Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{4}\right) +\left(\frac{10}{10}\right) +\left(\frac{-7}{-6}\right)\\= \frac{5}{4}+ \frac{10}{10}+\frac{7}{6}\\=\frac{5}{4}+\frac{1}{1}+\frac{7}{6}\\=\frac{15}{12}+\frac{12}{12}+\frac{14}{12}\\=\frac{15+12+14}{12}\\=\frac{41}{12}\)
2. \(+\left(\frac{4}{7}\right) +\left(\frac{4}{-8}\right) +\left(\frac{-11}{-12}\right)\\= \frac{4}{7}- \frac{4}{8}+\frac{11}{12}\\=\frac{4}{7}-\frac{1}{2}+\frac{11}{12}\\=\frac{48}{84}-\frac{42}{84}+\frac{77}{84}\\=\frac{48-42+77}{84}\\=\frac{83}{84}\)
3. \(-\left(\frac{-7}{-8}\right) -\left(\frac{-2}{-9}\right) -\left(\frac{-6}{-3}\right)\\= \frac{-7}{8}- \frac{2}{9}-\frac{6}{3}\\=\frac{-7}{8}-\frac{2}{9}-\frac{2}{1}\\=\frac{-63}{72}-\frac{16}{72}-\frac{144}{72}\\=\frac{-63-16-144}{72}\\=\frac{-223}{72}\)
4. \(-\left(\frac{-8}{7}\right) +\left(\frac{8}{10}\right) +\left(\frac{-12}{4}\right)\\= \frac{8}{7}+ \frac{8}{10}-\frac{12}{4}\\=\frac{8}{7}+\frac{4}{5}-\frac{3}{1}\\=\frac{40}{35}+\frac{28}{35}-\frac{105}{35}\\=\frac{40+28-105}{35}\\=\frac{-37}{35}\)
5. \(-\left(\frac{7}{3}\right) +\left(\frac{9}{9}\right) +\left(\frac{-2}{-3}\right)\\= \frac{-7}{3}+ \frac{9}{9}+\frac{2}{3}\\=\frac{-7}{3}+\frac{1}{1}+\frac{2}{3}\\=\frac{-7+1+2}{3}\\=\frac{-4}{3}\)
6. \(+\left(\frac{10}{9}\right) -\left(\frac{8}{-9}\right) +\left(\frac{9}{-5}\right)\\= \frac{10}{9}+ \frac{8}{9}-\frac{9}{5}\\=\frac{50}{45}+\frac{40}{45}-\frac{81}{45}\\=\frac{50+40-81}{45}\\=\frac{9}{45}\\=\frac{1}{5}\)
7. \(+\left(\frac{9}{7}\right) +\left(\frac{6}{-7}\right) -\left(\frac{8}{-8}\right)\\= \frac{9}{7}- \frac{6}{7}+\frac{8}{8}\\=\frac{9}{7}-\frac{6}{7}+\frac{1}{1}\\=\frac{9-6+1}{7}\\=\frac{4}{7}\)
8. \(+\left(\frac{-4}{-7}\right) +\left(\frac{10}{10}\right) +\left(\frac{-10}{12}\right)\\= \frac{4}{7}+ \frac{10}{10}-\frac{10}{12}\\=\frac{4}{7}+\frac{1}{1}-\frac{5}{6}\\=\frac{24}{42}+\frac{42}{42}-\frac{35}{42}\\=\frac{24+42-35}{42}\\=\frac{31}{42}\)
9. \(+\left(\frac{9}{8}\right) -\left(\frac{2}{-3}\right) -\left(\frac{4}{-2}\right)\\= \frac{9}{8}+ \frac{2}{3}+\frac{4}{2}\\=\frac{9}{8}+\frac{2}{3}+\frac{2}{1}\\=\frac{27}{24}+\frac{16}{24}+\frac{48}{24}\\=\frac{27+16+48}{24}\\=\frac{91}{24}\)
10. \(-\left(\frac{6}{5}\right) +\left(\frac{-4}{-3}\right) -\left(\frac{-5}{-3}\right)\\= \frac{-6}{5}+ \frac{4}{3}-\frac{5}{3}\\=\frac{-18}{15}+\frac{20}{15}-\frac{25}{15}\\=\frac{-18+20-25}{15}\\=\frac{-23}{15}\)
11. \(-\left(\frac{2}{3}\right) +\left(\frac{4}{-4}\right) +\left(\frac{7}{-2}\right)\\= \frac{-2}{3}- \frac{4}{4}-\frac{7}{2}\\=\frac{-2}{3}-\frac{1}{1}-\frac{7}{2}\\=\frac{-4}{6}-\frac{6}{6}-\frac{21}{6}\\=\frac{-4-6-21}{6}\\=\frac{-31}{6}\)
12. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-8}{2}\right) -\left(\frac{-2}{5}\right)\\= \frac{-6}{5}+ \frac{8}{2}+\frac{2}{5}\\=\frac{-6}{5}+\frac{4}{1}+\frac{2}{5}\\=\frac{-6+4+2}{5}\\=\frac{0}{5}\\=\frac{0}{1}\)