Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{5}\right) +\left(\frac{4}{-5}\right) +\left(\frac{7}{3}\right)\\= \frac{4}{5}- \frac{4}{5}+\frac{7}{3}\\=\frac{12}{15}-\frac{12}{15}+\frac{35}{15}\\=\frac{12-12+35}{15}\\=\frac{35}{15}\\=\frac{7}{3}\)
2. \(+\left(\frac{-9}{2}\right) +\left(\frac{-10}{5}\right) +\left(\frac{4}{4}\right)\\= \frac{-9}{2}- \frac{10}{5}+\frac{4}{4}\\=\frac{-9}{2}-\frac{2}{1}+\frac{1}{1}\\=\frac{-9-2+1}{2}\\=\frac{-10}{2}\\=\frac{-5}{1}\)
3. \(+\left(\frac{-4}{-9}\right) -\left(\frac{-6}{-2}\right) +\left(\frac{-6}{5}\right)\\= \frac{4}{9}- \frac{6}{2}-\frac{6}{5}\\=\frac{4}{9}-\frac{3}{1}-\frac{6}{5}\\=\frac{20}{45}-\frac{135}{45}-\frac{54}{45}\\=\frac{20-135-54}{45}\\=\frac{-169}{45}\)
4. \(-\left(\frac{8}{7}\right) +\left(\frac{7}{-3}\right) +\left(\frac{2}{-5}\right)\\= \frac{-8}{7}- \frac{7}{3}-\frac{2}{5}\\=\frac{-120}{105}-\frac{245}{105}-\frac{42}{105}\\=\frac{-120-245-42}{105}\\=\frac{-407}{105}\)
5. \(-\left(\frac{-7}{-2}\right) +\left(\frac{-4}{7}\right) -\left(\frac{-7}{-6}\right)\\= \frac{-7}{2}- \frac{4}{7}-\frac{7}{6}\\=\frac{-147}{42}-\frac{24}{42}-\frac{49}{42}\\=\frac{-147-24-49}{42}\\=\frac{-220}{42}\\=\frac{-110}{21}\)
6. \(-\left(\frac{-5}{-6}\right) +\left(\frac{8}{3}\right) +\left(\frac{-4}{11}\right)\\= \frac{-5}{6}+ \frac{8}{3}-\frac{4}{11}\\=\frac{-55}{66}+\frac{176}{66}-\frac{24}{66}\\=\frac{-55+176-24}{66}\\=\frac{97}{66}\)
7. \(-\left(\frac{-4}{-5}\right) -\left(\frac{4}{-4}\right) +\left(\frac{10}{7}\right)\\= \frac{-4}{5}+ \frac{4}{4}+\frac{10}{7}\\=\frac{-4}{5}+\frac{1}{1}+\frac{10}{7}\\=\frac{-28}{35}+\frac{35}{35}+\frac{50}{35}\\=\frac{-28+35+50}{35}\\=\frac{57}{35}\)
8. \(-\left(\frac{10}{9}\right) -\left(\frac{10}{-4}\right) -\left(\frac{2}{8}\right)\\= \frac{-10}{9}+ \frac{10}{4}-\frac{2}{8}\\=\frac{-10}{9}+\frac{5}{2}-\frac{1}{4}\\=\frac{-40}{36}+\frac{90}{36}-\frac{9}{36}\\=\frac{-40+90-9}{36}\\=\frac{41}{36}\)
9. \(-\left(\frac{10}{7}\right) -\left(\frac{-5}{9}\right) -\left(\frac{7}{7}\right)\\= \frac{-10}{7}+ \frac{5}{9}-\frac{7}{7}\\=\frac{-10}{7}+\frac{5}{9}-\frac{1}{1}\\=\frac{-90}{63}+\frac{35}{63}-\frac{63}{63}\\=\frac{-90+35-63}{63}\\=\frac{-118}{63}\)
10. \(-\left(\frac{-5}{3}\right) +\left(\frac{-3}{-8}\right) -\left(\frac{-9}{4}\right)\\= \frac{5}{3}+ \frac{3}{8}+\frac{9}{4}\\=\frac{40}{24}+\frac{9}{24}+\frac{54}{24}\\=\frac{40+9+54}{24}\\=\frac{103}{24}\)
11. \(-\left(\frac{-6}{5}\right) -\left(\frac{-4}{-3}\right) -\left(\frac{-9}{-9}\right)\\= \frac{6}{5}- \frac{4}{3}-\frac{9}{9}\\=\frac{6}{5}-\frac{4}{3}-\frac{1}{1}\\=\frac{18}{15}-\frac{20}{15}-\frac{15}{15}\\=\frac{18-20-15}{15}\\=\frac{-17}{15}\)
12. \(+\left(\frac{-10}{-7}\right) -\left(\frac{6}{-6}\right) -\left(\frac{-8}{10}\right)\\= \frac{10}{7}+ \frac{6}{6}+\frac{8}{10}\\=\frac{10}{7}+\frac{1}{1}+\frac{4}{5}\\=\frac{50}{35}+\frac{35}{35}+\frac{28}{35}\\=\frac{50+35+28}{35}\\=\frac{113}{35}\)