Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{7}\right) -\left(\frac{4}{5}\right) +\left(\frac{2}{7}\right)\\= \frac{2}{7}- \frac{4}{5}+\frac{2}{7}\\=\frac{10}{35}-\frac{28}{35}+\frac{10}{35}\\=\frac{10-28+10}{35}\\=\frac{-8}{35}\)
2. \(-\left(\frac{5}{2}\right) -\left(\frac{7}{-4}\right) +\left(\frac{-7}{-10}\right)\\= \frac{-5}{2}+ \frac{7}{4}+\frac{7}{10}\\=\frac{-50}{20}+\frac{35}{20}+\frac{14}{20}\\=\frac{-50+35+14}{20}\\=\frac{-1}{20}\)
3. \(+\left(\frac{-5}{6}\right) -\left(\frac{-2}{3}\right) -\left(\frac{-9}{10}\right)\\= \frac{-5}{6}+ \frac{2}{3}+\frac{9}{10}\\=\frac{-25}{30}+\frac{20}{30}+\frac{27}{30}\\=\frac{-25+20+27}{30}\\=\frac{22}{30}\\=\frac{11}{15}\)
4. \(+\left(\frac{7}{-2}\right) +\left(\frac{-9}{5}\right) +\left(\frac{6}{-8}\right)\\= \frac{-7}{2}- \frac{9}{5}-\frac{6}{8}\\=\frac{-7}{2}-\frac{9}{5}-\frac{3}{4}\\=\frac{-70}{20}-\frac{36}{20}-\frac{15}{20}\\=\frac{-70-36-15}{20}\\=\frac{-121}{20}\)
5. \(-\left(\frac{9}{2}\right) +\left(\frac{9}{3}\right) -\left(\frac{-7}{-4}\right)\\= \frac{-9}{2}+ \frac{9}{3}-\frac{7}{4}\\=\frac{-9}{2}+\frac{3}{1}-\frac{7}{4}\\=\frac{-18}{4}+\frac{12}{4}-\frac{7}{4}\\=\frac{-18+12-7}{4}\\=\frac{-13}{4}\)
6. \(-\left(\frac{-3}{-2}\right) -\left(\frac{8}{-3}\right) -\left(\frac{12}{9}\right)\\= \frac{-3}{2}+ \frac{8}{3}-\frac{12}{9}\\=\frac{-3}{2}+\frac{8}{3}-\frac{4}{3}\\=\frac{-9}{6}+\frac{16}{6}-\frac{8}{6}\\=\frac{-9+16-8}{6}\\=\frac{-1}{6}\)
7. \(+\left(\frac{-3}{-2}\right) +\left(\frac{4}{7}\right) +\left(\frac{-8}{-12}\right)\\= \frac{3}{2}+ \frac{4}{7}+\frac{8}{12}\\=\frac{3}{2}+\frac{4}{7}+\frac{2}{3}\\=\frac{63}{42}+\frac{24}{42}+\frac{28}{42}\\=\frac{63+24+28}{42}\\=\frac{115}{42}\)
8. \(+\left(\frac{6}{5}\right) +\left(\frac{-6}{-9}\right) -\left(\frac{-3}{5}\right)\\= \frac{6}{5}+ \frac{6}{9}+\frac{3}{5}\\=\frac{6}{5}+\frac{2}{3}+\frac{3}{5}\\=\frac{18}{15}+\frac{10}{15}+\frac{9}{15}\\=\frac{18+10+9}{15}\\=\frac{37}{15}\)
9. \(-\left(\frac{-4}{3}\right) +\left(\frac{5}{-7}\right) +\left(\frac{-4}{10}\right)\\= \frac{4}{3}- \frac{5}{7}-\frac{4}{10}\\=\frac{4}{3}-\frac{5}{7}-\frac{2}{5}\\=\frac{140}{105}-\frac{75}{105}-\frac{42}{105}\\=\frac{140-75-42}{105}\\=\frac{23}{105}\)
10. \(+\left(\frac{-10}{-7}\right) +\left(\frac{10}{-9}\right) +\left(\frac{-7}{8}\right)\\= \frac{10}{7}- \frac{10}{9}-\frac{7}{8}\\=\frac{720}{504}-\frac{560}{504}-\frac{441}{504}\\=\frac{720-560-441}{504}\\=\frac{-281}{504}\)
11. \(+\left(\frac{-7}{-6}\right) +\left(\frac{5}{7}\right) -\left(\frac{6}{11}\right)\\= \frac{7}{6}+ \frac{5}{7}-\frac{6}{11}\\=\frac{539}{462}+\frac{330}{462}-\frac{252}{462}\\=\frac{539+330-252}{462}\\=\frac{617}{462}\)
12. \(-\left(\frac{-2}{-7}\right) +\left(\frac{7}{3}\right) +\left(\frac{-12}{4}\right)\\= \frac{-2}{7}+ \frac{7}{3}-\frac{12}{4}\\=\frac{-2}{7}+\frac{7}{3}-\frac{3}{1}\\=\frac{-6}{21}+\frac{49}{21}-\frac{63}{21}\\=\frac{-6+49-63}{21}\\=\frac{-20}{21}\)