Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{-5}\right) +\left(\frac{-7}{-10}\right) +\left(\frac{7}{-12}\right)\\= \frac{7}{5}+ \frac{7}{10}-\frac{7}{12}\\=\frac{84}{60}+\frac{42}{60}-\frac{35}{60}\\=\frac{84+42-35}{60}\\=\frac{91}{60}\)
2. \(+\left(\frac{4}{3}\right) -\left(\frac{-5}{6}\right) +\left(\frac{8}{10}\right)\\= \frac{4}{3}+ \frac{5}{6}+\frac{8}{10}\\=\frac{4}{3}+\frac{5}{6}+\frac{4}{5}\\=\frac{40}{30}+\frac{25}{30}+\frac{24}{30}\\=\frac{40+25+24}{30}\\=\frac{89}{30}\)
3. \(+\left(\frac{-9}{7}\right) -\left(\frac{-9}{-8}\right) +\left(\frac{-10}{-6}\right)\\= \frac{-9}{7}- \frac{9}{8}+\frac{10}{6}\\=\frac{-9}{7}-\frac{9}{8}+\frac{5}{3}\\=\frac{-216}{168}-\frac{189}{168}+\frac{280}{168}\\=\frac{-216-189+280}{168}\\=\frac{-125}{168}\)
4. \(+\left(\frac{-3}{7}\right) -\left(\frac{9}{4}\right) -\left(\frac{-7}{-3}\right)\\= \frac{-3}{7}- \frac{9}{4}-\frac{7}{3}\\=\frac{-36}{84}-\frac{189}{84}-\frac{196}{84}\\=\frac{-36-189-196}{84}\\=\frac{-421}{84}\)
5. \(+\left(\frac{2}{7}\right) -\left(\frac{-7}{-3}\right) -\left(\frac{-7}{7}\right)\\= \frac{2}{7}- \frac{7}{3}+\frac{7}{7}\\=\frac{2}{7}-\frac{7}{3}+\frac{1}{1}\\=\frac{6}{21}-\frac{49}{21}+\frac{21}{21}\\=\frac{6-49+21}{21}\\=\frac{-22}{21}\)
6. \(-\left(\frac{9}{-8}\right) -\left(\frac{-9}{-5}\right) -\left(\frac{3}{-3}\right)\\= \frac{9}{8}- \frac{9}{5}+\frac{3}{3}\\=\frac{9}{8}-\frac{9}{5}+\frac{1}{1}\\=\frac{45}{40}-\frac{72}{40}+\frac{40}{40}\\=\frac{45-72+40}{40}\\=\frac{13}{40}\)
7. \(-\left(\frac{4}{-5}\right) +\left(\frac{10}{-10}\right) -\left(\frac{-11}{-12}\right)\\= \frac{4}{5}- \frac{10}{10}-\frac{11}{12}\\=\frac{4}{5}-\frac{1}{1}-\frac{11}{12}\\=\frac{48}{60}-\frac{60}{60}-\frac{55}{60}\\=\frac{48-60-55}{60}\\=\frac{-67}{60}\)
8. \(+\left(\frac{6}{5}\right) -\left(\frac{-10}{5}\right) +\left(\frac{5}{2}\right)\\= \frac{6}{5}+ \frac{10}{5}+\frac{5}{2}\\=\frac{6}{5}+\frac{2}{1}+\frac{5}{2}\\=\frac{12}{10}+\frac{20}{10}+\frac{25}{10}\\=\frac{12+20+25}{10}\\=\frac{57}{10}\)
9. \(-\left(\frac{9}{8}\right) +\left(\frac{5}{7}\right) +\left(\frac{3}{-6}\right)\\= \frac{-9}{8}+ \frac{5}{7}-\frac{3}{6}\\=\frac{-9}{8}+\frac{5}{7}-\frac{1}{2}\\=\frac{-63}{56}+\frac{40}{56}-\frac{28}{56}\\=\frac{-63+40-28}{56}\\=\frac{-51}{56}\)
10. \(+\left(\frac{2}{5}\right) -\left(\frac{-3}{3}\right) +\left(\frac{-3}{9}\right)\\= \frac{2}{5}+ \frac{3}{3}-\frac{3}{9}\\=\frac{2}{5}+\frac{1}{1}-\frac{1}{3}\\=\frac{6}{15}+\frac{15}{15}-\frac{5}{15}\\=\frac{6+15-5}{15}\\=\frac{16}{15}\)
11. \(-\left(\frac{-7}{5}\right) +\left(\frac{-4}{4}\right) +\left(\frac{-3}{-6}\right)\\= \frac{7}{5}- \frac{4}{4}+\frac{3}{6}\\=\frac{7}{5}-\frac{1}{1}+\frac{1}{2}\\=\frac{14}{10}-\frac{10}{10}+\frac{5}{10}\\=\frac{14-10+5}{10}\\=\frac{9}{10}\)
12. \(-\left(\frac{9}{7}\right) +\left(\frac{10}{3}\right) -\left(\frac{10}{4}\right)\\= \frac{-9}{7}+ \frac{10}{3}-\frac{10}{4}\\=\frac{-9}{7}+\frac{10}{3}-\frac{5}{2}\\=\frac{-54}{42}+\frac{140}{42}-\frac{105}{42}\\=\frac{-54+140-105}{42}\\=\frac{-19}{42}\)