Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{-7}\right) -\left(\frac{-2}{-7}\right) -\left(\frac{-9}{10}\right)\\= \frac{-10}{7}- \frac{2}{7}+\frac{9}{10}\\=\frac{-100}{70}-\frac{20}{70}+\frac{63}{70}\\=\frac{-100-20+63}{70}\\=\frac{-57}{70}\)
2. \(+\left(\frac{2}{3}\right) +\left(\frac{-7}{7}\right) -\left(\frac{-2}{-5}\right)\\= \frac{2}{3}- \frac{7}{7}-\frac{2}{5}\\=\frac{2}{3}-\frac{1}{1}-\frac{2}{5}\\=\frac{10}{15}-\frac{15}{15}-\frac{6}{15}\\=\frac{10-15-6}{15}\\=\frac{-11}{15}\)
3. \(+\left(\frac{10}{9}\right) +\left(\frac{10}{-9}\right) +\left(\frac{-4}{11}\right)\\= \frac{10}{9}- \frac{10}{9}-\frac{4}{11}\\=\frac{110}{99}-\frac{110}{99}-\frac{36}{99}\\=\frac{110-110-36}{99}\\=\frac{-36}{99}\\=\frac{-4}{11}\)
4. \(-\left(\frac{-5}{8}\right) -\left(\frac{2}{-4}\right) -\left(\frac{-9}{3}\right)\\= \frac{5}{8}+ \frac{2}{4}+\frac{9}{3}\\=\frac{5}{8}+\frac{1}{2}+\frac{3}{1}\\=\frac{5+1+3}{8}\\=\frac{9}{8}\)
5. \(+\left(\frac{6}{-7}\right) +\left(\frac{2}{-2}\right) +\left(\frac{-6}{-5}\right)\\= \frac{-6}{7}- \frac{2}{2}+\frac{6}{5}\\=\frac{-6}{7}-\frac{1}{1}+\frac{6}{5}\\=\frac{-30}{35}-\frac{35}{35}+\frac{42}{35}\\=\frac{-30-35+42}{35}\\=\frac{-23}{35}\)
6. \(-\left(\frac{8}{-3}\right) -\left(\frac{-9}{-5}\right) +\left(\frac{-11}{-5}\right)\\= \frac{8}{3}- \frac{9}{5}+\frac{11}{5}\\=\frac{40}{15}-\frac{27}{15}+\frac{33}{15}\\=\frac{40-27+33}{15}\\=\frac{46}{15}\)
7. \(-\left(\frac{7}{-9}\right) +\left(\frac{5}{9}\right) +\left(\frac{8}{-3}\right)\\= \frac{7}{9}+ \frac{5}{9}-\frac{8}{3}\\=\frac{7+5-8}{9}\\=\frac{4}{9}\)
8. \(-\left(\frac{8}{-3}\right) -\left(\frac{-4}{10}\right) +\left(\frac{8}{-2}\right)\\= \frac{8}{3}+ \frac{4}{10}-\frac{8}{2}\\=\frac{8}{3}+\frac{2}{5}-\frac{4}{1}\\=\frac{40}{15}+\frac{6}{15}-\frac{60}{15}\\=\frac{40+6-60}{15}\\=\frac{-14}{15}\)
9. \(-\left(\frac{-6}{-5}\right) +\left(\frac{10}{9}\right) +\left(\frac{5}{2}\right)\\= \frac{-6}{5}+ \frac{10}{9}+\frac{5}{2}\\=\frac{-108}{90}+\frac{100}{90}+\frac{225}{90}\\=\frac{-108+100+225}{90}\\=\frac{217}{90}\)
10. \(+\left(\frac{3}{-5}\right) +\left(\frac{-7}{-2}\right) -\left(\frac{5}{12}\right)\\= \frac{-3}{5}+ \frac{7}{2}-\frac{5}{12}\\=\frac{-36}{60}+\frac{210}{60}-\frac{25}{60}\\=\frac{-36+210-25}{60}\\=\frac{149}{60}\)
11. \(+\left(\frac{10}{-3}\right) -\left(\frac{-4}{3}\right) -\left(\frac{6}{-4}\right)\\= \frac{-10}{3}+ \frac{4}{3}+\frac{6}{4}\\=\frac{-10}{3}+\frac{4}{3}+\frac{3}{2}\\=\frac{-20}{6}+\frac{8}{6}+\frac{9}{6}\\=\frac{-20+8+9}{6}\\=\frac{-3}{6}\\=\frac{-1}{2}\)
12. \(+\left(\frac{9}{4}\right) +\left(\frac{-5}{-4}\right) +\left(\frac{5}{9}\right)\\= \frac{9}{4}+ \frac{5}{4}+\frac{5}{9}\\=\frac{81}{36}+\frac{45}{36}+\frac{20}{36}\\=\frac{81+45+20}{36}\\=\frac{146}{36}\\=\frac{73}{18}\)