Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{7}\right) -\left(\frac{7}{-7}\right) +\left(\frac{-9}{-11}\right)\\= \frac{-10}{7}+ \frac{7}{7}+\frac{9}{11}\\=\frac{-10}{7}+\frac{1}{1}+\frac{9}{11}\\=\frac{-110}{77}+\frac{77}{77}+\frac{63}{77}\\=\frac{-110+77+63}{77}\\=\frac{30}{77}\)
2. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-7}{-5}\right) -\left(\frac{-9}{-4}\right)\\= \frac{6}{5}- \frac{7}{5}-\frac{9}{4}\\=\frac{24}{20}-\frac{28}{20}-\frac{45}{20}\\=\frac{24-28-45}{20}\\=\frac{-49}{20}\)
3. \(-\left(\frac{5}{-6}\right) -\left(\frac{10}{-6}\right) +\left(\frac{-5}{11}\right)\\= \frac{5}{6}+ \frac{10}{6}-\frac{5}{11}\\=\frac{5}{6}+\frac{5}{3}-\frac{5}{11}\\=\frac{55}{66}+\frac{110}{66}-\frac{30}{66}\\=\frac{55+110-30}{66}\\=\frac{135}{66}\\=\frac{45}{22}\)
4. \(-\left(\frac{3}{8}\right) +\left(\frac{2}{-9}\right) -\left(\frac{-2}{-5}\right)\\= \frac{-3}{8}- \frac{2}{9}-\frac{2}{5}\\=\frac{-135}{360}-\frac{80}{360}-\frac{144}{360}\\=\frac{-135-80-144}{360}\\=\frac{-359}{360}\)
5. \(+\left(\frac{7}{2}\right) +\left(\frac{-6}{4}\right) +\left(\frac{3}{-7}\right)\\= \frac{7}{2}- \frac{6}{4}-\frac{3}{7}\\=\frac{7}{2}-\frac{3}{2}-\frac{3}{7}\\=\frac{49}{14}-\frac{21}{14}-\frac{6}{14}\\=\frac{49-21-6}{14}\\=\frac{22}{14}\\=\frac{11}{7}\)
6. \(+\left(\frac{-2}{7}\right) -\left(\frac{3}{-10}\right) +\left(\frac{-6}{7}\right)\\= \frac{-2}{7}+ \frac{3}{10}-\frac{6}{7}\\=\frac{-20}{70}+\frac{21}{70}-\frac{60}{70}\\=\frac{-20+21-60}{70}\\=\frac{-59}{70}\)
7. \(+\left(\frac{3}{7}\right) -\left(\frac{-3}{-8}\right) -\left(\frac{9}{-10}\right)\\= \frac{3}{7}- \frac{3}{8}+\frac{9}{10}\\=\frac{120}{280}-\frac{105}{280}+\frac{252}{280}\\=\frac{120-105+252}{280}\\=\frac{267}{280}\)
8. \(+\left(\frac{9}{-2}\right) +\left(\frac{9}{-8}\right) +\left(\frac{-5}{3}\right)\\= \frac{-9}{2}- \frac{9}{8}-\frac{5}{3}\\=\frac{-108}{24}-\frac{27}{24}-\frac{40}{24}\\=\frac{-108-27-40}{24}\\=\frac{-175}{24}\)
9. \(+\left(\frac{-8}{-9}\right) +\left(\frac{10}{8}\right) -\left(\frac{-7}{10}\right)\\= \frac{8}{9}+ \frac{10}{8}+\frac{7}{10}\\=\frac{8}{9}+\frac{5}{4}+\frac{7}{10}\\=\frac{160}{180}+\frac{225}{180}+\frac{126}{180}\\=\frac{160+225+126}{180}\\=\frac{511}{180}\)
10. \(+\left(\frac{-3}{-7}\right) -\left(\frac{8}{-5}\right) -\left(\frac{-12}{-5}\right)\\= \frac{3}{7}+ \frac{8}{5}-\frac{12}{5}\\=\frac{15}{35}+\frac{56}{35}-\frac{84}{35}\\=\frac{15+56-84}{35}\\=\frac{-13}{35}\)
11. \(-\left(\frac{7}{8}\right) +\left(\frac{-2}{5}\right) +\left(\frac{-12}{6}\right)\\= \frac{-7}{8}- \frac{2}{5}-\frac{12}{6}\\=\frac{-7}{8}-\frac{2}{5}-\frac{2}{1}\\=\frac{-35}{40}-\frac{16}{40}-\frac{80}{40}\\=\frac{-35-16-80}{40}\\=\frac{-131}{40}\)
12. \(-\left(\frac{10}{7}\right) +\left(\frac{-3}{-8}\right) +\left(\frac{-4}{12}\right)\\= \frac{-10}{7}+ \frac{3}{8}-\frac{4}{12}\\=\frac{-10}{7}+\frac{3}{8}-\frac{1}{3}\\=\frac{-240}{168}+\frac{63}{168}-\frac{56}{168}\\=\frac{-240+63-56}{168}\\=\frac{-233}{168}\)