Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{7}\right) +\left(\frac{-8}{-8}\right) +\left(\frac{7}{12}\right)\\= \frac{-3}{7}+ \frac{8}{8}+\frac{7}{12}\\=\frac{-3}{7}+\frac{1}{1}+\frac{7}{12}\\=\frac{-36}{84}+\frac{84}{84}+\frac{49}{84}\\=\frac{-36+84+49}{84}\\=\frac{97}{84}\)
2. \(+\left(\frac{-3}{2}\right) -\left(\frac{-7}{9}\right) -\left(\frac{-12}{8}\right)\\= \frac{-3}{2}+ \frac{7}{9}+\frac{12}{8}\\=\frac{-3}{2}+\frac{7}{9}+\frac{3}{2}\\=\frac{-27}{18}+\frac{14}{18}+\frac{27}{18}\\=\frac{-27+14+27}{18}\\=\frac{14}{18}\\=\frac{7}{9}\)
3. \(-\left(\frac{2}{-3}\right) +\left(\frac{9}{-4}\right) -\left(\frac{12}{-9}\right)\\= \frac{2}{3}- \frac{9}{4}+\frac{12}{9}\\=\frac{2}{3}-\frac{9}{4}+\frac{4}{3}\\=\frac{8}{12}-\frac{27}{12}+\frac{16}{12}\\=\frac{8-27+16}{12}\\=\frac{-3}{12}\\=\frac{-1}{4}\)
4. \(+\left(\frac{4}{-9}\right) -\left(\frac{-3}{-4}\right) +\left(\frac{-6}{-4}\right)\\= \frac{-4}{9}- \frac{3}{4}+\frac{6}{4}\\=\frac{-4}{9}-\frac{3}{4}+\frac{3}{2}\\=\frac{-16}{36}-\frac{27}{36}+\frac{54}{36}\\=\frac{-16-27+54}{36}\\=\frac{11}{36}\)
5. \(+\left(\frac{-7}{-5}\right) -\left(\frac{7}{5}\right) +\left(\frac{-8}{-6}\right)\\= \frac{7}{5}- \frac{7}{5}+\frac{8}{6}\\=\frac{7}{5}-\frac{7}{5}+\frac{4}{3}\\=\frac{21}{15}-\frac{21}{15}+\frac{20}{15}\\=\frac{21-21+20}{15}\\=\frac{20}{15}\\=\frac{4}{3}\)
6. \(+\left(\frac{5}{-6}\right) -\left(\frac{10}{-2}\right) +\left(\frac{-7}{-3}\right)\\= \frac{-5}{6}+ \frac{10}{2}+\frac{7}{3}\\=\frac{-5}{6}+\frac{5}{1}+\frac{7}{3}\\=\frac{-5+5+7}{6}\\=\frac{7}{6}\)
7. \(+\left(\frac{-4}{5}\right) -\left(\frac{2}{-10}\right) +\left(\frac{7}{12}\right)\\= \frac{-4}{5}+ \frac{2}{10}+\frac{7}{12}\\=\frac{-4}{5}+\frac{1}{5}+\frac{7}{12}\\=\frac{-48}{60}+\frac{12}{60}+\frac{35}{60}\\=\frac{-48+12+35}{60}\\=\frac{-1}{60}\)
8. \(-\left(\frac{7}{9}\right) -\left(\frac{-4}{5}\right) +\left(\frac{5}{-6}\right)\\= \frac{-7}{9}+ \frac{4}{5}-\frac{5}{6}\\=\frac{-70}{90}+\frac{72}{90}-\frac{75}{90}\\=\frac{-70+72-75}{90}\\=\frac{-73}{90}\)
9. \(-\left(\frac{-6}{5}\right) +\left(\frac{-7}{-9}\right) -\left(\frac{7}{-11}\right)\\= \frac{6}{5}+ \frac{7}{9}+\frac{7}{11}\\=\frac{594}{495}+\frac{385}{495}+\frac{315}{495}\\=\frac{594+385+315}{495}\\=\frac{1294}{495}\)
10. \(-\left(\frac{-6}{5}\right) -\left(\frac{2}{-10}\right) -\left(\frac{-10}{-8}\right)\\= \frac{6}{5}+ \frac{2}{10}-\frac{10}{8}\\=\frac{6}{5}+\frac{1}{5}-\frac{5}{4}\\=\frac{24}{20}+\frac{4}{20}-\frac{25}{20}\\=\frac{24+4-25}{20}\\=\frac{3}{20}\)
11. \(-\left(\frac{-6}{-7}\right) +\left(\frac{-10}{-10}\right) -\left(\frac{4}{5}\right)\\= \frac{-6}{7}+ \frac{10}{10}-\frac{4}{5}\\=\frac{-6}{7}+\frac{1}{1}-\frac{4}{5}\\=\frac{-30}{35}+\frac{35}{35}-\frac{28}{35}\\=\frac{-30+35-28}{35}\\=\frac{-23}{35}\)
12. \(-\left(\frac{-6}{5}\right) -\left(\frac{4}{-3}\right) +\left(\frac{4}{2}\right)\\= \frac{6}{5}+ \frac{4}{3}+\frac{4}{2}\\=\frac{6}{5}+\frac{4}{3}+\frac{2}{1}\\=\frac{18}{15}+\frac{20}{15}+\frac{30}{15}\\=\frac{18+20+30}{15}\\=\frac{68}{15}\)