Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{-7}\right) +\left(\frac{-9}{-4}\right) -\left(\frac{2}{11}\right)\\= \frac{8}{7}+ \frac{9}{4}-\frac{2}{11}\\=\frac{352}{308}+\frac{693}{308}-\frac{56}{308}\\=\frac{352+693-56}{308}\\=\frac{989}{308}\)
2. \(+\left(\frac{-8}{3}\right) +\left(\frac{-3}{10}\right) +\left(\frac{-7}{-11}\right)\\= \frac{-8}{3}- \frac{3}{10}+\frac{7}{11}\\=\frac{-880}{330}-\frac{99}{330}+\frac{210}{330}\\=\frac{-880-99+210}{330}\\=\frac{-769}{330}\)
3. \(+\left(\frac{3}{-4}\right) +\left(\frac{-4}{8}\right) +\left(\frac{-12}{4}\right)\\= \frac{-3}{4}- \frac{4}{8}-\frac{12}{4}\\=\frac{-3}{4}-\frac{1}{2}-\frac{3}{1}\\=\frac{-3-1-3}{4}\\=\frac{-7}{4}\)
4. \(-\left(\frac{6}{-5}\right) +\left(\frac{-6}{4}\right) -\left(\frac{-4}{-3}\right)\\= \frac{6}{5}- \frac{6}{4}-\frac{4}{3}\\=\frac{6}{5}-\frac{3}{2}-\frac{4}{3}\\=\frac{36}{30}-\frac{45}{30}-\frac{40}{30}\\=\frac{36-45-40}{30}\\=\frac{-49}{30}\)
5. \(+\left(\frac{4}{5}\right) -\left(\frac{-7}{9}\right) -\left(\frac{5}{-5}\right)\\= \frac{4}{5}+ \frac{7}{9}+\frac{5}{5}\\=\frac{4}{5}+\frac{7}{9}+\frac{1}{1}\\=\frac{36}{45}+\frac{35}{45}+\frac{45}{45}\\=\frac{36+35+45}{45}\\=\frac{116}{45}\)
6. \(+\left(\frac{-6}{-5}\right) -\left(\frac{8}{-5}\right) +\left(\frac{-9}{-7}\right)\\= \frac{6}{5}+ \frac{8}{5}+\frac{9}{7}\\=\frac{42}{35}+\frac{56}{35}+\frac{45}{35}\\=\frac{42+56+45}{35}\\=\frac{143}{35}\)
7. \(+\left(\frac{4}{3}\right) -\left(\frac{9}{-3}\right) -\left(\frac{-11}{-3}\right)\\= \frac{4}{3}+ \frac{9}{3}-\frac{11}{3}\\=\frac{4}{3}+\frac{3}{1}-\frac{11}{3}\\=\frac{4+3-11}{3}\\=\frac{-4}{3}\)
8. \(-\left(\frac{-5}{-9}\right) -\left(\frac{-9}{-5}\right) -\left(\frac{11}{-3}\right)\\= \frac{-5}{9}- \frac{9}{5}+\frac{11}{3}\\=\frac{-25}{45}-\frac{81}{45}+\frac{165}{45}\\=\frac{-25-81+165}{45}\\=\frac{59}{45}\)
9. \(-\left(\frac{-10}{3}\right) +\left(\frac{-5}{9}\right) +\left(\frac{-8}{6}\right)\\= \frac{10}{3}- \frac{5}{9}-\frac{8}{6}\\=\frac{10}{3}-\frac{5}{9}-\frac{4}{3}\\=\frac{30}{9}-\frac{5}{9}-\frac{12}{9}\\=\frac{30-5-12}{9}\\=\frac{13}{9}\)
10. \(+\left(\frac{-10}{-9}\right) -\left(\frac{-9}{-5}\right) +\left(\frac{-8}{6}\right)\\= \frac{10}{9}- \frac{9}{5}-\frac{8}{6}\\=\frac{10}{9}-\frac{9}{5}-\frac{4}{3}\\=\frac{50}{45}-\frac{81}{45}-\frac{60}{45}\\=\frac{50-81-60}{45}\\=\frac{-91}{45}\)
11. \(+\left(\frac{-4}{-5}\right) -\left(\frac{-6}{-2}\right) -\left(\frac{-4}{2}\right)\\= \frac{4}{5}- \frac{6}{2}+\frac{4}{2}\\=\frac{4}{5}-\frac{3}{1}+\frac{2}{1}\\=\frac{4-3+2}{5}\\=\frac{3}{5}\)
12. \(+\left(\frac{-10}{-3}\right) +\left(\frac{-9}{-9}\right) +\left(\frac{5}{-4}\right)\\= \frac{10}{3}+ \frac{9}{9}-\frac{5}{4}\\=\frac{10}{3}+\frac{1}{1}-\frac{5}{4}\\=\frac{40}{12}+\frac{12}{12}-\frac{15}{12}\\=\frac{40+12-15}{12}\\=\frac{37}{12}\)