Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{4}\right) +\left(\frac{-8}{5}\right) +\left(\frac{4}{9}\right)\\= \frac{5}{4}- \frac{8}{5}+\frac{4}{9}\\=\frac{225}{180}-\frac{288}{180}+\frac{80}{180}\\=\frac{225-288+80}{180}\\=\frac{17}{180}\)
2. \(+\left(\frac{-5}{-3}\right) -\left(\frac{-2}{5}\right) -\left(\frac{-9}{12}\right)\\= \frac{5}{3}+ \frac{2}{5}+\frac{9}{12}\\=\frac{5}{3}+\frac{2}{5}+\frac{3}{4}\\=\frac{100}{60}+\frac{24}{60}+\frac{45}{60}\\=\frac{100+24+45}{60}\\=\frac{169}{60}\)
3. \(-\left(\frac{2}{5}\right) +\left(\frac{-6}{-7}\right) +\left(\frac{-8}{8}\right)\\= \frac{-2}{5}+ \frac{6}{7}-\frac{8}{8}\\=\frac{-2}{5}+\frac{6}{7}-\frac{1}{1}\\=\frac{-14}{35}+\frac{30}{35}-\frac{35}{35}\\=\frac{-14+30-35}{35}\\=\frac{-19}{35}\)
4. \(-\left(\frac{8}{-5}\right) +\left(\frac{10}{2}\right) -\left(\frac{10}{8}\right)\\= \frac{8}{5}+ \frac{10}{2}-\frac{10}{8}\\=\frac{8}{5}+\frac{5}{1}-\frac{5}{4}\\=\frac{32}{20}+\frac{100}{20}-\frac{25}{20}\\=\frac{32+100-25}{20}\\=\frac{107}{20}\)
5. \(-\left(\frac{10}{-3}\right) -\left(\frac{-9}{3}\right) -\left(\frac{5}{5}\right)\\= \frac{10}{3}+ \frac{9}{3}-\frac{5}{5}\\=\frac{10}{3}+\frac{3}{1}-\frac{1}{1}\\=\frac{10+3-1}{3}\\=\frac{12}{3}\\=\frac{4}{1}\)
6. \(-\left(\frac{8}{5}\right) -\left(\frac{-8}{-10}\right) -\left(\frac{2}{-5}\right)\\= \frac{-8}{5}- \frac{8}{10}+\frac{2}{5}\\=\frac{-8}{5}-\frac{4}{5}+\frac{2}{5}\\=\frac{-8-4+2}{5}\\=\frac{-10}{5}\\=\frac{-2}{1}\)
7. \(-\left(\frac{4}{9}\right) -\left(\frac{9}{-6}\right) -\left(\frac{-8}{-9}\right)\\= \frac{-4}{9}+ \frac{9}{6}-\frac{8}{9}\\=\frac{-4}{9}+\frac{3}{2}-\frac{8}{9}\\=\frac{-8}{18}+\frac{27}{18}-\frac{16}{18}\\=\frac{-8+27-16}{18}\\=\frac{3}{18}\\=\frac{1}{6}\)
8. \(-\left(\frac{-9}{-2}\right) +\left(\frac{-2}{9}\right) -\left(\frac{-12}{-12}\right)\\= \frac{-9}{2}- \frac{2}{9}-\frac{12}{12}\\=\frac{-9}{2}-\frac{2}{9}-\frac{1}{1}\\=\frac{-81}{18}-\frac{4}{18}-\frac{18}{18}\\=\frac{-81-4-18}{18}\\=\frac{-103}{18}\)
9. \(-\left(\frac{6}{7}\right) -\left(\frac{2}{9}\right) +\left(\frac{-2}{-11}\right)\\= \frac{-6}{7}- \frac{2}{9}+\frac{2}{11}\\=\frac{-594}{693}-\frac{154}{693}+\frac{126}{693}\\=\frac{-594-154+126}{693}\\=\frac{-622}{693}\)
10. \(+\left(\frac{7}{8}\right) -\left(\frac{10}{4}\right) +\left(\frac{-8}{-11}\right)\\= \frac{7}{8}- \frac{10}{4}+\frac{8}{11}\\=\frac{7}{8}-\frac{5}{2}+\frac{8}{11}\\=\frac{77}{88}-\frac{220}{88}+\frac{64}{88}\\=\frac{77-220+64}{88}\\=\frac{-79}{88}\)
11. \(-\left(\frac{5}{-3}\right) -\left(\frac{-7}{7}\right) -\left(\frac{12}{-5}\right)\\= \frac{5}{3}+ \frac{7}{7}+\frac{12}{5}\\=\frac{5}{3}+\frac{1}{1}+\frac{12}{5}\\=\frac{25}{15}+\frac{15}{15}+\frac{36}{15}\\=\frac{25+15+36}{15}\\=\frac{76}{15}\)
12. \(+\left(\frac{10}{-7}\right) +\left(\frac{10}{-4}\right) +\left(\frac{-12}{-7}\right)\\= \frac{-10}{7}- \frac{10}{4}+\frac{12}{7}\\=\frac{-10}{7}-\frac{5}{2}+\frac{12}{7}\\=\frac{-20}{14}-\frac{35}{14}+\frac{24}{14}\\=\frac{-20-35+24}{14}\\=\frac{-31}{14}\)