Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{-2}\right) -\left(\frac{-9}{-6}\right) +\left(\frac{-7}{-11}\right)\\= \frac{-3}{2}- \frac{9}{6}+\frac{7}{11}\\=\frac{-3}{2}-\frac{3}{2}+\frac{7}{11}\\=\frac{-33}{22}-\frac{33}{22}+\frac{14}{22}\\=\frac{-33-33+14}{22}\\=\frac{-52}{22}\\=\frac{-26}{11}\)
2. \(+\left(\frac{6}{-5}\right) +\left(\frac{10}{5}\right) -\left(\frac{-4}{-6}\right)\\= \frac{-6}{5}+ \frac{10}{5}-\frac{4}{6}\\=\frac{-6}{5}+\frac{2}{1}-\frac{2}{3}\\=\frac{-18}{15}+\frac{30}{15}-\frac{10}{15}\\=\frac{-18+30-10}{15}\\=\frac{2}{15}\)
3. \(+\left(\frac{-6}{-7}\right) +\left(\frac{-6}{-10}\right) +\left(\frac{9}{5}\right)\\= \frac{6}{7}+ \frac{6}{10}+\frac{9}{5}\\=\frac{6}{7}+\frac{3}{5}+\frac{9}{5}\\=\frac{30}{35}+\frac{21}{35}+\frac{63}{35}\\=\frac{30+21+63}{35}\\=\frac{114}{35}\)
4. \(-\left(\frac{-3}{8}\right) -\left(\frac{-7}{10}\right) -\left(\frac{7}{-5}\right)\\= \frac{3}{8}+ \frac{7}{10}+\frac{7}{5}\\=\frac{15}{40}+\frac{28}{40}+\frac{56}{40}\\=\frac{15+28+56}{40}\\=\frac{99}{40}\)
5. \(-\left(\frac{-10}{7}\right) -\left(\frac{-6}{-7}\right) +\left(\frac{-6}{10}\right)\\= \frac{10}{7}- \frac{6}{7}-\frac{6}{10}\\=\frac{10}{7}-\frac{6}{7}-\frac{3}{5}\\=\frac{50}{35}-\frac{30}{35}-\frac{21}{35}\\=\frac{50-30-21}{35}\\=\frac{-1}{35}\)
6. \(-\left(\frac{5}{7}\right) -\left(\frac{9}{-10}\right) +\left(\frac{-4}{2}\right)\\= \frac{-5}{7}+ \frac{9}{10}-\frac{4}{2}\\=\frac{-5}{7}+\frac{9}{10}-\frac{2}{1}\\=\frac{-50}{70}+\frac{63}{70}-\frac{140}{70}\\=\frac{-50+63-140}{70}\\=\frac{-127}{70}\)
7. \(+\left(\frac{7}{-2}\right) +\left(\frac{6}{-6}\right) +\left(\frac{8}{-12}\right)\\= \frac{-7}{2}- \frac{6}{6}-\frac{8}{12}\\=\frac{-7}{2}-\frac{1}{1}-\frac{2}{3}\\=\frac{-21}{6}-\frac{6}{6}-\frac{4}{6}\\=\frac{-21-6-4}{6}\\=\frac{-31}{6}\)
8. \(-\left(\frac{-9}{2}\right) -\left(\frac{-7}{4}\right) -\left(\frac{-5}{3}\right)\\= \frac{9}{2}+ \frac{7}{4}+\frac{5}{3}\\=\frac{54}{12}+\frac{21}{12}+\frac{20}{12}\\=\frac{54+21+20}{12}\\=\frac{95}{12}\)
9. \(+\left(\frac{-4}{-7}\right) -\left(\frac{-9}{2}\right) +\left(\frac{7}{8}\right)\\= \frac{4}{7}+ \frac{9}{2}+\frac{7}{8}\\=\frac{32}{56}+\frac{252}{56}+\frac{49}{56}\\=\frac{32+252+49}{56}\\=\frac{333}{56}\)
10. \(+\left(\frac{-8}{-3}\right) +\left(\frac{-10}{10}\right) -\left(\frac{12}{-7}\right)\\= \frac{8}{3}- \frac{10}{10}+\frac{12}{7}\\=\frac{8}{3}-\frac{1}{1}+\frac{12}{7}\\=\frac{56}{21}-\frac{21}{21}+\frac{36}{21}\\=\frac{56-21+36}{21}\\=\frac{71}{21}\)
11. \(-\left(\frac{8}{-5}\right) -\left(\frac{7}{5}\right) -\left(\frac{6}{6}\right)\\= \frac{8}{5}- \frac{7}{5}-\frac{6}{6}\\=\frac{8}{5}-\frac{7}{5}-\frac{1}{1}\\=\frac{8-7-1}{5}\\=\frac{0}{5}\\=\frac{0}{1}\)
12. \(+\left(\frac{9}{-4}\right) -\left(\frac{4}{-3}\right) -\left(\frac{6}{9}\right)\\= \frac{-9}{4}+ \frac{4}{3}-\frac{6}{9}\\=\frac{-9}{4}+\frac{4}{3}-\frac{2}{3}\\=\frac{-27}{12}+\frac{16}{12}-\frac{8}{12}\\=\frac{-27+16-8}{12}\\=\frac{-19}{12}\)