Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{-5}\right) +\left(\frac{-3}{-3}\right) +\left(\frac{2}{5}\right)\\= \frac{2}{5}+ \frac{3}{3}+\frac{2}{5}\\=\frac{2}{5}+\frac{1}{1}+\frac{2}{5}\\=\frac{2+1+2}{5}\\=\frac{5}{5}\\=\frac{1}{1}\)
2. \(+\left(\frac{-9}{8}\right) +\left(\frac{-7}{9}\right) +\left(\frac{-7}{-2}\right)\\= \frac{-9}{8}- \frac{7}{9}+\frac{7}{2}\\=\frac{-81}{72}-\frac{56}{72}+\frac{252}{72}\\=\frac{-81-56+252}{72}\\=\frac{115}{72}\)
3. \(-\left(\frac{-3}{8}\right) -\left(\frac{6}{-6}\right) +\left(\frac{3}{6}\right)\\= \frac{3}{8}+ \frac{6}{6}+\frac{3}{6}\\=\frac{3}{8}+\frac{1}{1}+\frac{1}{2}\\=\frac{3+1+1}{8}\\=\frac{5}{8}\)
4. \(-\left(\frac{8}{7}\right) -\left(\frac{2}{-5}\right) +\left(\frac{-5}{9}\right)\\= \frac{-8}{7}+ \frac{2}{5}-\frac{5}{9}\\=\frac{-360}{315}+\frac{126}{315}-\frac{175}{315}\\=\frac{-360+126-175}{315}\\=\frac{-409}{315}\)
5. \(-\left(\frac{-5}{2}\right) -\left(\frac{-8}{10}\right) -\left(\frac{6}{2}\right)\\= \frac{5}{2}+ \frac{8}{10}-\frac{6}{2}\\=\frac{5}{2}+\frac{4}{5}-\frac{3}{1}\\=\frac{25}{10}+\frac{8}{10}-\frac{30}{10}\\=\frac{25+8-30}{10}\\=\frac{3}{10}\)
6. \(-\left(\frac{-4}{3}\right) +\left(\frac{6}{10}\right) -\left(\frac{-8}{5}\right)\\= \frac{4}{3}+ \frac{6}{10}+\frac{8}{5}\\=\frac{4}{3}+\frac{3}{5}+\frac{8}{5}\\=\frac{20}{15}+\frac{9}{15}+\frac{24}{15}\\=\frac{20+9+24}{15}\\=\frac{53}{15}\)
7. \(+\left(\frac{10}{-7}\right) +\left(\frac{-5}{9}\right) -\left(\frac{-6}{-3}\right)\\= \frac{-10}{7}- \frac{5}{9}-\frac{6}{3}\\=\frac{-10}{7}-\frac{5}{9}-\frac{2}{1}\\=\frac{-90}{63}-\frac{35}{63}-\frac{126}{63}\\=\frac{-90-35-126}{63}\\=\frac{-251}{63}\)
8. \(-\left(\frac{-8}{-3}\right) +\left(\frac{-2}{6}\right) -\left(\frac{3}{8}\right)\\= \frac{-8}{3}- \frac{2}{6}-\frac{3}{8}\\=\frac{-8}{3}-\frac{1}{3}-\frac{3}{8}\\=\frac{-64}{24}-\frac{8}{24}-\frac{9}{24}\\=\frac{-64-8-9}{24}\\=\frac{-81}{24}\\=\frac{-27}{8}\)
9. \(-\left(\frac{7}{-8}\right) +\left(\frac{-10}{-5}\right) +\left(\frac{-9}{4}\right)\\= \frac{7}{8}+ \frac{10}{5}-\frac{9}{4}\\=\frac{7}{8}+\frac{2}{1}-\frac{9}{4}\\=\frac{7+2-9}{8}\\=\frac{0}{8}\\=\frac{0}{1}\)
10. \(-\left(\frac{-5}{-9}\right) -\left(\frac{-3}{-3}\right) +\left(\frac{-5}{8}\right)\\= \frac{-5}{9}- \frac{3}{3}-\frac{5}{8}\\=\frac{-5}{9}-\frac{1}{1}-\frac{5}{8}\\=\frac{-40}{72}-\frac{72}{72}-\frac{45}{72}\\=\frac{-40-72-45}{72}\\=\frac{-157}{72}\)
11. \(-\left(\frac{-8}{-7}\right) -\left(\frac{-5}{2}\right) -\left(\frac{8}{11}\right)\\= \frac{-8}{7}+ \frac{5}{2}-\frac{8}{11}\\=\frac{-176}{154}+\frac{385}{154}-\frac{112}{154}\\=\frac{-176+385-112}{154}\\=\frac{97}{154}\)
12. \(-\left(\frac{5}{-8}\right) +\left(\frac{4}{-6}\right) +\left(\frac{-9}{3}\right)\\= \frac{5}{8}- \frac{4}{6}-\frac{9}{3}\\=\frac{5}{8}-\frac{2}{3}-\frac{3}{1}\\=\frac{15}{24}-\frac{16}{24}-\frac{72}{24}\\=\frac{15-16-72}{24}\\=\frac{-73}{24}\)