Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{8}{3}\right) -\left(\frac{-10}{-5}\right) +\left(\frac{9}{-5}\right)\\= \frac{8}{3}- \frac{10}{5}-\frac{9}{5}\\=\frac{8}{3}-\frac{2}{1}-\frac{9}{5}\\=\frac{40}{15}-\frac{30}{15}-\frac{27}{15}\\=\frac{40-30-27}{15}\\=\frac{-17}{15}\)
2. \(+\left(\frac{-4}{-9}\right) -\left(\frac{9}{9}\right) +\left(\frac{12}{6}\right)\\= \frac{4}{9}- \frac{9}{9}+\frac{12}{6}\\=\frac{4}{9}-\frac{1}{1}+\frac{2}{1}\\=\frac{4-1+2}{9}\\=\frac{5}{9}\)
3. \(+\left(\frac{7}{-8}\right) -\left(\frac{9}{-8}\right) -\left(\frac{10}{-12}\right)\\= \frac{-7}{8}+ \frac{9}{8}+\frac{10}{12}\\=\frac{-7}{8}+\frac{9}{8}+\frac{5}{6}\\=\frac{-21}{24}+\frac{27}{24}+\frac{20}{24}\\=\frac{-21+27+20}{24}\\=\frac{26}{24}\\=\frac{13}{12}\)
4. \(-\left(\frac{3}{8}\right) -\left(\frac{6}{5}\right) -\left(\frac{9}{-12}\right)\\= \frac{-3}{8}- \frac{6}{5}+\frac{9}{12}\\=\frac{-3}{8}-\frac{6}{5}+\frac{3}{4}\\=\frac{-15}{40}-\frac{48}{40}+\frac{30}{40}\\=\frac{-15-48+30}{40}\\=\frac{-33}{40}\)
5. \(-\left(\frac{7}{-8}\right) +\left(\frac{-6}{-9}\right) -\left(\frac{-2}{-11}\right)\\= \frac{7}{8}+ \frac{6}{9}-\frac{2}{11}\\=\frac{7}{8}+\frac{2}{3}-\frac{2}{11}\\=\frac{231}{264}+\frac{176}{264}-\frac{48}{264}\\=\frac{231+176-48}{264}\\=\frac{359}{264}\)
6. \(-\left(\frac{-4}{7}\right) +\left(\frac{-7}{-9}\right) +\left(\frac{11}{4}\right)\\= \frac{4}{7}+ \frac{7}{9}+\frac{11}{4}\\=\frac{144}{252}+\frac{196}{252}+\frac{693}{252}\\=\frac{144+196+693}{252}\\=\frac{1033}{252}\)
7. \(-\left(\frac{-7}{-9}\right) -\left(\frac{-6}{7}\right) -\left(\frac{12}{5}\right)\\= \frac{-7}{9}+ \frac{6}{7}-\frac{12}{5}\\=\frac{-245}{315}+\frac{270}{315}-\frac{756}{315}\\=\frac{-245+270-756}{315}\\=\frac{-731}{315}\)
8. \(+\left(\frac{-7}{4}\right) -\left(\frac{-5}{8}\right) -\left(\frac{11}{-5}\right)\\= \frac{-7}{4}+ \frac{5}{8}+\frac{11}{5}\\=\frac{-70}{40}+\frac{25}{40}+\frac{88}{40}\\=\frac{-70+25+88}{40}\\=\frac{43}{40}\)
9. \(-\left(\frac{-9}{-2}\right) +\left(\frac{2}{-7}\right) -\left(\frac{-3}{8}\right)\\= \frac{-9}{2}- \frac{2}{7}+\frac{3}{8}\\=\frac{-252}{56}-\frac{16}{56}+\frac{21}{56}\\=\frac{-252-16+21}{56}\\=\frac{-247}{56}\)
10. \(+\left(\frac{-2}{-7}\right) +\left(\frac{6}{10}\right) -\left(\frac{12}{6}\right)\\= \frac{2}{7}+ \frac{6}{10}-\frac{12}{6}\\=\frac{2}{7}+\frac{3}{5}-\frac{2}{1}\\=\frac{10}{35}+\frac{21}{35}-\frac{70}{35}\\=\frac{10+21-70}{35}\\=\frac{-39}{35}\)
11. \(+\left(\frac{6}{5}\right) -\left(\frac{10}{-4}\right) +\left(\frac{2}{-12}\right)\\= \frac{6}{5}+ \frac{10}{4}-\frac{2}{12}\\=\frac{6}{5}+\frac{5}{2}-\frac{1}{6}\\=\frac{36}{30}+\frac{75}{30}-\frac{5}{30}\\=\frac{36+75-5}{30}\\=\frac{106}{30}\\=\frac{53}{15}\)
12. \(-\left(\frac{7}{8}\right) -\left(\frac{6}{10}\right) +\left(\frac{8}{5}\right)\\= \frac{-7}{8}- \frac{6}{10}+\frac{8}{5}\\=\frac{-7}{8}-\frac{3}{5}+\frac{8}{5}\\=\frac{-35}{40}-\frac{24}{40}+\frac{64}{40}\\=\frac{-35-24+64}{40}\\=\frac{5}{40}\\=\frac{1}{8}\)