Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{7}{5}\right) -\left(\frac{4}{10}\right) -\left(\frac{3}{-8}\right)\\= \frac{7}{5}- \frac{4}{10}+\frac{3}{8}\\=\frac{7}{5}-\frac{2}{5}+\frac{3}{8}\\=\frac{56}{40}-\frac{16}{40}+\frac{15}{40}\\=\frac{56-16+15}{40}\\=\frac{55}{40}\\=\frac{11}{8}\)
2. \(+\left(\frac{6}{7}\right) +\left(\frac{-10}{4}\right) +\left(\frac{5}{10}\right)\\= \frac{6}{7}- \frac{10}{4}+\frac{5}{10}\\=\frac{6}{7}-\frac{5}{2}+\frac{1}{2}\\=\frac{12}{14}-\frac{35}{14}+\frac{7}{14}\\=\frac{12-35+7}{14}\\=\frac{-16}{14}\\=\frac{-8}{7}\)
3. \(-\left(\frac{4}{3}\right) -\left(\frac{-7}{-5}\right) +\left(\frac{3}{8}\right)\\= \frac{-4}{3}- \frac{7}{5}+\frac{3}{8}\\=\frac{-160}{120}-\frac{168}{120}+\frac{45}{120}\\=\frac{-160-168+45}{120}\\=\frac{-283}{120}\)
4. \(-\left(\frac{-7}{-9}\right) +\left(\frac{-6}{6}\right) -\left(\frac{-6}{-3}\right)\\= \frac{-7}{9}- \frac{6}{6}-\frac{6}{3}\\=\frac{-7}{9}-\frac{1}{1}-\frac{2}{1}\\=\frac{-7-1-2}{9}\\=\frac{-10}{9}\)
5. \(-\left(\frac{-4}{-5}\right) -\left(\frac{-8}{-4}\right) -\left(\frac{-9}{-11}\right)\\= \frac{-4}{5}- \frac{8}{4}-\frac{9}{11}\\=\frac{-4}{5}-\frac{2}{1}-\frac{9}{11}\\=\frac{-44}{55}-\frac{110}{55}-\frac{45}{55}\\=\frac{-44-110-45}{55}\\=\frac{-199}{55}\)
6. \(+\left(\frac{-5}{2}\right) -\left(\frac{5}{5}\right) +\left(\frac{-5}{2}\right)\\= \frac{-5}{2}- \frac{5}{5}-\frac{5}{2}\\=\frac{-5}{2}-\frac{1}{1}-\frac{5}{2}\\=\frac{-5-1-5}{2}\\=\frac{-11}{2}\)
7. \(+\left(\frac{6}{-5}\right) +\left(\frac{-3}{9}\right) -\left(\frac{-6}{-3}\right)\\= \frac{-6}{5}- \frac{3}{9}-\frac{6}{3}\\=\frac{-6}{5}-\frac{1}{3}-\frac{2}{1}\\=\frac{-18}{15}-\frac{5}{15}-\frac{30}{15}\\=\frac{-18-5-30}{15}\\=\frac{-53}{15}\)
8. \(-\left(\frac{9}{-5}\right) -\left(\frac{-5}{-2}\right) +\left(\frac{11}{-9}\right)\\= \frac{9}{5}- \frac{5}{2}-\frac{11}{9}\\=\frac{162}{90}-\frac{225}{90}-\frac{110}{90}\\=\frac{162-225-110}{90}\\=\frac{-173}{90}\)
9. \(-\left(\frac{10}{7}\right) -\left(\frac{6}{5}\right) -\left(\frac{-4}{-10}\right)\\= \frac{-10}{7}- \frac{6}{5}-\frac{4}{10}\\=\frac{-10}{7}-\frac{6}{5}-\frac{2}{5}\\=\frac{-50}{35}-\frac{42}{35}-\frac{14}{35}\\=\frac{-50-42-14}{35}\\=\frac{-106}{35}\)
10. \(+\left(\frac{-7}{-2}\right) +\left(\frac{-9}{-2}\right) +\left(\frac{-10}{-4}\right)\\= \frac{7}{2}+ \frac{9}{2}+\frac{10}{4}\\=\frac{7}{2}+\frac{9}{2}+\frac{5}{2}\\=\frac{7+9+5}{2}\\=\frac{21}{2}\)
11. \(+\left(\frac{-5}{8}\right) +\left(\frac{-8}{-6}\right) +\left(\frac{-5}{-6}\right)\\= \frac{-5}{8}+ \frac{8}{6}+\frac{5}{6}\\=\frac{-5}{8}+\frac{4}{3}+\frac{5}{6}\\=\frac{-15}{24}+\frac{32}{24}+\frac{20}{24}\\=\frac{-15+32+20}{24}\\=\frac{37}{24}\)
12. \(-\left(\frac{2}{9}\right) -\left(\frac{-5}{4}\right) +\left(\frac{-9}{-7}\right)\\= \frac{-2}{9}+ \frac{5}{4}+\frac{9}{7}\\=\frac{-56}{252}+\frac{315}{252}+\frac{324}{252}\\=\frac{-56+315+324}{252}\\=\frac{583}{252}\)