Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{8}\right) -\left(\frac{-10}{4}\right) -\left(\frac{-9}{12}\right)\\= \frac{3}{8}+ \frac{10}{4}+\frac{9}{12}\\=\frac{3}{8}+\frac{5}{2}+\frac{3}{4}\\=\frac{3+5+3}{8}\\=\frac{11}{8}\)
2. \(+\left(\frac{-9}{2}\right) +\left(\frac{9}{3}\right) +\left(\frac{2}{-10}\right)\\= \frac{-9}{2}+ \frac{9}{3}-\frac{2}{10}\\=\frac{-9}{2}+\frac{3}{1}-\frac{1}{5}\\=\frac{-45}{10}+\frac{30}{10}-\frac{2}{10}\\=\frac{-45+30-2}{10}\\=\frac{-17}{10}\)
3. \(+\left(\frac{-7}{-9}\right) +\left(\frac{5}{-3}\right) -\left(\frac{-6}{3}\right)\\= \frac{7}{9}- \frac{5}{3}+\frac{6}{3}\\=\frac{7}{9}-\frac{5}{3}+\frac{2}{1}\\=\frac{7-5+2}{9}\\=\frac{4}{9}\)
4. \(-\left(\frac{6}{5}\right) -\left(\frac{-9}{10}\right) +\left(\frac{10}{-9}\right)\\= \frac{-6}{5}+ \frac{9}{10}-\frac{10}{9}\\=\frac{-108}{90}+\frac{81}{90}-\frac{100}{90}\\=\frac{-108+81-100}{90}\\=\frac{-127}{90}\)
5. \(+\left(\frac{-7}{-6}\right) -\left(\frac{-6}{-8}\right) +\left(\frac{9}{-2}\right)\\= \frac{7}{6}- \frac{6}{8}-\frac{9}{2}\\=\frac{7}{6}-\frac{3}{4}-\frac{9}{2}\\=\frac{14}{12}-\frac{9}{12}-\frac{54}{12}\\=\frac{14-9-54}{12}\\=\frac{-49}{12}\)
6. \(+\left(\frac{-4}{-9}\right) +\left(\frac{5}{2}\right) -\left(\frac{10}{3}\right)\\= \frac{4}{9}+ \frac{5}{2}-\frac{10}{3}\\=\frac{8}{18}+\frac{45}{18}-\frac{60}{18}\\=\frac{8+45-60}{18}\\=\frac{-7}{18}\)
7. \(+\left(\frac{10}{-7}\right) -\left(\frac{-3}{-10}\right) +\left(\frac{5}{-7}\right)\\= \frac{-10}{7}- \frac{3}{10}-\frac{5}{7}\\=\frac{-100}{70}-\frac{21}{70}-\frac{50}{70}\\=\frac{-100-21-50}{70}\\=\frac{-171}{70}\)
8. \(-\left(\frac{2}{9}\right) +\left(\frac{-3}{-6}\right) -\left(\frac{8}{-6}\right)\\= \frac{-2}{9}+ \frac{3}{6}+\frac{8}{6}\\=\frac{-2}{9}+\frac{1}{2}+\frac{4}{3}\\=\frac{-4}{18}+\frac{9}{18}+\frac{24}{18}\\=\frac{-4+9+24}{18}\\=\frac{29}{18}\)
9. \(+\left(\frac{-3}{-7}\right) +\left(\frac{-5}{-5}\right) +\left(\frac{-6}{-4}\right)\\= \frac{3}{7}+ \frac{5}{5}+\frac{6}{4}\\=\frac{3}{7}+\frac{1}{1}+\frac{3}{2}\\=\frac{6}{14}+\frac{14}{14}+\frac{21}{14}\\=\frac{6+14+21}{14}\\=\frac{41}{14}\)
10. \(+\left(\frac{2}{5}\right) -\left(\frac{4}{-8}\right) +\left(\frac{-11}{-3}\right)\\= \frac{2}{5}+ \frac{4}{8}+\frac{11}{3}\\=\frac{2}{5}+\frac{1}{2}+\frac{11}{3}\\=\frac{12}{30}+\frac{15}{30}+\frac{110}{30}\\=\frac{12+15+110}{30}\\=\frac{137}{30}\)
11. \(-\left(\frac{3}{2}\right) +\left(\frac{-7}{-6}\right) -\left(\frac{-4}{9}\right)\\= \frac{-3}{2}+ \frac{7}{6}+\frac{4}{9}\\=\frac{-27}{18}+\frac{21}{18}+\frac{8}{18}\\=\frac{-27+21+8}{18}\\=\frac{2}{18}\\=\frac{1}{9}\)
12. \(-\left(\frac{9}{-7}\right) -\left(\frac{9}{-10}\right) -\left(\frac{-11}{-8}\right)\\= \frac{9}{7}+ \frac{9}{10}-\frac{11}{8}\\=\frac{360}{280}+\frac{252}{280}-\frac{385}{280}\\=\frac{360+252-385}{280}\\=\frac{227}{280}\)