Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{9}\right) -\left(\frac{-3}{10}\right) +\left(\frac{-3}{-7}\right)\\= \frac{4}{9}+ \frac{3}{10}+\frac{3}{7}\\=\frac{280}{630}+\frac{189}{630}+\frac{270}{630}\\=\frac{280+189+270}{630}\\=\frac{739}{630}\)
2. \(-\left(\frac{2}{-9}\right) +\left(\frac{5}{-3}\right) -\left(\frac{9}{12}\right)\\= \frac{2}{9}- \frac{5}{3}-\frac{9}{12}\\=\frac{2}{9}-\frac{5}{3}-\frac{3}{4}\\=\frac{8}{36}-\frac{60}{36}-\frac{27}{36}\\=\frac{8-60-27}{36}\\=\frac{-79}{36}\)
3. \(-\left(\frac{6}{-5}\right) +\left(\frac{9}{9}\right) +\left(\frac{7}{-9}\right)\\= \frac{6}{5}+ \frac{9}{9}-\frac{7}{9}\\=\frac{6}{5}+\frac{1}{1}-\frac{7}{9}\\=\frac{54}{45}+\frac{45}{45}-\frac{35}{45}\\=\frac{54+45-35}{45}\\=\frac{64}{45}\)
4. \(-\left(\frac{3}{8}\right) +\left(\frac{-3}{5}\right) +\left(\frac{6}{3}\right)\\= \frac{-3}{8}- \frac{3}{5}+\frac{6}{3}\\=\frac{-3}{8}-\frac{3}{5}+\frac{2}{1}\\=\frac{-15}{40}-\frac{24}{40}+\frac{80}{40}\\=\frac{-15-24+80}{40}\\=\frac{41}{40}\)
5. \(+\left(\frac{9}{-4}\right) +\left(\frac{9}{9}\right) -\left(\frac{-12}{4}\right)\\= \frac{-9}{4}+ \frac{9}{9}+\frac{12}{4}\\=\frac{-9}{4}+\frac{1}{1}+\frac{3}{1}\\=\frac{-9+1+3}{4}\\=\frac{-5}{4}\)
6. \(-\left(\frac{2}{-3}\right) -\left(\frac{-5}{-4}\right) +\left(\frac{7}{-8}\right)\\= \frac{2}{3}- \frac{5}{4}-\frac{7}{8}\\=\frac{16}{24}-\frac{30}{24}-\frac{21}{24}\\=\frac{16-30-21}{24}\\=\frac{-35}{24}\)
7. \(-\left(\frac{10}{7}\right) -\left(\frac{-2}{9}\right) -\left(\frac{3}{-7}\right)\\= \frac{-10}{7}+ \frac{2}{9}+\frac{3}{7}\\=\frac{-90}{63}+\frac{14}{63}+\frac{27}{63}\\=\frac{-90+14+27}{63}\\=\frac{-49}{63}\\=\frac{-7}{9}\)
8. \(+\left(\frac{-8}{-3}\right) -\left(\frac{-9}{10}\right) +\left(\frac{8}{10}\right)\\= \frac{8}{3}+ \frac{9}{10}+\frac{8}{10}\\=\frac{8}{3}+\frac{9}{10}+\frac{4}{5}\\=\frac{80}{30}+\frac{27}{30}+\frac{24}{30}\\=\frac{80+27+24}{30}\\=\frac{131}{30}\)
9. \(-\left(\frac{8}{5}\right) -\left(\frac{-10}{6}\right) +\left(\frac{12}{-9}\right)\\= \frac{-8}{5}+ \frac{10}{6}-\frac{12}{9}\\=\frac{-8}{5}+\frac{5}{3}-\frac{4}{3}\\=\frac{-24}{15}+\frac{25}{15}-\frac{20}{15}\\=\frac{-24+25-20}{15}\\=\frac{-19}{15}\)
10. \(+\left(\frac{9}{4}\right) -\left(\frac{4}{10}\right) +\left(\frac{-3}{-8}\right)\\= \frac{9}{4}- \frac{4}{10}+\frac{3}{8}\\=\frac{9}{4}-\frac{2}{5}+\frac{3}{8}\\=\frac{90}{40}-\frac{16}{40}+\frac{15}{40}\\=\frac{90-16+15}{40}\\=\frac{89}{40}\)
11. \(+\left(\frac{5}{3}\right) -\left(\frac{-8}{-8}\right) +\left(\frac{12}{7}\right)\\= \frac{5}{3}- \frac{8}{8}+\frac{12}{7}\\=\frac{5}{3}-\frac{1}{1}+\frac{12}{7}\\=\frac{35}{21}-\frac{21}{21}+\frac{36}{21}\\=\frac{35-21+36}{21}\\=\frac{50}{21}\)
12. \(-\left(\frac{-9}{4}\right) +\left(\frac{10}{5}\right) -\left(\frac{12}{-3}\right)\\= \frac{9}{4}+ \frac{10}{5}+\frac{12}{3}\\=\frac{9}{4}+\frac{2}{1}+\frac{4}{1}\\=\frac{9+2+4}{4}\\=\frac{15}{4}\)