Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{5}\right) +\left(\frac{4}{2}\right) +\left(\frac{-7}{-8}\right)\\= \frac{-8}{5}+ \frac{4}{2}+\frac{7}{8}\\=\frac{-8}{5}+\frac{2}{1}+\frac{7}{8}\\=\frac{-64}{40}+\frac{80}{40}+\frac{35}{40}\\=\frac{-64+80+35}{40}\\=\frac{51}{40}\)
2. \(-\left(\frac{-7}{2}\right) -\left(\frac{3}{-5}\right) -\left(\frac{-4}{-7}\right)\\= \frac{7}{2}+ \frac{3}{5}-\frac{4}{7}\\=\frac{245}{70}+\frac{42}{70}-\frac{40}{70}\\=\frac{245+42-40}{70}\\=\frac{247}{70}\)
3. \(-\left(\frac{8}{-7}\right) -\left(\frac{7}{6}\right) +\left(\frac{12}{-3}\right)\\= \frac{8}{7}- \frac{7}{6}-\frac{12}{3}\\=\frac{8}{7}-\frac{7}{6}-\frac{4}{1}\\=\frac{48}{42}-\frac{49}{42}-\frac{168}{42}\\=\frac{48-49-168}{42}\\=\frac{-169}{42}\)
4. \(-\left(\frac{9}{7}\right) -\left(\frac{10}{-5}\right) -\left(\frac{-6}{10}\right)\\= \frac{-9}{7}+ \frac{10}{5}+\frac{6}{10}\\=\frac{-9}{7}+\frac{2}{1}+\frac{3}{5}\\=\frac{-45}{35}+\frac{70}{35}+\frac{21}{35}\\=\frac{-45+70+21}{35}\\=\frac{46}{35}\)
5. \(-\left(\frac{2}{-7}\right) +\left(\frac{-2}{5}\right) -\left(\frac{-3}{7}\right)\\= \frac{2}{7}- \frac{2}{5}+\frac{3}{7}\\=\frac{10}{35}-\frac{14}{35}+\frac{15}{35}\\=\frac{10-14+15}{35}\\=\frac{11}{35}\)
6. \(+\left(\frac{-4}{-7}\right) -\left(\frac{-6}{5}\right) +\left(\frac{-7}{-10}\right)\\= \frac{4}{7}+ \frac{6}{5}+\frac{7}{10}\\=\frac{40}{70}+\frac{84}{70}+\frac{49}{70}\\=\frac{40+84+49}{70}\\=\frac{173}{70}\)
7. \(+\left(\frac{5}{-2}\right) +\left(\frac{3}{7}\right) +\left(\frac{5}{8}\right)\\= \frac{-5}{2}+ \frac{3}{7}+\frac{5}{8}\\=\frac{-140}{56}+\frac{24}{56}+\frac{35}{56}\\=\frac{-140+24+35}{56}\\=\frac{-81}{56}\)
8. \(-\left(\frac{4}{5}\right) +\left(\frac{9}{9}\right) +\left(\frac{-10}{-2}\right)\\= \frac{-4}{5}+ \frac{9}{9}+\frac{10}{2}\\=\frac{-4}{5}+\frac{1}{1}+\frac{5}{1}\\=\frac{-4+1+5}{5}\\=\frac{2}{5}\)
9. \(-\left(\frac{10}{-9}\right) +\left(\frac{10}{-10}\right) +\left(\frac{10}{7}\right)\\= \frac{10}{9}- \frac{10}{10}+\frac{10}{7}\\=\frac{10}{9}-\frac{1}{1}+\frac{10}{7}\\=\frac{70}{63}-\frac{63}{63}+\frac{90}{63}\\=\frac{70-63+90}{63}\\=\frac{97}{63}\)
10. \(+\left(\frac{7}{4}\right) +\left(\frac{9}{-3}\right) -\left(\frac{7}{12}\right)\\= \frac{7}{4}- \frac{9}{3}-\frac{7}{12}\\=\frac{7}{4}-\frac{3}{1}-\frac{7}{12}\\=\frac{21}{12}-\frac{36}{12}-\frac{7}{12}\\=\frac{21-36-7}{12}\\=\frac{-22}{12}\\=\frac{-11}{6}\)
11. \(+\left(\frac{-7}{6}\right) -\left(\frac{9}{-6}\right) +\left(\frac{4}{-7}\right)\\= \frac{-7}{6}+ \frac{9}{6}-\frac{4}{7}\\=\frac{-7}{6}+\frac{3}{2}-\frac{4}{7}\\=\frac{-49}{42}+\frac{63}{42}-\frac{24}{42}\\=\frac{-49+63-24}{42}\\=\frac{-10}{42}\\=\frac{-5}{21}\)
12. \(-\left(\frac{7}{5}\right) +\left(\frac{6}{-9}\right) +\left(\frac{-9}{3}\right)\\= \frac{-7}{5}- \frac{6}{9}-\frac{9}{3}\\=\frac{-7}{5}-\frac{2}{3}-\frac{3}{1}\\=\frac{-21}{15}-\frac{10}{15}-\frac{45}{15}\\=\frac{-21-10-45}{15}\\=\frac{-76}{15}\)