Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{9}\right) -\left(\frac{8}{-3}\right) -\left(\frac{8}{-12}\right)\\= \frac{10}{9}+ \frac{8}{3}+\frac{8}{12}\\=\frac{10}{9}+\frac{8}{3}+\frac{2}{3}\\=\frac{10+8+2}{9}\\=\frac{20}{9}\)
2. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-10}{-6}\right) +\left(\frac{-4}{4}\right)\\= \frac{-6}{5}- \frac{10}{6}-\frac{4}{4}\\=\frac{-6}{5}-\frac{5}{3}-\frac{1}{1}\\=\frac{-18}{15}-\frac{25}{15}-\frac{15}{15}\\=\frac{-18-25-15}{15}\\=\frac{-58}{15}\)
3. \(-\left(\frac{5}{-8}\right) +\left(\frac{4}{6}\right) -\left(\frac{6}{5}\right)\\= \frac{5}{8}+ \frac{4}{6}-\frac{6}{5}\\=\frac{5}{8}+\frac{2}{3}-\frac{6}{5}\\=\frac{75}{120}+\frac{80}{120}-\frac{144}{120}\\=\frac{75+80-144}{120}\\=\frac{11}{120}\)
4. \(-\left(\frac{5}{3}\right) +\left(\frac{3}{-5}\right) +\left(\frac{6}{-5}\right)\\= \frac{-5}{3}- \frac{3}{5}-\frac{6}{5}\\=\frac{-25}{15}-\frac{9}{15}-\frac{18}{15}\\=\frac{-25-9-18}{15}\\=\frac{-52}{15}\)
5. \(+\left(\frac{-9}{2}\right) -\left(\frac{-6}{10}\right) -\left(\frac{9}{-4}\right)\\= \frac{-9}{2}+ \frac{6}{10}+\frac{9}{4}\\=\frac{-9}{2}+\frac{3}{5}+\frac{9}{4}\\=\frac{-90}{20}+\frac{12}{20}+\frac{45}{20}\\=\frac{-90+12+45}{20}\\=\frac{-33}{20}\)
6. \(-\left(\frac{7}{-5}\right) +\left(\frac{-7}{-8}\right) -\left(\frac{5}{-10}\right)\\= \frac{7}{5}+ \frac{7}{8}+\frac{5}{10}\\=\frac{7}{5}+\frac{7}{8}+\frac{1}{2}\\=\frac{56}{40}+\frac{35}{40}+\frac{20}{40}\\=\frac{56+35+20}{40}\\=\frac{111}{40}\)
7. \(+\left(\frac{-8}{-9}\right) -\left(\frac{-6}{6}\right) -\left(\frac{7}{-11}\right)\\= \frac{8}{9}+ \frac{6}{6}+\frac{7}{11}\\=\frac{8}{9}+\frac{1}{1}+\frac{7}{11}\\=\frac{88}{99}+\frac{99}{99}+\frac{63}{99}\\=\frac{88+99+63}{99}\\=\frac{250}{99}\)
8. \(+\left(\frac{9}{4}\right) -\left(\frac{2}{7}\right) -\left(\frac{-5}{4}\right)\\= \frac{9}{4}- \frac{2}{7}+\frac{5}{4}\\=\frac{63}{28}-\frac{8}{28}+\frac{35}{28}\\=\frac{63-8+35}{28}\\=\frac{90}{28}\\=\frac{45}{14}\)
9. \(+\left(\frac{9}{-4}\right) +\left(\frac{-9}{3}\right) -\left(\frac{4}{3}\right)\\= \frac{-9}{4}- \frac{9}{3}-\frac{4}{3}\\=\frac{-9}{4}-\frac{3}{1}-\frac{4}{3}\\=\frac{-27}{12}-\frac{36}{12}-\frac{16}{12}\\=\frac{-27-36-16}{12}\\=\frac{-79}{12}\)
10. \(+\left(\frac{6}{7}\right) +\left(\frac{-2}{10}\right) -\left(\frac{-8}{2}\right)\\= \frac{6}{7}- \frac{2}{10}+\frac{8}{2}\\=\frac{6}{7}-\frac{1}{5}+\frac{4}{1}\\=\frac{30}{35}-\frac{7}{35}+\frac{140}{35}\\=\frac{30-7+140}{35}\\=\frac{163}{35}\)
11. \(-\left(\frac{5}{3}\right) +\left(\frac{8}{10}\right) +\left(\frac{9}{-3}\right)\\= \frac{-5}{3}+ \frac{8}{10}-\frac{9}{3}\\=\frac{-5}{3}+\frac{4}{5}-\frac{3}{1}\\=\frac{-25}{15}+\frac{12}{15}-\frac{45}{15}\\=\frac{-25+12-45}{15}\\=\frac{-58}{15}\)
12. \(-\left(\frac{-2}{3}\right) -\left(\frac{-10}{8}\right) -\left(\frac{8}{6}\right)\\= \frac{2}{3}+ \frac{10}{8}-\frac{8}{6}\\=\frac{2}{3}+\frac{5}{4}-\frac{4}{3}\\=\frac{8}{12}+\frac{15}{12}-\frac{16}{12}\\=\frac{8+15-16}{12}\\=\frac{7}{12}\)