Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{-7}\right) -\left(\frac{4}{2}\right) +\left(\frac{-11}{4}\right)\\= \frac{10}{7}- \frac{4}{2}-\frac{11}{4}\\=\frac{10}{7}-\frac{2}{1}-\frac{11}{4}\\=\frac{40}{28}-\frac{56}{28}-\frac{77}{28}\\=\frac{40-56-77}{28}\\=\frac{-93}{28}\)
2. \(+\left(\frac{10}{-7}\right) -\left(\frac{10}{9}\right) -\left(\frac{-7}{5}\right)\\= \frac{-10}{7}- \frac{10}{9}+\frac{7}{5}\\=\frac{-450}{315}-\frac{350}{315}+\frac{441}{315}\\=\frac{-450-350+441}{315}\\=\frac{-359}{315}\)
3. \(-\left(\frac{2}{9}\right) -\left(\frac{5}{4}\right) -\left(\frac{-12}{11}\right)\\= \frac{-2}{9}- \frac{5}{4}+\frac{12}{11}\\=\frac{-88}{396}-\frac{495}{396}+\frac{432}{396}\\=\frac{-88-495+432}{396}\\=\frac{-151}{396}\)
4. \(-\left(\frac{-8}{-3}\right) +\left(\frac{-10}{-6}\right) -\left(\frac{-6}{10}\right)\\= \frac{-8}{3}+ \frac{10}{6}+\frac{6}{10}\\=\frac{-8}{3}+\frac{5}{3}+\frac{3}{5}\\=\frac{-40}{15}+\frac{25}{15}+\frac{9}{15}\\=\frac{-40+25+9}{15}\\=\frac{-6}{15}\\=\frac{-2}{5}\)
5. \(+\left(\frac{-3}{4}\right) +\left(\frac{-4}{6}\right) +\left(\frac{5}{12}\right)\\= \frac{-3}{4}- \frac{4}{6}+\frac{5}{12}\\=\frac{-3}{4}-\frac{2}{3}+\frac{5}{12}\\=\frac{-9}{12}-\frac{8}{12}+\frac{5}{12}\\=\frac{-9-8+5}{12}\\=\frac{-12}{12}\\=\frac{-1}{1}\)
6. \(+\left(\frac{2}{-7}\right) -\left(\frac{10}{6}\right) +\left(\frac{-7}{-8}\right)\\= \frac{-2}{7}- \frac{10}{6}+\frac{7}{8}\\=\frac{-2}{7}-\frac{5}{3}+\frac{7}{8}\\=\frac{-48}{168}-\frac{280}{168}+\frac{147}{168}\\=\frac{-48-280+147}{168}\\=\frac{-181}{168}\)
7. \(+\left(\frac{7}{-9}\right) -\left(\frac{8}{10}\right) -\left(\frac{-10}{-9}\right)\\= \frac{-7}{9}- \frac{8}{10}-\frac{10}{9}\\=\frac{-7}{9}-\frac{4}{5}-\frac{10}{9}\\=\frac{-35}{45}-\frac{36}{45}-\frac{50}{45}\\=\frac{-35-36-50}{45}\\=\frac{-121}{45}\)
8. \(-\left(\frac{8}{-7}\right) -\left(\frac{7}{9}\right) +\left(\frac{8}{10}\right)\\= \frac{8}{7}- \frac{7}{9}+\frac{8}{10}\\=\frac{8}{7}-\frac{7}{9}+\frac{4}{5}\\=\frac{360}{315}-\frac{245}{315}+\frac{252}{315}\\=\frac{360-245+252}{315}\\=\frac{367}{315}\)
9. \(+\left(\frac{3}{-7}\right) -\left(\frac{2}{-7}\right) -\left(\frac{-12}{-11}\right)\\= \frac{-3}{7}+ \frac{2}{7}-\frac{12}{11}\\=\frac{-33}{77}+\frac{22}{77}-\frac{84}{77}\\=\frac{-33+22-84}{77}\\=\frac{-95}{77}\)
10. \(-\left(\frac{3}{-4}\right) +\left(\frac{10}{8}\right) +\left(\frac{4}{-8}\right)\\= \frac{3}{4}+ \frac{10}{8}-\frac{4}{8}\\=\frac{3}{4}+\frac{5}{4}-\frac{1}{2}\\=\frac{3+5-1}{4}\\=\frac{7}{4}\)
11. \(+\left(\frac{-4}{-9}\right) -\left(\frac{5}{-4}\right) -\left(\frac{-3}{4}\right)\\= \frac{4}{9}+ \frac{5}{4}+\frac{3}{4}\\=\frac{16}{36}+\frac{45}{36}+\frac{27}{36}\\=\frac{16+45+27}{36}\\=\frac{88}{36}\\=\frac{22}{9}\)
12. \(-\left(\frac{9}{-8}\right) -\left(\frac{6}{-3}\right) -\left(\frac{-3}{-9}\right)\\= \frac{9}{8}+ \frac{6}{3}-\frac{3}{9}\\=\frac{9}{8}+\frac{2}{1}-\frac{1}{3}\\=\frac{27}{24}+\frac{48}{24}-\frac{8}{24}\\=\frac{27+48-8}{24}\\=\frac{67}{24}\)