Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{-7}\right) -\left(\frac{-3}{2}\right) +\left(\frac{-4}{-10}\right)\\= \frac{6}{7}+ \frac{3}{2}+\frac{4}{10}\\=\frac{6}{7}+\frac{3}{2}+\frac{2}{5}\\=\frac{60}{70}+\frac{105}{70}+\frac{28}{70}\\=\frac{60+105+28}{70}\\=\frac{193}{70}\)
2. \(+\left(\frac{-3}{-2}\right) +\left(\frac{2}{9}\right) +\left(\frac{6}{11}\right)\\= \frac{3}{2}+ \frac{2}{9}+\frac{6}{11}\\=\frac{297}{198}+\frac{44}{198}+\frac{108}{198}\\=\frac{297+44+108}{198}\\=\frac{449}{198}\)
3. \(-\left(\frac{-7}{-3}\right) +\left(\frac{-10}{3}\right) +\left(\frac{-4}{11}\right)\\= \frac{-7}{3}- \frac{10}{3}-\frac{4}{11}\\=\frac{-77}{33}-\frac{110}{33}-\frac{12}{33}\\=\frac{-77-110-12}{33}\\=\frac{-199}{33}\)
4. \(-\left(\frac{-5}{8}\right) +\left(\frac{9}{6}\right) +\left(\frac{-4}{-6}\right)\\= \frac{5}{8}+ \frac{9}{6}+\frac{4}{6}\\=\frac{5}{8}+\frac{3}{2}+\frac{2}{3}\\=\frac{15}{24}+\frac{36}{24}+\frac{16}{24}\\=\frac{15+36+16}{24}\\=\frac{67}{24}\)
5. \(-\left(\frac{-7}{4}\right) -\left(\frac{8}{9}\right) -\left(\frac{7}{3}\right)\\= \frac{7}{4}- \frac{8}{9}-\frac{7}{3}\\=\frac{63}{36}-\frac{32}{36}-\frac{84}{36}\\=\frac{63-32-84}{36}\\=\frac{-53}{36}\)
6. \(-\left(\frac{10}{9}\right) -\left(\frac{-5}{-8}\right) -\left(\frac{-8}{11}\right)\\= \frac{-10}{9}- \frac{5}{8}+\frac{8}{11}\\=\frac{-880}{792}-\frac{495}{792}+\frac{576}{792}\\=\frac{-880-495+576}{792}\\=\frac{-799}{792}\)
7. \(+\left(\frac{-4}{-7}\right) +\left(\frac{3}{10}\right) +\left(\frac{9}{11}\right)\\= \frac{4}{7}+ \frac{3}{10}+\frac{9}{11}\\=\frac{440}{770}+\frac{231}{770}+\frac{630}{770}\\=\frac{440+231+630}{770}\\=\frac{1301}{770}\)
8. \(+\left(\frac{-10}{-9}\right) -\left(\frac{8}{5}\right) -\left(\frac{10}{9}\right)\\= \frac{10}{9}- \frac{8}{5}-\frac{10}{9}\\=\frac{50}{45}-\frac{72}{45}-\frac{50}{45}\\=\frac{50-72-50}{45}\\=\frac{-72}{45}\\=\frac{-8}{5}\)
9. \(-\left(\frac{2}{-5}\right) -\left(\frac{9}{7}\right) +\left(\frac{3}{-3}\right)\\= \frac{2}{5}- \frac{9}{7}-\frac{3}{3}\\=\frac{2}{5}-\frac{9}{7}-\frac{1}{1}\\=\frac{14}{35}-\frac{45}{35}-\frac{35}{35}\\=\frac{14-45-35}{35}\\=\frac{-66}{35}\)
10. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-9}{9}\right) -\left(\frac{4}{5}\right)\\= \frac{-6}{5}+ \frac{9}{9}-\frac{4}{5}\\=\frac{-6}{5}+\frac{1}{1}-\frac{4}{5}\\=\frac{-6+1-4}{5}\\=\frac{-9}{5}\)
11. \(-\left(\frac{10}{-9}\right) +\left(\frac{2}{6}\right) +\left(\frac{11}{-7}\right)\\= \frac{10}{9}+ \frac{2}{6}-\frac{11}{7}\\=\frac{10}{9}+\frac{1}{3}-\frac{11}{7}\\=\frac{70}{63}+\frac{21}{63}-\frac{99}{63}\\=\frac{70+21-99}{63}\\=\frac{-8}{63}\)
12. \(+\left(\frac{-9}{-4}\right) +\left(\frac{-2}{10}\right) +\left(\frac{-6}{-9}\right)\\= \frac{9}{4}- \frac{2}{10}+\frac{6}{9}\\=\frac{9}{4}-\frac{1}{5}+\frac{2}{3}\\=\frac{135}{60}-\frac{12}{60}+\frac{40}{60}\\=\frac{135-12+40}{60}\\=\frac{163}{60}\)