Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{7}\right) +\left(\frac{8}{-4}\right) +\left(\frac{7}{-3}\right)\\= \frac{-2}{7}- \frac{8}{4}-\frac{7}{3}\\=\frac{-2}{7}-\frac{2}{1}-\frac{7}{3}\\=\frac{-6}{21}-\frac{42}{21}-\frac{49}{21}\\=\frac{-6-42-49}{21}\\=\frac{-97}{21}\)
2. \(-\left(\frac{10}{7}\right) +\left(\frac{7}{2}\right) +\left(\frac{-9}{11}\right)\\= \frac{-10}{7}+ \frac{7}{2}-\frac{9}{11}\\=\frac{-220}{154}+\frac{539}{154}-\frac{126}{154}\\=\frac{-220+539-126}{154}\\=\frac{193}{154}\)
3. \(+\left(\frac{-10}{7}\right) +\left(\frac{-7}{4}\right) -\left(\frac{-11}{11}\right)\\= \frac{-10}{7}- \frac{7}{4}+\frac{11}{11}\\=\frac{-10}{7}-\frac{7}{4}+\frac{1}{1}\\=\frac{-40}{28}-\frac{49}{28}+\frac{28}{28}\\=\frac{-40-49+28}{28}\\=\frac{-61}{28}\)
4. \(+\left(\frac{6}{-5}\right) +\left(\frac{-10}{-5}\right) +\left(\frac{6}{-3}\right)\\= \frac{-6}{5}+ \frac{10}{5}-\frac{6}{3}\\=\frac{-6}{5}+\frac{2}{1}-\frac{2}{1}\\=\frac{-6+2-2}{5}\\=\frac{-6}{5}\)
5. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-9}{-10}\right) -\left(\frac{8}{-2}\right)\\= \frac{-10}{7}+ \frac{9}{10}+\frac{8}{2}\\=\frac{-10}{7}+\frac{9}{10}+\frac{4}{1}\\=\frac{-100}{70}+\frac{63}{70}+\frac{280}{70}\\=\frac{-100+63+280}{70}\\=\frac{243}{70}\)
6. \(+\left(\frac{-4}{-3}\right) -\left(\frac{-2}{3}\right) -\left(\frac{-8}{-9}\right)\\= \frac{4}{3}+ \frac{2}{3}-\frac{8}{9}\\=\frac{12}{9}+\frac{6}{9}-\frac{8}{9}\\=\frac{12+6-8}{9}\\=\frac{10}{9}\)
7. \(-\left(\frac{-10}{-7}\right) -\left(\frac{-10}{-7}\right) -\left(\frac{-11}{6}\right)\\= \frac{-10}{7}- \frac{10}{7}+\frac{11}{6}\\=\frac{-60}{42}-\frac{60}{42}+\frac{77}{42}\\=\frac{-60-60+77}{42}\\=\frac{-43}{42}\)
8. \(+\left(\frac{-3}{5}\right) +\left(\frac{7}{-5}\right) +\left(\frac{5}{11}\right)\\= \frac{-3}{5}- \frac{7}{5}+\frac{5}{11}\\=\frac{-33}{55}-\frac{77}{55}+\frac{25}{55}\\=\frac{-33-77+25}{55}\\=\frac{-85}{55}\\=\frac{-17}{11}\)
9. \(+\left(\frac{-5}{-2}\right) -\left(\frac{-8}{6}\right) -\left(\frac{3}{-6}\right)\\= \frac{5}{2}+ \frac{8}{6}+\frac{3}{6}\\=\frac{5}{2}+\frac{4}{3}+\frac{1}{2}\\=\frac{15}{6}+\frac{8}{6}+\frac{3}{6}\\=\frac{15+8+3}{6}\\=\frac{26}{6}\\=\frac{13}{3}\)
10. \(-\left(\frac{10}{-7}\right) +\left(\frac{-10}{8}\right) +\left(\frac{10}{-7}\right)\\= \frac{10}{7}- \frac{10}{8}-\frac{10}{7}\\=\frac{10}{7}-\frac{5}{4}-\frac{10}{7}\\=\frac{40}{28}-\frac{35}{28}-\frac{40}{28}\\=\frac{40-35-40}{28}\\=\frac{-35}{28}\\=\frac{-5}{4}\)
11. \(+\left(\frac{-6}{5}\right) -\left(\frac{-3}{6}\right) +\left(\frac{-8}{-12}\right)\\= \frac{-6}{5}+ \frac{3}{6}+\frac{8}{12}\\=\frac{-6}{5}+\frac{1}{2}+\frac{2}{3}\\=\frac{-36}{30}+\frac{15}{30}+\frac{20}{30}\\=\frac{-36+15+20}{30}\\=\frac{-1}{30}\)
12. \(-\left(\frac{2}{-7}\right) +\left(\frac{9}{5}\right) -\left(\frac{2}{-8}\right)\\= \frac{2}{7}+ \frac{9}{5}+\frac{2}{8}\\=\frac{2}{7}+\frac{9}{5}+\frac{1}{4}\\=\frac{40}{140}+\frac{252}{140}+\frac{35}{140}\\=\frac{40+252+35}{140}\\=\frac{327}{140}\)