Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{7}\right) -\left(\frac{-10}{-8}\right) -\left(\frac{11}{-2}\right)\\= \frac{-10}{7}- \frac{10}{8}+\frac{11}{2}\\=\frac{-10}{7}-\frac{5}{4}+\frac{11}{2}\\=\frac{-40}{28}-\frac{35}{28}+\frac{154}{28}\\=\frac{-40-35+154}{28}\\=\frac{79}{28}\)
2. \(-\left(\frac{6}{5}\right) -\left(\frac{9}{5}\right) +\left(\frac{3}{-3}\right)\\= \frac{-6}{5}- \frac{9}{5}-\frac{3}{3}\\=\frac{-6}{5}-\frac{9}{5}-\frac{1}{1}\\=\frac{-6-9-1}{5}\\=\frac{-16}{5}\)
3. \(+\left(\frac{10}{7}\right) +\left(\frac{-6}{-4}\right) +\left(\frac{-11}{-8}\right)\\= \frac{10}{7}+ \frac{6}{4}+\frac{11}{8}\\=\frac{10}{7}+\frac{3}{2}+\frac{11}{8}\\=\frac{80}{56}+\frac{84}{56}+\frac{77}{56}\\=\frac{80+84+77}{56}\\=\frac{241}{56}\)
4. \(-\left(\frac{-4}{-3}\right) +\left(\frac{-2}{-10}\right) -\left(\frac{7}{-2}\right)\\= \frac{-4}{3}+ \frac{2}{10}+\frac{7}{2}\\=\frac{-4}{3}+\frac{1}{5}+\frac{7}{2}\\=\frac{-40}{30}+\frac{6}{30}+\frac{105}{30}\\=\frac{-40+6+105}{30}\\=\frac{71}{30}\)
5. \(-\left(\frac{6}{7}\right) +\left(\frac{-4}{4}\right) +\left(\frac{-8}{-3}\right)\\= \frac{-6}{7}- \frac{4}{4}+\frac{8}{3}\\=\frac{-6}{7}-\frac{1}{1}+\frac{8}{3}\\=\frac{-18}{21}-\frac{21}{21}+\frac{56}{21}\\=\frac{-18-21+56}{21}\\=\frac{17}{21}\)
6. \(+\left(\frac{3}{-4}\right) +\left(\frac{-9}{8}\right) -\left(\frac{-3}{10}\right)\\= \frac{-3}{4}- \frac{9}{8}+\frac{3}{10}\\=\frac{-30}{40}-\frac{45}{40}+\frac{12}{40}\\=\frac{-30-45+12}{40}\\=\frac{-63}{40}\)
7. \(-\left(\frac{2}{9}\right) +\left(\frac{-3}{10}\right) -\left(\frac{11}{10}\right)\\= \frac{-2}{9}- \frac{3}{10}-\frac{11}{10}\\=\frac{-20}{90}-\frac{27}{90}-\frac{99}{90}\\=\frac{-20-27-99}{90}\\=\frac{-146}{90}\\=\frac{-73}{45}\)
8. \(-\left(\frac{9}{7}\right) +\left(\frac{-3}{-2}\right) -\left(\frac{-2}{9}\right)\\= \frac{-9}{7}+ \frac{3}{2}+\frac{2}{9}\\=\frac{-162}{126}+\frac{189}{126}+\frac{28}{126}\\=\frac{-162+189+28}{126}\\=\frac{55}{126}\)
9. \(-\left(\frac{-3}{-8}\right) +\left(\frac{-3}{4}\right) +\left(\frac{-7}{-4}\right)\\= \frac{-3}{8}- \frac{3}{4}+\frac{7}{4}\\=\frac{-3-3+7}{8}\\=\frac{1}{8}\)
10. \(-\left(\frac{-3}{-7}\right) -\left(\frac{5}{-10}\right) +\left(\frac{6}{8}\right)\\= \frac{-3}{7}+ \frac{5}{10}+\frac{6}{8}\\=\frac{-3}{7}+\frac{1}{2}+\frac{3}{4}\\=\frac{-12}{28}+\frac{14}{28}+\frac{21}{28}\\=\frac{-12+14+21}{28}\\=\frac{23}{28}\)
11. \(-\left(\frac{3}{-5}\right) +\left(\frac{9}{-10}\right) -\left(\frac{-7}{-6}\right)\\= \frac{3}{5}- \frac{9}{10}-\frac{7}{6}\\=\frac{18}{30}-\frac{27}{30}-\frac{35}{30}\\=\frac{18-27-35}{30}\\=\frac{-44}{30}\\=\frac{-22}{15}\)
12. \(-\left(\frac{-9}{-7}\right) -\left(\frac{9}{3}\right) +\left(\frac{-5}{8}\right)\\= \frac{-9}{7}- \frac{9}{3}-\frac{5}{8}\\=\frac{-9}{7}-\frac{3}{1}-\frac{5}{8}\\=\frac{-72}{56}-\frac{168}{56}-\frac{35}{56}\\=\frac{-72-168-35}{56}\\=\frac{-275}{56}\)