Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{9}\right) -\left(\frac{4}{-8}\right) -\left(\frac{6}{-5}\right)\\= \frac{5}{9}+ \frac{4}{8}+\frac{6}{5}\\=\frac{5}{9}+\frac{1}{2}+\frac{6}{5}\\=\frac{50}{90}+\frac{45}{90}+\frac{108}{90}\\=\frac{50+45+108}{90}\\=\frac{203}{90}\)
2. \(-\left(\frac{6}{5}\right) -\left(\frac{2}{2}\right) -\left(\frac{-6}{-9}\right)\\= \frac{-6}{5}- \frac{2}{2}-\frac{6}{9}\\=\frac{-6}{5}-\frac{1}{1}-\frac{2}{3}\\=\frac{-18}{15}-\frac{15}{15}-\frac{10}{15}\\=\frac{-18-15-10}{15}\\=\frac{-43}{15}\)
3. \(+\left(\frac{9}{4}\right) -\left(\frac{3}{-9}\right) +\left(\frac{-2}{-8}\right)\\= \frac{9}{4}+ \frac{3}{9}+\frac{2}{8}\\=\frac{9}{4}+\frac{1}{3}+\frac{1}{4}\\=\frac{27}{12}+\frac{4}{12}+\frac{3}{12}\\=\frac{27+4+3}{12}\\=\frac{34}{12}\\=\frac{17}{6}\)
4. \(+\left(\frac{-5}{-6}\right) +\left(\frac{-5}{3}\right) +\left(\frac{6}{5}\right)\\= \frac{5}{6}- \frac{5}{3}+\frac{6}{5}\\=\frac{25}{30}-\frac{50}{30}+\frac{36}{30}\\=\frac{25-50+36}{30}\\=\frac{11}{30}\)
5. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-7}{6}\right) -\left(\frac{-6}{-5}\right)\\= \frac{-6}{5}+ \frac{7}{6}-\frac{6}{5}\\=\frac{-36}{30}+\frac{35}{30}-\frac{36}{30}\\=\frac{-36+35-36}{30}\\=\frac{-37}{30}\)
6. \(+\left(\frac{-2}{-7}\right) -\left(\frac{3}{-2}\right) +\left(\frac{-5}{-2}\right)\\= \frac{2}{7}+ \frac{3}{2}+\frac{5}{2}\\=\frac{4}{14}+\frac{21}{14}+\frac{35}{14}\\=\frac{4+21+35}{14}\\=\frac{60}{14}\\=\frac{30}{7}\)
7. \(+\left(\frac{7}{5}\right) -\left(\frac{-4}{8}\right) +\left(\frac{12}{-6}\right)\\= \frac{7}{5}+ \frac{4}{8}-\frac{12}{6}\\=\frac{7}{5}+\frac{1}{2}-\frac{2}{1}\\=\frac{14}{10}+\frac{5}{10}-\frac{20}{10}\\=\frac{14+5-20}{10}\\=\frac{-1}{10}\)
8. \(-\left(\frac{5}{9}\right) -\left(\frac{2}{2}\right) +\left(\frac{7}{-5}\right)\\= \frac{-5}{9}- \frac{2}{2}-\frac{7}{5}\\=\frac{-5}{9}-\frac{1}{1}-\frac{7}{5}\\=\frac{-25}{45}-\frac{45}{45}-\frac{63}{45}\\=\frac{-25-45-63}{45}\\=\frac{-133}{45}\)
9. \(+\left(\frac{-7}{8}\right) +\left(\frac{8}{4}\right) -\left(\frac{11}{6}\right)\\= \frac{-7}{8}+ \frac{8}{4}-\frac{11}{6}\\=\frac{-7}{8}+\frac{2}{1}-\frac{11}{6}\\=\frac{-21}{24}+\frac{48}{24}-\frac{44}{24}\\=\frac{-21+48-44}{24}\\=\frac{-17}{24}\)
10. \(+\left(\frac{-10}{3}\right) +\left(\frac{8}{9}\right) +\left(\frac{-9}{-8}\right)\\= \frac{-10}{3}+ \frac{8}{9}+\frac{9}{8}\\=\frac{-240}{72}+\frac{64}{72}+\frac{81}{72}\\=\frac{-240+64+81}{72}\\=\frac{-95}{72}\)
11. \(-\left(\frac{6}{5}\right) +\left(\frac{-3}{10}\right) -\left(\frac{6}{10}\right)\\= \frac{-6}{5}- \frac{3}{10}-\frac{6}{10}\\=\frac{-6}{5}-\frac{3}{10}-\frac{3}{5}\\=\frac{-12}{10}-\frac{3}{10}-\frac{6}{10}\\=\frac{-12-3-6}{10}\\=\frac{-21}{10}\)
12. \(-\left(\frac{4}{5}\right) -\left(\frac{9}{-7}\right) +\left(\frac{-6}{5}\right)\\= \frac{-4}{5}+ \frac{9}{7}-\frac{6}{5}\\=\frac{-28}{35}+\frac{45}{35}-\frac{42}{35}\\=\frac{-28+45-42}{35}\\=\frac{-25}{35}\\=\frac{-5}{7}\)