Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{2}\right) +\left(\frac{9}{-10}\right) -\left(\frac{3}{6}\right)\\= \frac{9}{2}- \frac{9}{10}-\frac{3}{6}\\=\frac{9}{2}-\frac{9}{10}-\frac{1}{2}\\=\frac{45}{10}-\frac{9}{10}-\frac{5}{10}\\=\frac{45-9-5}{10}\\=\frac{31}{10}\)
2. \(-\left(\frac{-3}{-8}\right) +\left(\frac{-2}{10}\right) -\left(\frac{2}{-8}\right)\\= \frac{-3}{8}- \frac{2}{10}+\frac{2}{8}\\=\frac{-3}{8}-\frac{1}{5}+\frac{1}{4}\\=\frac{-15}{40}-\frac{8}{40}+\frac{10}{40}\\=\frac{-15-8+10}{40}\\=\frac{-13}{40}\)
3. \(+\left(\frac{-2}{-5}\right) -\left(\frac{-6}{4}\right) -\left(\frac{-6}{-9}\right)\\= \frac{2}{5}+ \frac{6}{4}-\frac{6}{9}\\=\frac{2}{5}+\frac{3}{2}-\frac{2}{3}\\=\frac{12}{30}+\frac{45}{30}-\frac{20}{30}\\=\frac{12+45-20}{30}\\=\frac{37}{30}\)
4. \(+\left(\frac{-2}{-3}\right) +\left(\frac{-5}{-8}\right) +\left(\frac{-6}{3}\right)\\= \frac{2}{3}+ \frac{5}{8}-\frac{6}{3}\\=\frac{2}{3}+\frac{5}{8}-\frac{2}{1}\\=\frac{16}{24}+\frac{15}{24}-\frac{48}{24}\\=\frac{16+15-48}{24}\\=\frac{-17}{24}\)
5. \(-\left(\frac{-2}{-5}\right) +\left(\frac{8}{-8}\right) -\left(\frac{-4}{-10}\right)\\= \frac{-2}{5}- \frac{8}{8}-\frac{4}{10}\\=\frac{-2}{5}-\frac{1}{1}-\frac{2}{5}\\=\frac{-2-1-2}{5}\\=\frac{-5}{5}\\=\frac{-1}{1}\)
6. \(+\left(\frac{-2}{7}\right) +\left(\frac{-6}{-2}\right) +\left(\frac{-3}{-3}\right)\\= \frac{-2}{7}+ \frac{6}{2}+\frac{3}{3}\\=\frac{-2}{7}+\frac{3}{1}+\frac{1}{1}\\=\frac{-2+3+1}{7}\\=\frac{2}{7}\)
7. \(+\left(\frac{9}{-5}\right) +\left(\frac{-3}{6}\right) -\left(\frac{-3}{-7}\right)\\= \frac{-9}{5}- \frac{3}{6}-\frac{3}{7}\\=\frac{-9}{5}-\frac{1}{2}-\frac{3}{7}\\=\frac{-126}{70}-\frac{35}{70}-\frac{30}{70}\\=\frac{-126-35-30}{70}\\=\frac{-191}{70}\)
8. \(+\left(\frac{8}{9}\right) -\left(\frac{-2}{-4}\right) +\left(\frac{-6}{-5}\right)\\= \frac{8}{9}- \frac{2}{4}+\frac{6}{5}\\=\frac{8}{9}-\frac{1}{2}+\frac{6}{5}\\=\frac{80}{90}-\frac{45}{90}+\frac{108}{90}\\=\frac{80-45+108}{90}\\=\frac{143}{90}\)
9. \(+\left(\frac{-3}{7}\right) -\left(\frac{-5}{-5}\right) -\left(\frac{11}{-11}\right)\\= \frac{-3}{7}- \frac{5}{5}+\frac{11}{11}\\=\frac{-3}{7}-\frac{1}{1}+\frac{1}{1}\\=\frac{-3-1+1}{7}\\=\frac{-3}{7}\)
10. \(+\left(\frac{-7}{-4}\right) +\left(\frac{-5}{9}\right) -\left(\frac{2}{10}\right)\\= \frac{7}{4}- \frac{5}{9}-\frac{2}{10}\\=\frac{7}{4}-\frac{5}{9}-\frac{1}{5}\\=\frac{315}{180}-\frac{100}{180}-\frac{36}{180}\\=\frac{315-100-36}{180}\\=\frac{179}{180}\)
11. \(+\left(\frac{-10}{-7}\right) +\left(\frac{-8}{6}\right) +\left(\frac{-6}{-12}\right)\\= \frac{10}{7}- \frac{8}{6}+\frac{6}{12}\\=\frac{10}{7}-\frac{4}{3}+\frac{1}{2}\\=\frac{60}{42}-\frac{56}{42}+\frac{21}{42}\\=\frac{60-56+21}{42}\\=\frac{25}{42}\)
12. \(+\left(\frac{9}{-4}\right) +\left(\frac{4}{-10}\right) +\left(\frac{-7}{6}\right)\\= \frac{-9}{4}- \frac{4}{10}-\frac{7}{6}\\=\frac{-9}{4}-\frac{2}{5}-\frac{7}{6}\\=\frac{-135}{60}-\frac{24}{60}-\frac{70}{60}\\=\frac{-135-24-70}{60}\\=\frac{-229}{60}\)