Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{2}\right) +\left(\frac{9}{-2}\right) -\left(\frac{-5}{-3}\right)\\= \frac{-7}{2}- \frac{9}{2}-\frac{5}{3}\\=\frac{-21}{6}-\frac{27}{6}-\frac{10}{6}\\=\frac{-21-27-10}{6}\\=\frac{-58}{6}\\=\frac{-29}{3}\)
2. \(+\left(\frac{4}{7}\right) +\left(\frac{3}{4}\right) -\left(\frac{-10}{-9}\right)\\= \frac{4}{7}+ \frac{3}{4}-\frac{10}{9}\\=\frac{144}{252}+\frac{189}{252}-\frac{280}{252}\\=\frac{144+189-280}{252}\\=\frac{53}{252}\)
3. \(-\left(\frac{-7}{-8}\right) +\left(\frac{-8}{9}\right) -\left(\frac{-5}{9}\right)\\= \frac{-7}{8}- \frac{8}{9}+\frac{5}{9}\\=\frac{-63}{72}-\frac{64}{72}+\frac{40}{72}\\=\frac{-63-64+40}{72}\\=\frac{-87}{72}\\=\frac{-29}{24}\)
4. \(+\left(\frac{-5}{3}\right) -\left(\frac{9}{6}\right) -\left(\frac{-6}{3}\right)\\= \frac{-5}{3}- \frac{9}{6}+\frac{6}{3}\\=\frac{-5}{3}-\frac{3}{2}+\frac{2}{1}\\=\frac{-10}{6}-\frac{9}{6}+\frac{12}{6}\\=\frac{-10-9+12}{6}\\=\frac{-7}{6}\)
5. \(-\left(\frac{4}{3}\right) -\left(\frac{7}{6}\right) -\left(\frac{-8}{5}\right)\\= \frac{-4}{3}- \frac{7}{6}+\frac{8}{5}\\=\frac{-40}{30}-\frac{35}{30}+\frac{48}{30}\\=\frac{-40-35+48}{30}\\=\frac{-27}{30}\\=\frac{-9}{10}\)
6. \(-\left(\frac{-8}{-5}\right) -\left(\frac{8}{-3}\right) -\left(\frac{6}{-12}\right)\\= \frac{-8}{5}+ \frac{8}{3}+\frac{6}{12}\\=\frac{-8}{5}+\frac{8}{3}+\frac{1}{2}\\=\frac{-48}{30}+\frac{80}{30}+\frac{15}{30}\\=\frac{-48+80+15}{30}\\=\frac{47}{30}\)
7. \(+\left(\frac{7}{4}\right) +\left(\frac{-3}{2}\right) +\left(\frac{11}{10}\right)\\= \frac{7}{4}- \frac{3}{2}+\frac{11}{10}\\=\frac{35}{20}-\frac{30}{20}+\frac{22}{20}\\=\frac{35-30+22}{20}\\=\frac{27}{20}\)
8. \(+\left(\frac{10}{3}\right) -\left(\frac{-10}{2}\right) -\left(\frac{-10}{-10}\right)\\= \frac{10}{3}+ \frac{10}{2}-\frac{10}{10}\\=\frac{10}{3}+\frac{5}{1}-\frac{1}{1}\\=\frac{10+5-1}{3}\\=\frac{14}{3}\)
9. \(+\left(\frac{-10}{7}\right) -\left(\frac{-7}{-6}\right) -\left(\frac{-12}{-4}\right)\\= \frac{-10}{7}- \frac{7}{6}-\frac{12}{4}\\=\frac{-10}{7}-\frac{7}{6}-\frac{3}{1}\\=\frac{-60}{42}-\frac{49}{42}-\frac{126}{42}\\=\frac{-60-49-126}{42}\\=\frac{-235}{42}\)
10. \(+\left(\frac{6}{7}\right) -\left(\frac{6}{-5}\right) -\left(\frac{-2}{12}\right)\\= \frac{6}{7}+ \frac{6}{5}+\frac{2}{12}\\=\frac{6}{7}+\frac{6}{5}+\frac{1}{6}\\=\frac{180}{210}+\frac{252}{210}+\frac{35}{210}\\=\frac{180+252+35}{210}\\=\frac{467}{210}\)
11. \(+\left(\frac{6}{-5}\right) +\left(\frac{-10}{5}\right) -\left(\frac{-4}{-3}\right)\\= \frac{-6}{5}- \frac{10}{5}-\frac{4}{3}\\=\frac{-6}{5}-\frac{2}{1}-\frac{4}{3}\\=\frac{-18}{15}-\frac{30}{15}-\frac{20}{15}\\=\frac{-18-30-20}{15}\\=\frac{-68}{15}\)
12. \(-\left(\frac{7}{4}\right) +\left(\frac{-6}{-5}\right) +\left(\frac{-5}{-3}\right)\\= \frac{-7}{4}+ \frac{6}{5}+\frac{5}{3}\\=\frac{-105}{60}+\frac{72}{60}+\frac{100}{60}\\=\frac{-105+72+100}{60}\\=\frac{67}{60}\)