Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{-6}\right) +\left(\frac{4}{-9}\right) +\left(\frac{-3}{2}\right)\\= \frac{-5}{6}- \frac{4}{9}-\frac{3}{2}\\=\frac{-15}{18}-\frac{8}{18}-\frac{27}{18}\\=\frac{-15-8-27}{18}\\=\frac{-50}{18}\\=\frac{-25}{9}\)
2. \(+\left(\frac{4}{5}\right) +\left(\frac{7}{9}\right) +\left(\frac{-2}{-7}\right)\\= \frac{4}{5}+ \frac{7}{9}+\frac{2}{7}\\=\frac{252}{315}+\frac{245}{315}+\frac{90}{315}\\=\frac{252+245+90}{315}\\=\frac{587}{315}\)
3. \(-\left(\frac{10}{7}\right) +\left(\frac{3}{3}\right) -\left(\frac{-6}{2}\right)\\= \frac{-10}{7}+ \frac{3}{3}+\frac{6}{2}\\=\frac{-10}{7}+\frac{1}{1}+\frac{3}{1}\\=\frac{-10+1+3}{7}\\=\frac{-6}{7}\)
4. \(-\left(\frac{-9}{2}\right) -\left(\frac{-5}{9}\right) +\left(\frac{4}{-5}\right)\\= \frac{9}{2}+ \frac{5}{9}-\frac{4}{5}\\=\frac{405}{90}+\frac{50}{90}-\frac{72}{90}\\=\frac{405+50-72}{90}\\=\frac{383}{90}\)
5. \(+\left(\frac{-2}{-7}\right) -\left(\frac{-2}{-2}\right) -\left(\frac{-5}{6}\right)\\= \frac{2}{7}- \frac{2}{2}+\frac{5}{6}\\=\frac{2}{7}-\frac{1}{1}+\frac{5}{6}\\=\frac{12}{42}-\frac{42}{42}+\frac{35}{42}\\=\frac{12-42+35}{42}\\=\frac{5}{42}\)
6. \(-\left(\frac{-4}{-5}\right) +\left(\frac{7}{6}\right) +\left(\frac{-10}{-10}\right)\\= \frac{-4}{5}+ \frac{7}{6}+\frac{10}{10}\\=\frac{-4}{5}+\frac{7}{6}+\frac{1}{1}\\=\frac{-24}{30}+\frac{35}{30}+\frac{30}{30}\\=\frac{-24+35+30}{30}\\=\frac{41}{30}\)
7. \(-\left(\frac{-10}{-3}\right) +\left(\frac{3}{-8}\right) -\left(\frac{3}{9}\right)\\= \frac{-10}{3}- \frac{3}{8}-\frac{3}{9}\\=\frac{-10}{3}-\frac{3}{8}-\frac{1}{3}\\=\frac{-80}{24}-\frac{9}{24}-\frac{8}{24}\\=\frac{-80-9-8}{24}\\=\frac{-97}{24}\)
8. \(-\left(\frac{-4}{-5}\right) +\left(\frac{2}{10}\right) -\left(\frac{-4}{11}\right)\\= \frac{-4}{5}+ \frac{2}{10}+\frac{4}{11}\\=\frac{-4}{5}+\frac{1}{5}+\frac{4}{11}\\=\frac{-44}{55}+\frac{11}{55}+\frac{20}{55}\\=\frac{-44+11+20}{55}\\=\frac{-13}{55}\)
9. \(-\left(\frac{8}{3}\right) +\left(\frac{6}{-3}\right) -\left(\frac{-12}{-7}\right)\\= \frac{-8}{3}- \frac{6}{3}-\frac{12}{7}\\=\frac{-8}{3}-\frac{2}{1}-\frac{12}{7}\\=\frac{-56}{21}-\frac{42}{21}-\frac{36}{21}\\=\frac{-56-42-36}{21}\\=\frac{-134}{21}\)
10. \(+\left(\frac{-6}{5}\right) +\left(\frac{7}{2}\right) +\left(\frac{4}{-11}\right)\\= \frac{-6}{5}+ \frac{7}{2}-\frac{4}{11}\\=\frac{-132}{110}+\frac{385}{110}-\frac{40}{110}\\=\frac{-132+385-40}{110}\\=\frac{213}{110}\)
11. \(-\left(\frac{8}{7}\right) +\left(\frac{3}{-3}\right) +\left(\frac{-7}{7}\right)\\= \frac{-8}{7}- \frac{3}{3}-\frac{7}{7}\\=\frac{-8}{7}-\frac{1}{1}-\frac{1}{1}\\=\frac{-8-1-1}{7}\\=\frac{-10}{7}\)
12. \(+\left(\frac{-8}{5}\right) +\left(\frac{-6}{2}\right) +\left(\frac{11}{5}\right)\\= \frac{-8}{5}- \frac{6}{2}+\frac{11}{5}\\=\frac{-8}{5}-\frac{3}{1}+\frac{11}{5}\\=\frac{-8-3+11}{5}\\=\frac{0}{5}\\=\frac{0}{1}\)