Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-9}\right) -\left(\frac{-9}{-4}\right) +\left(\frac{-11}{-7}\right)\\= \frac{10}{9}- \frac{9}{4}+\frac{11}{7}\\=\frac{280}{252}-\frac{567}{252}+\frac{396}{252}\\=\frac{280-567+396}{252}\\=\frac{109}{252}\)
2. \(+\left(\frac{7}{2}\right) +\left(\frac{5}{-4}\right) +\left(\frac{11}{7}\right)\\= \frac{7}{2}- \frac{5}{4}+\frac{11}{7}\\=\frac{98}{28}-\frac{35}{28}+\frac{44}{28}\\=\frac{98-35+44}{28}\\=\frac{107}{28}\)
3. \(-\left(\frac{-4}{3}\right) -\left(\frac{3}{8}\right) +\left(\frac{-8}{-11}\right)\\= \frac{4}{3}- \frac{3}{8}+\frac{8}{11}\\=\frac{352}{264}-\frac{99}{264}+\frac{192}{264}\\=\frac{352-99+192}{264}\\=\frac{445}{264}\)
4. \(+\left(\frac{-7}{-9}\right) +\left(\frac{3}{10}\right) -\left(\frac{12}{-2}\right)\\= \frac{7}{9}+ \frac{3}{10}+\frac{12}{2}\\=\frac{7}{9}+\frac{3}{10}+\frac{6}{1}\\=\frac{70}{90}+\frac{27}{90}+\frac{540}{90}\\=\frac{70+27+540}{90}\\=\frac{637}{90}\)
5. \(+\left(\frac{3}{-7}\right) +\left(\frac{5}{2}\right) -\left(\frac{-9}{2}\right)\\= \frac{-3}{7}+ \frac{5}{2}+\frac{9}{2}\\=\frac{-6}{14}+\frac{35}{14}+\frac{63}{14}\\=\frac{-6+35+63}{14}\\=\frac{92}{14}\\=\frac{46}{7}\)
6. \(-\left(\frac{-5}{-6}\right) -\left(\frac{9}{-6}\right) +\left(\frac{8}{-8}\right)\\= \frac{-5}{6}+ \frac{9}{6}-\frac{8}{8}\\=\frac{-5}{6}+\frac{3}{2}-\frac{1}{1}\\=\frac{-5+3-1}{6}\\=\frac{-3}{6}\\=\frac{-1}{2}\)
7. \(+\left(\frac{-9}{-4}\right) -\left(\frac{-5}{3}\right) +\left(\frac{11}{10}\right)\\= \frac{9}{4}+ \frac{5}{3}+\frac{11}{10}\\=\frac{135}{60}+\frac{100}{60}+\frac{66}{60}\\=\frac{135+100+66}{60}\\=\frac{301}{60}\)
8. \(+\left(\frac{7}{2}\right) +\left(\frac{-10}{-3}\right) +\left(\frac{-4}{-10}\right)\\= \frac{7}{2}+ \frac{10}{3}+\frac{4}{10}\\=\frac{7}{2}+\frac{10}{3}+\frac{2}{5}\\=\frac{105}{30}+\frac{100}{30}+\frac{12}{30}\\=\frac{105+100+12}{30}\\=\frac{217}{30}\)
9. \(-\left(\frac{6}{-5}\right) -\left(\frac{-9}{10}\right) -\left(\frac{-2}{-3}\right)\\= \frac{6}{5}+ \frac{9}{10}-\frac{2}{3}\\=\frac{36}{30}+\frac{27}{30}-\frac{20}{30}\\=\frac{36+27-20}{30}\\=\frac{43}{30}\)
10. \(+\left(\frac{6}{-5}\right) -\left(\frac{-5}{4}\right) +\left(\frac{-3}{-11}\right)\\= \frac{-6}{5}+ \frac{5}{4}+\frac{3}{11}\\=\frac{-264}{220}+\frac{275}{220}+\frac{60}{220}\\=\frac{-264+275+60}{220}\\=\frac{71}{220}\)
11. \(-\left(\frac{-8}{5}\right) -\left(\frac{-2}{-10}\right) -\left(\frac{2}{7}\right)\\= \frac{8}{5}- \frac{2}{10}-\frac{2}{7}\\=\frac{8}{5}-\frac{1}{5}-\frac{2}{7}\\=\frac{56}{35}-\frac{7}{35}-\frac{10}{35}\\=\frac{56-7-10}{35}\\=\frac{39}{35}\)
12. \(+\left(\frac{4}{-7}\right) -\left(\frac{8}{6}\right) -\left(\frac{-3}{3}\right)\\= \frac{-4}{7}- \frac{8}{6}+\frac{3}{3}\\=\frac{-4}{7}-\frac{4}{3}+\frac{1}{1}\\=\frac{-12}{21}-\frac{28}{21}+\frac{21}{21}\\=\frac{-12-28+21}{21}\\=\frac{-19}{21}\)