Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{10}{-3}\right) -\left(\frac{6}{-8}\right) +\left(\frac{-12}{-6}\right)\\= \frac{-10}{3}+ \frac{6}{8}+\frac{12}{6}\\=\frac{-10}{3}+\frac{3}{4}+\frac{2}{1}\\=\frac{-40}{12}+\frac{9}{12}+\frac{24}{12}\\=\frac{-40+9+24}{12}\\=\frac{-7}{12}\)
2. \(-\left(\frac{2}{9}\right) -\left(\frac{9}{-8}\right) +\left(\frac{6}{-6}\right)\\= \frac{-2}{9}+ \frac{9}{8}-\frac{6}{6}\\=\frac{-2}{9}+\frac{9}{8}-\frac{1}{1}\\=\frac{-16}{72}+\frac{81}{72}-\frac{72}{72}\\=\frac{-16+81-72}{72}\\=\frac{-7}{72}\)
3. \(-\left(\frac{-8}{3}\right) +\left(\frac{-5}{10}\right) +\left(\frac{11}{-11}\right)\\= \frac{8}{3}- \frac{5}{10}-\frac{11}{11}\\=\frac{8}{3}-\frac{1}{2}-\frac{1}{1}\\=\frac{16}{6}-\frac{3}{6}-\frac{6}{6}\\=\frac{16-3-6}{6}\\=\frac{7}{6}\)
4. \(-\left(\frac{-2}{3}\right) +\left(\frac{9}{3}\right) -\left(\frac{11}{3}\right)\\= \frac{2}{3}+ \frac{9}{3}-\frac{11}{3}\\=\frac{2}{3}+\frac{3}{1}-\frac{11}{3}\\=\frac{2+3-11}{3}\\=\frac{-6}{3}\\=\frac{-2}{1}\)
5. \(+\left(\frac{-4}{-9}\right) -\left(\frac{-9}{6}\right) -\left(\frac{-8}{-5}\right)\\= \frac{4}{9}+ \frac{9}{6}-\frac{8}{5}\\=\frac{4}{9}+\frac{3}{2}-\frac{8}{5}\\=\frac{40}{90}+\frac{135}{90}-\frac{144}{90}\\=\frac{40+135-144}{90}\\=\frac{31}{90}\)
6. \(+\left(\frac{9}{-5}\right) +\left(\frac{-2}{3}\right) +\left(\frac{-12}{12}\right)\\= \frac{-9}{5}- \frac{2}{3}-\frac{12}{12}\\=\frac{-9}{5}-\frac{2}{3}-\frac{1}{1}\\=\frac{-27}{15}-\frac{10}{15}-\frac{15}{15}\\=\frac{-27-10-15}{15}\\=\frac{-52}{15}\)
7. \(+\left(\frac{8}{3}\right) -\left(\frac{9}{4}\right) -\left(\frac{10}{-4}\right)\\= \frac{8}{3}- \frac{9}{4}+\frac{10}{4}\\=\frac{8}{3}-\frac{9}{4}+\frac{5}{2}\\=\frac{32}{12}-\frac{27}{12}+\frac{30}{12}\\=\frac{32-27+30}{12}\\=\frac{35}{12}\)
8. \(-\left(\frac{-3}{8}\right) +\left(\frac{9}{-10}\right) +\left(\frac{11}{7}\right)\\= \frac{3}{8}- \frac{9}{10}+\frac{11}{7}\\=\frac{105}{280}-\frac{252}{280}+\frac{440}{280}\\=\frac{105-252+440}{280}\\=\frac{293}{280}\)
9. \(+\left(\frac{-7}{-8}\right) -\left(\frac{5}{7}\right) +\left(\frac{12}{2}\right)\\= \frac{7}{8}- \frac{5}{7}+\frac{12}{2}\\=\frac{7}{8}-\frac{5}{7}+\frac{6}{1}\\=\frac{49}{56}-\frac{40}{56}+\frac{336}{56}\\=\frac{49-40+336}{56}\\=\frac{345}{56}\)
10. \(+\left(\frac{5}{-4}\right) -\left(\frac{5}{10}\right) +\left(\frac{6}{11}\right)\\= \frac{-5}{4}- \frac{5}{10}+\frac{6}{11}\\=\frac{-5}{4}-\frac{1}{2}+\frac{6}{11}\\=\frac{-55}{44}-\frac{22}{44}+\frac{24}{44}\\=\frac{-55-22+24}{44}\\=\frac{-53}{44}\)
11. \(+\left(\frac{-5}{4}\right) -\left(\frac{10}{8}\right) -\left(\frac{-4}{10}\right)\\= \frac{-5}{4}- \frac{10}{8}+\frac{4}{10}\\=\frac{-5}{4}-\frac{5}{4}+\frac{2}{5}\\=\frac{-25}{20}-\frac{25}{20}+\frac{8}{20}\\=\frac{-25-25+8}{20}\\=\frac{-42}{20}\\=\frac{-21}{10}\)
12. \(-\left(\frac{4}{-7}\right) -\left(\frac{9}{-4}\right) -\left(\frac{3}{7}\right)\\= \frac{4}{7}+ \frac{9}{4}-\frac{3}{7}\\=\frac{16}{28}+\frac{63}{28}-\frac{12}{28}\\=\frac{16+63-12}{28}\\=\frac{67}{28}\)