Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{3}\right) -\left(\frac{4}{7}\right) -\left(\frac{10}{-6}\right)\\= \frac{2}{3}- \frac{4}{7}+\frac{10}{6}\\=\frac{2}{3}-\frac{4}{7}+\frac{5}{3}\\=\frac{14}{21}-\frac{12}{21}+\frac{35}{21}\\=\frac{14-12+35}{21}\\=\frac{37}{21}\)
2. \(-\left(\frac{8}{-9}\right) -\left(\frac{8}{-6}\right) +\left(\frac{-4}{-7}\right)\\= \frac{8}{9}+ \frac{8}{6}+\frac{4}{7}\\=\frac{8}{9}+\frac{4}{3}+\frac{4}{7}\\=\frac{56}{63}+\frac{84}{63}+\frac{36}{63}\\=\frac{56+84+36}{63}\\=\frac{176}{63}\)
3. \(-\left(\frac{-8}{-5}\right) +\left(\frac{-4}{8}\right) -\left(\frac{4}{-2}\right)\\= \frac{-8}{5}- \frac{4}{8}+\frac{4}{2}\\=\frac{-8}{5}-\frac{1}{2}+\frac{2}{1}\\=\frac{-16}{10}-\frac{5}{10}+\frac{20}{10}\\=\frac{-16-5+20}{10}\\=\frac{-1}{10}\)
4. \(-\left(\frac{2}{-3}\right) -\left(\frac{5}{6}\right) -\left(\frac{5}{-12}\right)\\= \frac{2}{3}- \frac{5}{6}+\frac{5}{12}\\=\frac{8}{12}-\frac{10}{12}+\frac{5}{12}\\=\frac{8-10+5}{12}\\=\frac{3}{12}\\=\frac{1}{4}\)
5. \(+\left(\frac{9}{5}\right) +\left(\frac{-2}{-7}\right) -\left(\frac{5}{2}\right)\\= \frac{9}{5}+ \frac{2}{7}-\frac{5}{2}\\=\frac{126}{70}+\frac{20}{70}-\frac{175}{70}\\=\frac{126+20-175}{70}\\=\frac{-29}{70}\)
6. \(-\left(\frac{9}{8}\right) -\left(\frac{-3}{3}\right) -\left(\frac{-3}{2}\right)\\= \frac{-9}{8}+ \frac{3}{3}+\frac{3}{2}\\=\frac{-9}{8}+\frac{1}{1}+\frac{3}{2}\\=\frac{-9+1+3}{8}\\=\frac{-5}{8}\)
7. \(-\left(\frac{4}{-9}\right) -\left(\frac{10}{-3}\right) -\left(\frac{-12}{-9}\right)\\= \frac{4}{9}+ \frac{10}{3}-\frac{12}{9}\\=\frac{4}{9}+\frac{10}{3}-\frac{4}{3}\\=\frac{4+10-4}{9}\\=\frac{10}{9}\)
8. \(+\left(\frac{-2}{-7}\right) -\left(\frac{-8}{-9}\right) +\left(\frac{-3}{5}\right)\\= \frac{2}{7}- \frac{8}{9}-\frac{3}{5}\\=\frac{90}{315}-\frac{280}{315}-\frac{189}{315}\\=\frac{90-280-189}{315}\\=\frac{-379}{315}\)
9. \(-\left(\frac{9}{-2}\right) +\left(\frac{2}{-5}\right) -\left(\frac{9}{-10}\right)\\= \frac{9}{2}- \frac{2}{5}+\frac{9}{10}\\=\frac{45}{10}-\frac{4}{10}+\frac{9}{10}\\=\frac{45-4+9}{10}\\=\frac{50}{10}\\=\frac{5}{1}\)
10. \(+\left(\frac{8}{-3}\right) +\left(\frac{3}{2}\right) +\left(\frac{11}{-11}\right)\\= \frac{-8}{3}+ \frac{3}{2}-\frac{11}{11}\\=\frac{-8}{3}+\frac{3}{2}-\frac{1}{1}\\=\frac{-16}{6}+\frac{9}{6}-\frac{6}{6}\\=\frac{-16+9-6}{6}\\=\frac{-13}{6}\)
11. \(-\left(\frac{9}{-2}\right) +\left(\frac{10}{-8}\right) -\left(\frac{9}{8}\right)\\= \frac{9}{2}- \frac{10}{8}-\frac{9}{8}\\=\frac{9}{2}-\frac{5}{4}-\frac{9}{8}\\=\frac{36}{8}-\frac{10}{8}-\frac{9}{8}\\=\frac{36-10-9}{8}\\=\frac{17}{8}\)
12. \(-\left(\frac{-4}{3}\right) -\left(\frac{-2}{-2}\right) +\left(\frac{9}{9}\right)\\= \frac{4}{3}- \frac{2}{2}+\frac{9}{9}\\=\frac{4}{3}-\frac{1}{1}+\frac{1}{1}\\=\frac{4-1+1}{3}\\=\frac{4}{3}\)