Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{-9}\right) +\left(\frac{10}{-4}\right) -\left(\frac{-10}{-3}\right)\\= \frac{2}{9}- \frac{10}{4}-\frac{10}{3}\\=\frac{2}{9}-\frac{5}{2}-\frac{10}{3}\\=\frac{4}{18}-\frac{45}{18}-\frac{60}{18}\\=\frac{4-45-60}{18}\\=\frac{-101}{18}\)
2. \(+\left(\frac{9}{-7}\right) +\left(\frac{5}{-8}\right) -\left(\frac{4}{10}\right)\\= \frac{-9}{7}- \frac{5}{8}-\frac{4}{10}\\=\frac{-9}{7}-\frac{5}{8}-\frac{2}{5}\\=\frac{-360}{280}-\frac{175}{280}-\frac{112}{280}\\=\frac{-360-175-112}{280}\\=\frac{-647}{280}\)
3. \(+\left(\frac{-10}{-7}\right) -\left(\frac{-9}{-9}\right) +\left(\frac{-6}{-5}\right)\\= \frac{10}{7}- \frac{9}{9}+\frac{6}{5}\\=\frac{10}{7}-\frac{1}{1}+\frac{6}{5}\\=\frac{50}{35}-\frac{35}{35}+\frac{42}{35}\\=\frac{50-35+42}{35}\\=\frac{57}{35}\)
4. \(-\left(\frac{5}{-8}\right) +\left(\frac{9}{5}\right) +\left(\frac{6}{-3}\right)\\= \frac{5}{8}+ \frac{9}{5}-\frac{6}{3}\\=\frac{5}{8}+\frac{9}{5}-\frac{2}{1}\\=\frac{25}{40}+\frac{72}{40}-\frac{80}{40}\\=\frac{25+72-80}{40}\\=\frac{17}{40}\)
5. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-6}{-9}\right) +\left(\frac{-2}{10}\right)\\= \frac{6}{5}+ \frac{6}{9}-\frac{2}{10}\\=\frac{6}{5}+\frac{2}{3}-\frac{1}{5}\\=\frac{18}{15}+\frac{10}{15}-\frac{3}{15}\\=\frac{18+10-3}{15}\\=\frac{25}{15}\\=\frac{5}{3}\)
6. \(+\left(\frac{-4}{-3}\right) -\left(\frac{-10}{5}\right) -\left(\frac{7}{6}\right)\\= \frac{4}{3}+ \frac{10}{5}-\frac{7}{6}\\=\frac{4}{3}+\frac{2}{1}-\frac{7}{6}\\=\frac{8}{6}+\frac{12}{6}-\frac{7}{6}\\=\frac{8+12-7}{6}\\=\frac{13}{6}\)
7. \(+\left(\frac{-5}{6}\right) +\left(\frac{6}{4}\right) -\left(\frac{9}{-10}\right)\\= \frac{-5}{6}+ \frac{6}{4}+\frac{9}{10}\\=\frac{-5}{6}+\frac{3}{2}+\frac{9}{10}\\=\frac{-25}{30}+\frac{45}{30}+\frac{27}{30}\\=\frac{-25+45+27}{30}\\=\frac{47}{30}\)
8. \(+\left(\frac{-5}{-6}\right) +\left(\frac{-2}{-6}\right) -\left(\frac{3}{-8}\right)\\= \frac{5}{6}+ \frac{2}{6}+\frac{3}{8}\\=\frac{5}{6}+\frac{1}{3}+\frac{3}{8}\\=\frac{20}{24}+\frac{8}{24}+\frac{9}{24}\\=\frac{20+8+9}{24}\\=\frac{37}{24}\)
9. \(-\left(\frac{7}{4}\right) -\left(\frac{9}{-7}\right) +\left(\frac{-12}{-11}\right)\\= \frac{-7}{4}+ \frac{9}{7}+\frac{12}{11}\\=\frac{-539}{308}+\frac{396}{308}+\frac{336}{308}\\=\frac{-539+396+336}{308}\\=\frac{193}{308}\)
10. \(+\left(\frac{2}{7}\right) +\left(\frac{-8}{-7}\right) +\left(\frac{-2}{-7}\right)\\= \frac{2}{7}+ \frac{8}{7}+\frac{2}{7}\\=\frac{2+8+2}{7}\\=\frac{12}{7}\)
11. \(-\left(\frac{7}{2}\right) +\left(\frac{2}{2}\right) -\left(\frac{-9}{-3}\right)\\= \frac{-7}{2}+ \frac{2}{2}-\frac{9}{3}\\=\frac{-7}{2}+\frac{1}{1}-\frac{3}{1}\\=\frac{-7+1-3}{2}\\=\frac{-9}{2}\)
12. \(+\left(\frac{7}{-5}\right) -\left(\frac{-9}{9}\right) -\left(\frac{9}{3}\right)\\= \frac{-7}{5}+ \frac{9}{9}-\frac{9}{3}\\=\frac{-7}{5}+\frac{1}{1}-\frac{3}{1}\\=\frac{-7+1-3}{5}\\=\frac{-9}{5}\)