Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{-7}\right) -\left(\frac{-7}{9}\right) -\left(\frac{3}{6}\right)\\= \frac{2}{7}+ \frac{7}{9}-\frac{3}{6}\\=\frac{2}{7}+\frac{7}{9}-\frac{1}{2}\\=\frac{36}{126}+\frac{98}{126}-\frac{63}{126}\\=\frac{36+98-63}{126}\\=\frac{71}{126}\)
2. \(+\left(\frac{-8}{-3}\right) -\left(\frac{2}{-2}\right) +\left(\frac{2}{-7}\right)\\= \frac{8}{3}+ \frac{2}{2}-\frac{2}{7}\\=\frac{8}{3}+\frac{1}{1}-\frac{2}{7}\\=\frac{56}{21}+\frac{21}{21}-\frac{6}{21}\\=\frac{56+21-6}{21}\\=\frac{71}{21}\)
3. \(+\left(\frac{-6}{-7}\right) -\left(\frac{3}{-5}\right) -\left(\frac{10}{-3}\right)\\= \frac{6}{7}+ \frac{3}{5}+\frac{10}{3}\\=\frac{90}{105}+\frac{63}{105}+\frac{350}{105}\\=\frac{90+63+350}{105}\\=\frac{503}{105}\)
4. \(+\left(\frac{5}{-4}\right) -\left(\frac{10}{-10}\right) -\left(\frac{6}{-10}\right)\\= \frac{-5}{4}+ \frac{10}{10}+\frac{6}{10}\\=\frac{-5}{4}+\frac{1}{1}+\frac{3}{5}\\=\frac{-25}{20}+\frac{20}{20}+\frac{12}{20}\\=\frac{-25+20+12}{20}\\=\frac{7}{20}\)
5. \(+\left(\frac{-8}{5}\right) -\left(\frac{3}{-2}\right) -\left(\frac{2}{10}\right)\\= \frac{-8}{5}+ \frac{3}{2}-\frac{2}{10}\\=\frac{-8}{5}+\frac{3}{2}-\frac{1}{5}\\=\frac{-16}{10}+\frac{15}{10}-\frac{2}{10}\\=\frac{-16+15-2}{10}\\=\frac{-3}{10}\)
6. \(+\left(\frac{-9}{-2}\right) +\left(\frac{-5}{10}\right) -\left(\frac{8}{-6}\right)\\= \frac{9}{2}- \frac{5}{10}+\frac{8}{6}\\=\frac{9}{2}-\frac{1}{2}+\frac{4}{3}\\=\frac{27}{6}-\frac{3}{6}+\frac{8}{6}\\=\frac{27-3+8}{6}\\=\frac{32}{6}\\=\frac{16}{3}\)
7. \(+\left(\frac{-3}{7}\right) +\left(\frac{-5}{-5}\right) -\left(\frac{-9}{-12}\right)\\= \frac{-3}{7}+ \frac{5}{5}-\frac{9}{12}\\=\frac{-3}{7}+\frac{1}{1}-\frac{3}{4}\\=\frac{-12}{28}+\frac{28}{28}-\frac{21}{28}\\=\frac{-12+28-21}{28}\\=\frac{-5}{28}\)
8. \(+\left(\frac{-5}{-3}\right) -\left(\frac{5}{-4}\right) +\left(\frac{3}{-12}\right)\\= \frac{5}{3}+ \frac{5}{4}-\frac{3}{12}\\=\frac{5}{3}+\frac{5}{4}-\frac{1}{4}\\=\frac{20}{12}+\frac{15}{12}-\frac{3}{12}\\=\frac{20+15-3}{12}\\=\frac{32}{12}\\=\frac{8}{3}\)
9. \(-\left(\frac{9}{-8}\right) -\left(\frac{6}{6}\right) -\left(\frac{11}{7}\right)\\= \frac{9}{8}- \frac{6}{6}-\frac{11}{7}\\=\frac{9}{8}-\frac{1}{1}-\frac{11}{7}\\=\frac{63}{56}-\frac{56}{56}-\frac{88}{56}\\=\frac{63-56-88}{56}\\=\frac{-81}{56}\)
10. \(+\left(\frac{-10}{-3}\right) +\left(\frac{-5}{2}\right) -\left(\frac{2}{5}\right)\\= \frac{10}{3}- \frac{5}{2}-\frac{2}{5}\\=\frac{100}{30}-\frac{75}{30}-\frac{12}{30}\\=\frac{100-75-12}{30}\\=\frac{13}{30}\)
11. \(-\left(\frac{-10}{-7}\right) +\left(\frac{9}{8}\right) +\left(\frac{-10}{-5}\right)\\= \frac{-10}{7}+ \frac{9}{8}+\frac{10}{5}\\=\frac{-10}{7}+\frac{9}{8}+\frac{2}{1}\\=\frac{-80}{56}+\frac{63}{56}+\frac{112}{56}\\=\frac{-80+63+112}{56}\\=\frac{95}{56}\)
12. \(-\left(\frac{3}{7}\right) -\left(\frac{9}{-2}\right) +\left(\frac{-8}{-12}\right)\\= \frac{-3}{7}+ \frac{9}{2}+\frac{8}{12}\\=\frac{-3}{7}+\frac{9}{2}+\frac{2}{3}\\=\frac{-18}{42}+\frac{189}{42}+\frac{28}{42}\\=\frac{-18+189+28}{42}\\=\frac{199}{42}\)