Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{8}{-7}\right) +\left(\frac{9}{-9}\right) +\left(\frac{10}{-7}\right)\\= \frac{-8}{7}- \frac{9}{9}-\frac{10}{7}\\=\frac{-8}{7}-\frac{1}{1}-\frac{10}{7}\\=\frac{-8-1-10}{7}\\=\frac{-19}{7}\)
2. \(-\left(\frac{-2}{9}\right) +\left(\frac{-9}{-5}\right) -\left(\frac{-7}{-4}\right)\\= \frac{2}{9}+ \frac{9}{5}-\frac{7}{4}\\=\frac{40}{180}+\frac{324}{180}-\frac{315}{180}\\=\frac{40+324-315}{180}\\=\frac{49}{180}\)
3. \(-\left(\frac{6}{7}\right) +\left(\frac{2}{-5}\right) -\left(\frac{2}{-9}\right)\\= \frac{-6}{7}- \frac{2}{5}+\frac{2}{9}\\=\frac{-270}{315}-\frac{126}{315}+\frac{70}{315}\\=\frac{-270-126+70}{315}\\=\frac{-326}{315}\)
4. \(+\left(\frac{-6}{-7}\right) -\left(\frac{5}{-9}\right) +\left(\frac{8}{12}\right)\\= \frac{6}{7}+ \frac{5}{9}+\frac{8}{12}\\=\frac{6}{7}+\frac{5}{9}+\frac{2}{3}\\=\frac{54}{63}+\frac{35}{63}+\frac{42}{63}\\=\frac{54+35+42}{63}\\=\frac{131}{63}\)
5. \(+\left(\frac{7}{-2}\right) +\left(\frac{-9}{2}\right) -\left(\frac{-12}{-5}\right)\\= \frac{-7}{2}- \frac{9}{2}-\frac{12}{5}\\=\frac{-35}{10}-\frac{45}{10}-\frac{24}{10}\\=\frac{-35-45-24}{10}\\=\frac{-104}{10}\\=\frac{-52}{5}\)
6. \(-\left(\frac{-4}{-5}\right) -\left(\frac{7}{6}\right) -\left(\frac{10}{-12}\right)\\= \frac{-4}{5}- \frac{7}{6}+\frac{10}{12}\\=\frac{-4}{5}-\frac{7}{6}+\frac{5}{6}\\=\frac{-24}{30}-\frac{35}{30}+\frac{25}{30}\\=\frac{-24-35+25}{30}\\=\frac{-34}{30}\\=\frac{-17}{15}\)
7. \(+\left(\frac{-10}{3}\right) -\left(\frac{2}{-6}\right) -\left(\frac{-8}{2}\right)\\= \frac{-10}{3}+ \frac{2}{6}+\frac{8}{2}\\=\frac{-10}{3}+\frac{1}{3}+\frac{4}{1}\\=\frac{-10+1+4}{3}\\=\frac{-5}{3}\)
8. \(+\left(\frac{-5}{2}\right) -\left(\frac{2}{-4}\right) -\left(\frac{8}{-8}\right)\\= \frac{-5}{2}+ \frac{2}{4}+\frac{8}{8}\\=\frac{-5}{2}+\frac{1}{2}+\frac{1}{1}\\=\frac{-5+1+1}{2}\\=\frac{-3}{2}\)
9. \(-\left(\frac{-6}{5}\right) +\left(\frac{-9}{2}\right) +\left(\frac{-8}{-6}\right)\\= \frac{6}{5}- \frac{9}{2}+\frac{8}{6}\\=\frac{6}{5}-\frac{9}{2}+\frac{4}{3}\\=\frac{36}{30}-\frac{135}{30}+\frac{40}{30}\\=\frac{36-135+40}{30}\\=\frac{-59}{30}\)
10. \(-\left(\frac{-6}{-5}\right) +\left(\frac{6}{2}\right) -\left(\frac{2}{-8}\right)\\= \frac{-6}{5}+ \frac{6}{2}+\frac{2}{8}\\=\frac{-6}{5}+\frac{3}{1}+\frac{1}{4}\\=\frac{-24}{20}+\frac{60}{20}+\frac{5}{20}\\=\frac{-24+60+5}{20}\\=\frac{41}{20}\)
11. \(-\left(\frac{-7}{2}\right) +\left(\frac{2}{-3}\right) -\left(\frac{2}{4}\right)\\= \frac{7}{2}- \frac{2}{3}-\frac{2}{4}\\=\frac{7}{2}-\frac{2}{3}-\frac{1}{2}\\=\frac{21}{6}-\frac{4}{6}-\frac{3}{6}\\=\frac{21-4-3}{6}\\=\frac{14}{6}\\=\frac{7}{3}\)
12. \(+\left(\frac{5}{7}\right) -\left(\frac{10}{-3}\right) +\left(\frac{11}{-2}\right)\\= \frac{5}{7}+ \frac{10}{3}-\frac{11}{2}\\=\frac{30}{42}+\frac{140}{42}-\frac{231}{42}\\=\frac{30+140-231}{42}\\=\frac{-61}{42}\)