Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{4}\right) +\left(\frac{-7}{10}\right) +\left(\frac{5}{-11}\right)\\= \frac{9}{4}- \frac{7}{10}-\frac{5}{11}\\=\frac{495}{220}-\frac{154}{220}-\frac{100}{220}\\=\frac{495-154-100}{220}\\=\frac{241}{220}\)
2. \(+\left(\frac{-5}{8}\right) -\left(\frac{4}{-5}\right) -\left(\frac{10}{-5}\right)\\= \frac{-5}{8}+ \frac{4}{5}+\frac{10}{5}\\=\frac{-5}{8}+\frac{4}{5}+\frac{2}{1}\\=\frac{-25}{40}+\frac{32}{40}+\frac{80}{40}\\=\frac{-25+32+80}{40}\\=\frac{87}{40}\)
3. \(+\left(\frac{2}{-5}\right) +\left(\frac{-5}{9}\right) +\left(\frac{-9}{7}\right)\\= \frac{-2}{5}- \frac{5}{9}-\frac{9}{7}\\=\frac{-126}{315}-\frac{175}{315}-\frac{405}{315}\\=\frac{-126-175-405}{315}\\=\frac{-706}{315}\)
4. \(+\left(\frac{4}{9}\right) -\left(\frac{9}{-8}\right) +\left(\frac{8}{10}\right)\\= \frac{4}{9}+ \frac{9}{8}+\frac{8}{10}\\=\frac{4}{9}+\frac{9}{8}+\frac{4}{5}\\=\frac{160}{360}+\frac{405}{360}+\frac{288}{360}\\=\frac{160+405+288}{360}\\=\frac{853}{360}\)
5. \(-\left(\frac{5}{-4}\right) +\left(\frac{-4}{-9}\right) +\left(\frac{-2}{-2}\right)\\= \frac{5}{4}+ \frac{4}{9}+\frac{2}{2}\\=\frac{5}{4}+\frac{4}{9}+\frac{1}{1}\\=\frac{45}{36}+\frac{16}{36}+\frac{36}{36}\\=\frac{45+16+36}{36}\\=\frac{97}{36}\)
6. \(-\left(\frac{-9}{2}\right) +\left(\frac{-10}{2}\right) +\left(\frac{-2}{-8}\right)\\= \frac{9}{2}- \frac{10}{2}+\frac{2}{8}\\=\frac{9}{2}-\frac{5}{1}+\frac{1}{4}\\=\frac{18}{4}-\frac{20}{4}+\frac{1}{4}\\=\frac{18-20+1}{4}\\=\frac{-1}{4}\)
7. \(-\left(\frac{10}{-3}\right) +\left(\frac{8}{-5}\right) -\left(\frac{9}{6}\right)\\= \frac{10}{3}- \frac{8}{5}-\frac{9}{6}\\=\frac{10}{3}-\frac{8}{5}-\frac{3}{2}\\=\frac{100}{30}-\frac{48}{30}-\frac{45}{30}\\=\frac{100-48-45}{30}\\=\frac{7}{30}\)
8. \(-\left(\frac{2}{7}\right) +\left(\frac{-8}{3}\right) +\left(\frac{8}{-4}\right)\\= \frac{-2}{7}- \frac{8}{3}-\frac{8}{4}\\=\frac{-2}{7}-\frac{8}{3}-\frac{2}{1}\\=\frac{-6}{21}-\frac{56}{21}-\frac{42}{21}\\=\frac{-6-56-42}{21}\\=\frac{-104}{21}\)
9. \(-\left(\frac{2}{-7}\right) -\left(\frac{7}{10}\right) -\left(\frac{4}{9}\right)\\= \frac{2}{7}- \frac{7}{10}-\frac{4}{9}\\=\frac{180}{630}-\frac{441}{630}-\frac{280}{630}\\=\frac{180-441-280}{630}\\=\frac{-541}{630}\)
10. \(-\left(\frac{-8}{-7}\right) -\left(\frac{-3}{-2}\right) -\left(\frac{-8}{-12}\right)\\= \frac{-8}{7}- \frac{3}{2}-\frac{8}{12}\\=\frac{-8}{7}-\frac{3}{2}-\frac{2}{3}\\=\frac{-48}{42}-\frac{63}{42}-\frac{28}{42}\\=\frac{-48-63-28}{42}\\=\frac{-139}{42}\)
11. \(-\left(\frac{7}{-8}\right) +\left(\frac{-8}{-10}\right) -\left(\frac{3}{4}\right)\\= \frac{7}{8}+ \frac{8}{10}-\frac{3}{4}\\=\frac{7}{8}+\frac{4}{5}-\frac{3}{4}\\=\frac{35}{40}+\frac{32}{40}-\frac{30}{40}\\=\frac{35+32-30}{40}\\=\frac{37}{40}\)
12. \(+\left(\frac{4}{-3}\right) -\left(\frac{8}{8}\right) -\left(\frac{-9}{-10}\right)\\= \frac{-4}{3}- \frac{8}{8}-\frac{9}{10}\\=\frac{-4}{3}-\frac{1}{1}-\frac{9}{10}\\=\frac{-40}{30}-\frac{30}{30}-\frac{27}{30}\\=\frac{-40-30-27}{30}\\=\frac{-97}{30}\)