Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{-9}\right) -\left(\frac{-4}{9}\right) +\left(\frac{-4}{-5}\right)\\= \frac{8}{9}+ \frac{4}{9}+\frac{4}{5}\\=\frac{40}{45}+\frac{20}{45}+\frac{36}{45}\\=\frac{40+20+36}{45}\\=\frac{96}{45}\\=\frac{32}{15}\)
2. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-3}{-8}\right) -\left(\frac{-11}{10}\right)\\= \frac{-10}{7}+ \frac{3}{8}+\frac{11}{10}\\=\frac{-400}{280}+\frac{105}{280}+\frac{308}{280}\\=\frac{-400+105+308}{280}\\=\frac{13}{280}\)
3. \(+\left(\frac{-7}{9}\right) +\left(\frac{-4}{-2}\right) -\left(\frac{-3}{7}\right)\\= \frac{-7}{9}+ \frac{4}{2}+\frac{3}{7}\\=\frac{-7}{9}+\frac{2}{1}+\frac{3}{7}\\=\frac{-49}{63}+\frac{126}{63}+\frac{27}{63}\\=\frac{-49+126+27}{63}\\=\frac{104}{63}\)
4. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-6}{3}\right) -\left(\frac{-7}{8}\right)\\= \frac{-6}{5}+ \frac{6}{3}+\frac{7}{8}\\=\frac{-6}{5}+\frac{2}{1}+\frac{7}{8}\\=\frac{-48}{40}+\frac{80}{40}+\frac{35}{40}\\=\frac{-48+80+35}{40}\\=\frac{67}{40}\)
5. \(+\left(\frac{-10}{-7}\right) -\left(\frac{-8}{-6}\right) -\left(\frac{-8}{6}\right)\\= \frac{10}{7}- \frac{8}{6}+\frac{8}{6}\\=\frac{10}{7}-\frac{4}{3}+\frac{4}{3}\\=\frac{30}{21}-\frac{28}{21}+\frac{28}{21}\\=\frac{30-28+28}{21}\\=\frac{30}{21}\\=\frac{10}{7}\)
6. \(+\left(\frac{-2}{-7}\right) -\left(\frac{3}{-9}\right) -\left(\frac{-6}{2}\right)\\= \frac{2}{7}+ \frac{3}{9}+\frac{6}{2}\\=\frac{2}{7}+\frac{1}{3}+\frac{3}{1}\\=\frac{6}{21}+\frac{7}{21}+\frac{63}{21}\\=\frac{6+7+63}{21}\\=\frac{76}{21}\)
7. \(+\left(\frac{-5}{8}\right) -\left(\frac{-6}{-7}\right) +\left(\frac{-5}{-5}\right)\\= \frac{-5}{8}- \frac{6}{7}+\frac{5}{5}\\=\frac{-5}{8}-\frac{6}{7}+\frac{1}{1}\\=\frac{-35}{56}-\frac{48}{56}+\frac{56}{56}\\=\frac{-35-48+56}{56}\\=\frac{-27}{56}\)
8. \(+\left(\frac{2}{-7}\right) -\left(\frac{-10}{8}\right) +\left(\frac{12}{11}\right)\\= \frac{-2}{7}+ \frac{10}{8}+\frac{12}{11}\\=\frac{-2}{7}+\frac{5}{4}+\frac{12}{11}\\=\frac{-88}{308}+\frac{385}{308}+\frac{336}{308}\\=\frac{-88+385+336}{308}\\=\frac{633}{308}\)
9. \(-\left(\frac{3}{-2}\right) -\left(\frac{8}{-2}\right) -\left(\frac{2}{8}\right)\\= \frac{3}{2}+ \frac{8}{2}-\frac{2}{8}\\=\frac{3}{2}+\frac{4}{1}-\frac{1}{4}\\=\frac{6}{4}+\frac{16}{4}-\frac{1}{4}\\=\frac{6+16-1}{4}\\=\frac{21}{4}\)
10. \(-\left(\frac{-8}{3}\right) -\left(\frac{-9}{-5}\right) +\left(\frac{6}{-2}\right)\\= \frac{8}{3}- \frac{9}{5}-\frac{6}{2}\\=\frac{8}{3}-\frac{9}{5}-\frac{3}{1}\\=\frac{40}{15}-\frac{27}{15}-\frac{45}{15}\\=\frac{40-27-45}{15}\\=\frac{-32}{15}\)
11. \(-\left(\frac{9}{5}\right) -\left(\frac{-5}{-7}\right) -\left(\frac{-8}{12}\right)\\= \frac{-9}{5}- \frac{5}{7}+\frac{8}{12}\\=\frac{-9}{5}-\frac{5}{7}+\frac{2}{3}\\=\frac{-189}{105}-\frac{75}{105}+\frac{70}{105}\\=\frac{-189-75+70}{105}\\=\frac{-194}{105}\)
12. \(+\left(\frac{4}{-9}\right) -\left(\frac{-2}{-8}\right) +\left(\frac{10}{2}\right)\\= \frac{-4}{9}- \frac{2}{8}+\frac{10}{2}\\=\frac{-4}{9}-\frac{1}{4}+\frac{5}{1}\\=\frac{-16}{36}-\frac{9}{36}+\frac{180}{36}\\=\frac{-16-9+180}{36}\\=\frac{155}{36}\)