Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{7}\right) -\left(\frac{-5}{-3}\right) +\left(\frac{-10}{10}\right)\\= \frac{5}{7}- \frac{5}{3}-\frac{10}{10}\\=\frac{5}{7}-\frac{5}{3}-\frac{1}{1}\\=\frac{15}{21}-\frac{35}{21}-\frac{21}{21}\\=\frac{15-35-21}{21}\\=\frac{-41}{21}\)
2. \(-\left(\frac{10}{7}\right) +\left(\frac{2}{-7}\right) -\left(\frac{3}{-4}\right)\\= \frac{-10}{7}- \frac{2}{7}+\frac{3}{4}\\=\frac{-40}{28}-\frac{8}{28}+\frac{21}{28}\\=\frac{-40-8+21}{28}\\=\frac{-27}{28}\)
3. \(-\left(\frac{-5}{9}\right) -\left(\frac{3}{-3}\right) +\left(\frac{-11}{-9}\right)\\= \frac{5}{9}+ \frac{3}{3}+\frac{11}{9}\\=\frac{5}{9}+\frac{1}{1}+\frac{11}{9}\\=\frac{5+1+11}{9}\\=\frac{17}{9}\)
4. \(+\left(\frac{6}{5}\right) -\left(\frac{9}{-9}\right) +\left(\frac{-10}{-8}\right)\\= \frac{6}{5}+ \frac{9}{9}+\frac{10}{8}\\=\frac{6}{5}+\frac{1}{1}+\frac{5}{4}\\=\frac{24}{20}+\frac{20}{20}+\frac{25}{20}\\=\frac{24+20+25}{20}\\=\frac{69}{20}\)
5. \(+\left(\frac{6}{5}\right) +\left(\frac{8}{5}\right) +\left(\frac{6}{-2}\right)\\= \frac{6}{5}+ \frac{8}{5}-\frac{6}{2}\\=\frac{6}{5}+\frac{8}{5}-\frac{3}{1}\\=\frac{6+8-3}{5}\\=\frac{11}{5}\)
6. \(+\left(\frac{-3}{5}\right) +\left(\frac{9}{-4}\right) -\left(\frac{-9}{-7}\right)\\= \frac{-3}{5}- \frac{9}{4}-\frac{9}{7}\\=\frac{-84}{140}-\frac{315}{140}-\frac{180}{140}\\=\frac{-84-315-180}{140}\\=\frac{-579}{140}\)
7. \(-\left(\frac{2}{-7}\right) +\left(\frac{-4}{10}\right) -\left(\frac{-12}{-8}\right)\\= \frac{2}{7}- \frac{4}{10}-\frac{12}{8}\\=\frac{2}{7}-\frac{2}{5}-\frac{3}{2}\\=\frac{20}{70}-\frac{28}{70}-\frac{105}{70}\\=\frac{20-28-105}{70}\\=\frac{-113}{70}\)
8. \(-\left(\frac{8}{7}\right) -\left(\frac{7}{2}\right) -\left(\frac{3}{-6}\right)\\= \frac{-8}{7}- \frac{7}{2}+\frac{3}{6}\\=\frac{-8}{7}-\frac{7}{2}+\frac{1}{2}\\=\frac{-16}{14}-\frac{49}{14}+\frac{7}{14}\\=\frac{-16-49+7}{14}\\=\frac{-58}{14}\\=\frac{-29}{7}\)
9. \(-\left(\frac{9}{2}\right) +\left(\frac{-9}{4}\right) -\left(\frac{8}{-11}\right)\\= \frac{-9}{2}- \frac{9}{4}+\frac{8}{11}\\=\frac{-198}{44}-\frac{99}{44}+\frac{32}{44}\\=\frac{-198-99+32}{44}\\=\frac{-265}{44}\)
10. \(-\left(\frac{5}{4}\right) -\left(\frac{-6}{2}\right) -\left(\frac{-4}{2}\right)\\= \frac{-5}{4}+ \frac{6}{2}+\frac{4}{2}\\=\frac{-5}{4}+\frac{3}{1}+\frac{2}{1}\\=\frac{-5+3+2}{4}\\=\frac{0}{4}\\=\frac{0}{1}\)
11. \(-\left(\frac{7}{-2}\right) -\left(\frac{7}{-5}\right) -\left(\frac{3}{10}\right)\\= \frac{7}{2}+ \frac{7}{5}-\frac{3}{10}\\=\frac{35}{10}+\frac{14}{10}-\frac{3}{10}\\=\frac{35+14-3}{10}\\=\frac{46}{10}\\=\frac{23}{5}\)
12. \(-\left(\frac{-7}{2}\right) +\left(\frac{-5}{-5}\right) -\left(\frac{-5}{8}\right)\\= \frac{7}{2}+ \frac{5}{5}+\frac{5}{8}\\=\frac{7}{2}+\frac{1}{1}+\frac{5}{8}\\=\frac{28}{8}+\frac{8}{8}+\frac{5}{8}\\=\frac{28+8+5}{8}\\=\frac{41}{8}\)