Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{9}\right) +\left(\frac{8}{-6}\right) +\left(\frac{-10}{-8}\right)\\= \frac{10}{9}- \frac{8}{6}+\frac{10}{8}\\=\frac{10}{9}-\frac{4}{3}+\frac{5}{4}\\=\frac{40}{36}-\frac{48}{36}+\frac{45}{36}\\=\frac{40-48+45}{36}\\=\frac{37}{36}\)
2. \(+\left(\frac{-6}{5}\right) -\left(\frac{3}{-9}\right) +\left(\frac{11}{12}\right)\\= \frac{-6}{5}+ \frac{3}{9}+\frac{11}{12}\\=\frac{-6}{5}+\frac{1}{3}+\frac{11}{12}\\=\frac{-72}{60}+\frac{20}{60}+\frac{55}{60}\\=\frac{-72+20+55}{60}\\=\frac{3}{60}\\=\frac{1}{20}\)
3. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-6}{-3}\right) +\left(\frac{8}{-7}\right)\\= \frac{-6}{5}- \frac{6}{3}-\frac{8}{7}\\=\frac{-6}{5}-\frac{2}{1}-\frac{8}{7}\\=\frac{-42}{35}-\frac{70}{35}-\frac{40}{35}\\=\frac{-42-70-40}{35}\\=\frac{-152}{35}\)
4. \(-\left(\frac{-8}{3}\right) -\left(\frac{-5}{8}\right) -\left(\frac{-12}{8}\right)\\= \frac{8}{3}+ \frac{5}{8}+\frac{12}{8}\\=\frac{8}{3}+\frac{5}{8}+\frac{3}{2}\\=\frac{64}{24}+\frac{15}{24}+\frac{36}{24}\\=\frac{64+15+36}{24}\\=\frac{115}{24}\)
5. \(+\left(\frac{-6}{5}\right) +\left(\frac{6}{8}\right) -\left(\frac{-3}{-11}\right)\\= \frac{-6}{5}+ \frac{6}{8}-\frac{3}{11}\\=\frac{-6}{5}+\frac{3}{4}-\frac{3}{11}\\=\frac{-264}{220}+\frac{165}{220}-\frac{60}{220}\\=\frac{-264+165-60}{220}\\=\frac{-159}{220}\)
6. \(-\left(\frac{-6}{-7}\right) +\left(\frac{7}{8}\right) +\left(\frac{-12}{-5}\right)\\= \frac{-6}{7}+ \frac{7}{8}+\frac{12}{5}\\=\frac{-240}{280}+\frac{245}{280}+\frac{672}{280}\\=\frac{-240+245+672}{280}\\=\frac{677}{280}\)
7. \(+\left(\frac{8}{-7}\right) -\left(\frac{5}{-8}\right) +\left(\frac{-5}{2}\right)\\= \frac{-8}{7}+ \frac{5}{8}-\frac{5}{2}\\=\frac{-64}{56}+\frac{35}{56}-\frac{140}{56}\\=\frac{-64+35-140}{56}\\=\frac{-169}{56}\)
8. \(-\left(\frac{-2}{-9}\right) +\left(\frac{-7}{4}\right) +\left(\frac{-2}{3}\right)\\= \frac{-2}{9}- \frac{7}{4}-\frac{2}{3}\\=\frac{-8}{36}-\frac{63}{36}-\frac{24}{36}\\=\frac{-8-63-24}{36}\\=\frac{-95}{36}\)
9. \(+\left(\frac{-8}{-7}\right) +\left(\frac{-9}{7}\right) +\left(\frac{-11}{-7}\right)\\= \frac{8}{7}- \frac{9}{7}+\frac{11}{7}\\=\frac{8-9+11}{7}\\=\frac{10}{7}\)
10. \(-\left(\frac{10}{3}\right) +\left(\frac{2}{7}\right) -\left(\frac{-6}{3}\right)\\= \frac{-10}{3}+ \frac{2}{7}+\frac{6}{3}\\=\frac{-10}{3}+\frac{2}{7}+\frac{2}{1}\\=\frac{-70}{21}+\frac{6}{21}+\frac{42}{21}\\=\frac{-70+6+42}{21}\\=\frac{-22}{21}\)
11. \(+\left(\frac{7}{2}\right) +\left(\frac{9}{6}\right) -\left(\frac{6}{9}\right)\\= \frac{7}{2}+ \frac{9}{6}-\frac{6}{9}\\=\frac{7}{2}+\frac{3}{2}-\frac{2}{3}\\=\frac{21}{6}+\frac{9}{6}-\frac{4}{6}\\=\frac{21+9-4}{6}\\=\frac{26}{6}\\=\frac{13}{3}\)
12. \(-\left(\frac{-4}{9}\right) +\left(\frac{6}{-4}\right) -\left(\frac{8}{11}\right)\\= \frac{4}{9}- \frac{6}{4}-\frac{8}{11}\\=\frac{4}{9}-\frac{3}{2}-\frac{8}{11}\\=\frac{88}{198}-\frac{297}{198}-\frac{144}{198}\\=\frac{88-297-144}{198}\\=\frac{-353}{198}\)