-8}{28}-\frac{49}{28}+\frac{14}{28}\\=\frac{-8-49+14}{28}\\=\frac{-43}{28}\)
3. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-8}{-2}\right) -\left(\frac{-11}{7}\right)\\= \frac{6}{5}+ \frac{8}{2}+\frac{11}{7}\\=\frac{6}{5}+\frac{4}{1}+\frac{11}{7}\\=\frac{42}{35}+\frac{140}{35}+\frac{55}{35}\\=\frac{42+140+55}{35}\\=\frac{237}{35}\)
4. \(-\left(\frac{-6}{-7}\right) -\left(\frac{7}{5}\right) +\left(\frac{10}{7}\right)\\= \frac{-6}{7}- \frac{7}{5}+\frac{10}{7}\\=\frac{-30}{35}-\frac{49}{35}+\frac{50}{35}\\=\frac{-30-49+50}{35}\\=\frac{-29}{35}\)
5. \(+\left(\frac{9}{8}\right) -\left(\frac{10}{5}\right) +\left(\frac{-3}{-7}\right)\\= \frac{9}{8}- \frac{10}{5}+\frac{3}{7}\\=\frac{9}{8}-\frac{2}{1}+\frac{3}{7}\\=\frac{63}{56}-\frac{112}{56}+\frac{24}{56}\\=\frac{63-112+24}{56}\\=\frac{-25}{56}\)
6. \(-\left(\frac{-4}{-9}\right) -\left(\frac{-3}{-5}\right) +\left(\frac{-2}{-6}\right)\\= \frac{-4}{9}- \frac{3}{5}+\frac{2}{6}\\=\frac{-4}{9}-\frac{3}{5}+\frac{1}{3}\\=\frac{-20}{45}-\frac{27}{45}+\frac{15}{45}\\=\frac{-20-27+15}{45}\\=\frac{-32}{45}\)
7. \(-\left(\frac{-9}{-2}\right) -\left(\frac{3}{-9}\right) -\left(\frac{8}{6}\right)\\= \frac{-9}{2}+ \frac{3}{9}-\frac{8}{6}\\=\frac{-9}{2}+\frac{1}{3}-\frac{4}{3}\\=\frac{-27}{6}+\frac{2}{6}-\frac{8}{6}\\=\frac{-27+2-8}{6}\\=\frac{-33}{6}\\=\frac{-11}{2}\)
8. \(-\left(\frac{-4}{-5}\right) +\left(\frac{5}{9}\right) +\left(\frac{-6}{4}\right)\\= \frac{-4}{5}+ \frac{5}{9}-\frac{6}{4}\\=\frac{-4}{5}+\frac{5}{9}-\frac{3}{2}\\=\frac{-72}{90}+\frac{50}{90}-\frac{135}{90}\\=\frac{-72+50-135}{90}\\=\frac{-157}{90}\)
9. \(-\left(\frac{9}{8}\right) +\left(\frac{-3}{9}\right) +\left(\frac{-5}{5}\right)\\= \frac{-9}{8}- \frac{3}{9}-\frac{5}{5}\\=\frac{-9}{8}-\frac{1}{3}-\frac{1}{1}\\=\frac{-27}{24}-\frac{8}{24}-\frac{24}{24}\\=\frac{-27-8-24}{24}\\=\frac{-59}{24}\)
10. \(+\left(\frac{-8}{7}\right) +\left(\frac{4}{-3}\right) -\left(\frac{-8}{12}\right)\\= \frac{-8}{7}- \frac{4}{3}+\frac{8}{12}\\=\frac{-8}{7}-\frac{4}{3}+\frac{2}{3}\\=\frac{-24}{21}-\frac{28}{21}+\frac{14}{21}\\=\frac{-24-28+14}{21}\\=\frac{-38}{21}\)
11. \(-\left(\frac{-4}{-7}\right) -\left(\frac{4}{-10}\right) +\left(\frac{-7}{-9}\right)\\= \frac{-4}{7}+ \frac{4}{10}+\frac{7}{9}\\=\frac{-4}{7}+\frac{2}{5}+\frac{7}{9}\\=\frac{-180}{315}+\frac{126}{315}+\frac{245}{315}\\=\frac{-180+126+245}{315}\\=\frac{191}{315}\)
12. \(+\left(\frac{8}{7}\right) +\left(\frac{-6}{2}\right) -\left(\frac{8}{3}\right)\\= \frac{8}{7}- \frac{6}{2}-\frac{8}{3}\\=\frac{8}{7}-\frac{3}{1}-\frac{8}{3}\\=\frac{24}{21}-\frac{63}{21}-\frac{56}{21}\\=\frac{24-63-56}{21}\\=\frac{-95}{21}\)