Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{8}{-9}\right) -\left(\frac{10}{3}\right) +\left(\frac{3}{2}\right)\\= \frac{-8}{9}- \frac{10}{3}+\frac{3}{2}\\=\frac{-16}{18}-\frac{60}{18}+\frac{27}{18}\\=\frac{-16-60+27}{18}\\=\frac{-49}{18}\)
2. \(-\left(\frac{8}{-5}\right) -\left(\frac{-9}{-6}\right) -\left(\frac{2}{9}\right)\\= \frac{8}{5}- \frac{9}{6}-\frac{2}{9}\\=\frac{8}{5}-\frac{3}{2}-\frac{2}{9}\\=\frac{144}{90}-\frac{135}{90}-\frac{20}{90}\\=\frac{144-135-20}{90}\\=\frac{-11}{90}\)
3. \(-\left(\frac{-4}{9}\right) -\left(\frac{-4}{3}\right) +\left(\frac{9}{8}\right)\\= \frac{4}{9}+ \frac{4}{3}+\frac{9}{8}\\=\frac{32}{72}+\frac{96}{72}+\frac{81}{72}\\=\frac{32+96+81}{72}\\=\frac{209}{72}\)
4. \(+\left(\frac{-7}{8}\right) -\left(\frac{5}{3}\right) -\left(\frac{5}{-11}\right)\\= \frac{-7}{8}- \frac{5}{3}+\frac{5}{11}\\=\frac{-231}{264}-\frac{440}{264}+\frac{120}{264}\\=\frac{-231-440+120}{264}\\=\frac{-551}{264}\)
5. \(-\left(\frac{-9}{-10}\right) +\left(\frac{7}{8}\right) +\left(\frac{-10}{-5}\right)\\= \frac{-9}{10}+ \frac{7}{8}+\frac{10}{5}\\=\frac{-9}{10}+\frac{7}{8}+\frac{2}{1}\\=\frac{-36}{40}+\frac{35}{40}+\frac{80}{40}\\=\frac{-36+35+80}{40}\\=\frac{79}{40}\)
6. \(+\left(\frac{5}{9}\right) -\left(\frac{2}{-10}\right) +\left(\frac{8}{-9}\right)\\= \frac{5}{9}+ \frac{2}{10}-\frac{8}{9}\\=\frac{5}{9}+\frac{1}{5}-\frac{8}{9}\\=\frac{25}{45}+\frac{9}{45}-\frac{40}{45}\\=\frac{25+9-40}{45}\\=\frac{-6}{45}\\=\frac{-2}{15}\)
7. \(-\left(\frac{7}{4}\right) -\left(\frac{-5}{10}\right) +\left(\frac{-4}{-5}\right)\\= \frac{-7}{4}+ \frac{5}{10}+\frac{4}{5}\\=\frac{-7}{4}+\frac{1}{2}+\frac{4}{5}\\=\frac{-35}{20}+\frac{10}{20}+\frac{16}{20}\\=\frac{-35+10+16}{20}\\=\frac{-9}{20}\)
8. \(+\left(\frac{6}{7}\right) +\left(\frac{2}{5}\right) +\left(\frac{-8}{11}\right)\\= \frac{6}{7}+ \frac{2}{5}-\frac{8}{11}\\=\frac{330}{385}+\frac{154}{385}-\frac{280}{385}\\=\frac{330+154-280}{385}\\=\frac{204}{385}\)
9. \(-\left(\frac{-6}{5}\right) +\left(\frac{8}{-7}\right) +\left(\frac{-12}{-8}\right)\\= \frac{6}{5}- \frac{8}{7}+\frac{12}{8}\\=\frac{6}{5}-\frac{8}{7}+\frac{3}{2}\\=\frac{84}{70}-\frac{80}{70}+\frac{105}{70}\\=\frac{84-80+105}{70}\\=\frac{109}{70}\)
10. \(+\left(\frac{10}{3}\right) +\left(\frac{-4}{5}\right) +\left(\frac{8}{-5}\right)\\= \frac{10}{3}- \frac{4}{5}-\frac{8}{5}\\=\frac{50}{15}-\frac{12}{15}-\frac{24}{15}\\=\frac{50-12-24}{15}\\=\frac{14}{15}\)
11. \(-\left(\frac{9}{10}\right) -\left(\frac{-8}{-3}\right) +\left(\frac{-12}{-11}\right)\\= \frac{-9}{10}- \frac{8}{3}+\frac{12}{11}\\=\frac{-297}{330}-\frac{880}{330}+\frac{360}{330}\\=\frac{-297-880+360}{330}\\=\frac{-817}{330}\)
12. \(+\left(\frac{9}{10}\right) -\left(\frac{-9}{2}\right) -\left(\frac{5}{9}\right)\\= \frac{9}{10}+ \frac{9}{2}-\frac{5}{9}\\=\frac{81}{90}+\frac{405}{90}-\frac{50}{90}\\=\frac{81+405-50}{90}\\=\frac{436}{90}\\=\frac{218}{45}\)