Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{-5}\right) -\left(\frac{-2}{7}\right) +\left(\frac{2}{4}\right)\\= \frac{9}{5}+ \frac{2}{7}+\frac{2}{4}\\=\frac{9}{5}+\frac{2}{7}+\frac{1}{2}\\=\frac{126}{70}+\frac{20}{70}+\frac{35}{70}\\=\frac{126+20+35}{70}\\=\frac{181}{70}\)
2. \(+\left(\frac{-6}{-5}\right) +\left(\frac{4}{5}\right) +\left(\frac{12}{7}\right)\\= \frac{6}{5}+ \frac{4}{5}+\frac{12}{7}\\=\frac{42}{35}+\frac{28}{35}+\frac{60}{35}\\=\frac{42+28+60}{35}\\=\frac{130}{35}\\=\frac{26}{7}\)
3. \(-\left(\frac{2}{-9}\right) -\left(\frac{-10}{-8}\right) +\left(\frac{-3}{5}\right)\\= \frac{2}{9}- \frac{10}{8}-\frac{3}{5}\\=\frac{2}{9}-\frac{5}{4}-\frac{3}{5}\\=\frac{40}{180}-\frac{225}{180}-\frac{108}{180}\\=\frac{40-225-108}{180}\\=\frac{-293}{180}\)
4. \(-\left(\frac{-8}{7}\right) +\left(\frac{7}{-3}\right) +\left(\frac{-2}{7}\right)\\= \frac{8}{7}- \frac{7}{3}-\frac{2}{7}\\=\frac{24}{21}-\frac{49}{21}-\frac{6}{21}\\=\frac{24-49-6}{21}\\=\frac{-31}{21}\)
5. \(+\left(\frac{-6}{5}\right) -\left(\frac{-2}{2}\right) +\left(\frac{-2}{6}\right)\\= \frac{-6}{5}+ \frac{2}{2}-\frac{2}{6}\\=\frac{-6}{5}+\frac{1}{1}-\frac{1}{3}\\=\frac{-18}{15}+\frac{15}{15}-\frac{5}{15}\\=\frac{-18+15-5}{15}\\=\frac{-8}{15}\)
6. \(+\left(\frac{-3}{-8}\right) -\left(\frac{-2}{-5}\right) -\left(\frac{-5}{-3}\right)\\= \frac{3}{8}- \frac{2}{5}-\frac{5}{3}\\=\frac{45}{120}-\frac{48}{120}-\frac{200}{120}\\=\frac{45-48-200}{120}\\=\frac{-203}{120}\)
7. \(-\left(\frac{-6}{5}\right) +\left(\frac{-5}{10}\right) +\left(\frac{-7}{-8}\right)\\= \frac{6}{5}- \frac{5}{10}+\frac{7}{8}\\=\frac{6}{5}-\frac{1}{2}+\frac{7}{8}\\=\frac{48}{40}-\frac{20}{40}+\frac{35}{40}\\=\frac{48-20+35}{40}\\=\frac{63}{40}\)
8. \(+\left(\frac{-6}{-5}\right) -\left(\frac{7}{8}\right) -\left(\frac{-2}{12}\right)\\= \frac{6}{5}- \frac{7}{8}+\frac{2}{12}\\=\frac{6}{5}-\frac{7}{8}+\frac{1}{6}\\=\frac{144}{120}-\frac{105}{120}+\frac{20}{120}\\=\frac{144-105+20}{120}\\=\frac{59}{120}\)
9. \(-\left(\frac{5}{8}\right) -\left(\frac{5}{7}\right) -\left(\frac{12}{4}\right)\\= \frac{-5}{8}- \frac{5}{7}-\frac{12}{4}\\=\frac{-5}{8}-\frac{5}{7}-\frac{3}{1}\\=\frac{-35}{56}-\frac{40}{56}-\frac{168}{56}\\=\frac{-35-40-168}{56}\\=\frac{-243}{56}\)
10. \(-\left(\frac{-9}{7}\right) -\left(\frac{-2}{2}\right) -\left(\frac{-7}{-8}\right)\\= \frac{9}{7}+ \frac{2}{2}-\frac{7}{8}\\=\frac{9}{7}+\frac{1}{1}-\frac{7}{8}\\=\frac{72}{56}+\frac{56}{56}-\frac{49}{56}\\=\frac{72+56-49}{56}\\=\frac{79}{56}\)
11. \(-\left(\frac{-8}{3}\right) +\left(\frac{4}{5}\right) +\left(\frac{-3}{2}\right)\\= \frac{8}{3}+ \frac{4}{5}-\frac{3}{2}\\=\frac{80}{30}+\frac{24}{30}-\frac{45}{30}\\=\frac{80+24-45}{30}\\=\frac{59}{30}\)
12. \(-\left(\frac{-2}{3}\right) -\left(\frac{-7}{-4}\right) +\left(\frac{2}{-5}\right)\\= \frac{2}{3}- \frac{7}{4}-\frac{2}{5}\\=\frac{40}{60}-\frac{105}{60}-\frac{24}{60}\\=\frac{40-105-24}{60}\\=\frac{-89}{60}\)