Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{6}{-5}\right) +\left(\frac{-8}{10}\right) +\left(\frac{-7}{-10}\right)\\= \frac{6}{5}- \frac{8}{10}+\frac{7}{10}\\=\frac{6}{5}-\frac{4}{5}+\frac{7}{10}\\=\frac{12}{10}-\frac{8}{10}+\frac{7}{10}\\=\frac{12-8+7}{10}\\=\frac{11}{10}\)
2. \(+\left(\frac{9}{-2}\right) +\left(\frac{8}{-3}\right) +\left(\frac{4}{-11}\right)\\= \frac{-9}{2}- \frac{8}{3}-\frac{4}{11}\\=\frac{-297}{66}-\frac{176}{66}-\frac{24}{66}\\=\frac{-297-176-24}{66}\\=\frac{-497}{66}\)
3. \(+\left(\frac{3}{-2}\right) -\left(\frac{2}{4}\right) +\left(\frac{-10}{-6}\right)\\= \frac{-3}{2}- \frac{2}{4}+\frac{10}{6}\\=\frac{-3}{2}-\frac{1}{2}+\frac{5}{3}\\=\frac{-9}{6}-\frac{3}{6}+\frac{10}{6}\\=\frac{-9-3+10}{6}\\=\frac{-2}{6}\\=\frac{-1}{3}\)
4. \(+\left(\frac{4}{3}\right) -\left(\frac{5}{-4}\right) +\left(\frac{-7}{2}\right)\\= \frac{4}{3}+ \frac{5}{4}-\frac{7}{2}\\=\frac{16}{12}+\frac{15}{12}-\frac{42}{12}\\=\frac{16+15-42}{12}\\=\frac{-11}{12}\)
5. \(-\left(\frac{-2}{-5}\right) -\left(\frac{-7}{10}\right) +\left(\frac{-2}{9}\right)\\= \frac{-2}{5}+ \frac{7}{10}-\frac{2}{9}\\=\frac{-36}{90}+\frac{63}{90}-\frac{20}{90}\\=\frac{-36+63-20}{90}\\=\frac{7}{90}\)
6. \(-\left(\frac{-4}{-9}\right) -\left(\frac{8}{7}\right) +\left(\frac{-11}{2}\right)\\= \frac{-4}{9}- \frac{8}{7}-\frac{11}{2}\\=\frac{-56}{126}-\frac{144}{126}-\frac{693}{126}\\=\frac{-56-144-693}{126}\\=\frac{-893}{126}\)
7. \(-\left(\frac{8}{7}\right) -\left(\frac{-6}{5}\right) +\left(\frac{8}{-2}\right)\\= \frac{-8}{7}+ \frac{6}{5}-\frac{8}{2}\\=\frac{-8}{7}+\frac{6}{5}-\frac{4}{1}\\=\frac{-40}{35}+\frac{42}{35}-\frac{140}{35}\\=\frac{-40+42-140}{35}\\=\frac{-138}{35}\)
8. \(+\left(\frac{3}{-4}\right) +\left(\frac{6}{-6}\right) -\left(\frac{-7}{3}\right)\\= \frac{-3}{4}- \frac{6}{6}+\frac{7}{3}\\=\frac{-3}{4}-\frac{1}{1}+\frac{7}{3}\\=\frac{-9}{12}-\frac{12}{12}+\frac{28}{12}\\=\frac{-9-12+28}{12}\\=\frac{7}{12}\)
9. \(+\left(\frac{4}{5}\right) +\left(\frac{-9}{9}\right) -\left(\frac{-9}{12}\right)\\= \frac{4}{5}- \frac{9}{9}+\frac{9}{12}\\=\frac{4}{5}-\frac{1}{1}+\frac{3}{4}\\=\frac{16}{20}-\frac{20}{20}+\frac{15}{20}\\=\frac{16-20+15}{20}\\=\frac{11}{20}\)
10. \(+\left(\frac{4}{-5}\right) +\left(\frac{8}{4}\right) +\left(\frac{8}{-3}\right)\\= \frac{-4}{5}+ \frac{8}{4}-\frac{8}{3}\\=\frac{-4}{5}+\frac{2}{1}-\frac{8}{3}\\=\frac{-12}{15}+\frac{30}{15}-\frac{40}{15}\\=\frac{-12+30-40}{15}\\=\frac{-22}{15}\)
11. \(-\left(\frac{2}{3}\right) +\left(\frac{3}{3}\right) +\left(\frac{-6}{-2}\right)\\= \frac{-2}{3}+ \frac{3}{3}+\frac{6}{2}\\=\frac{-2}{3}+\frac{1}{1}+\frac{3}{1}\\=\frac{-2+1+3}{3}\\=\frac{2}{3}\)
12. \(+\left(\frac{-10}{-7}\right) -\left(\frac{4}{5}\right) +\left(\frac{3}{3}\right)\\= \frac{10}{7}- \frac{4}{5}+\frac{3}{3}\\=\frac{10}{7}-\frac{4}{5}+\frac{1}{1}\\=\frac{50}{35}-\frac{28}{35}+\frac{35}{35}\\=\frac{50-28+35}{35}\\=\frac{57}{35}\)