Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{-9}\right) -\left(\frac{-10}{8}\right) -\left(\frac{-10}{-4}\right)\\= \frac{8}{9}+ \frac{10}{8}-\frac{10}{4}\\=\frac{8}{9}+\frac{5}{4}-\frac{5}{2}\\=\frac{32}{36}+\frac{45}{36}-\frac{90}{36}\\=\frac{32+45-90}{36}\\=\frac{-13}{36}\)
2. \(+\left(\frac{-8}{-7}\right) +\left(\frac{-7}{-7}\right) -\left(\frac{11}{5}\right)\\= \frac{8}{7}+ \frac{7}{7}-\frac{11}{5}\\=\frac{8}{7}+\frac{1}{1}-\frac{11}{5}\\=\frac{40}{35}+\frac{35}{35}-\frac{77}{35}\\=\frac{40+35-77}{35}\\=\frac{-2}{35}\)
3. \(-\left(\frac{3}{2}\right) +\left(\frac{10}{8}\right) +\left(\frac{-5}{-3}\right)\\= \frac{-3}{2}+ \frac{10}{8}+\frac{5}{3}\\=\frac{-3}{2}+\frac{5}{4}+\frac{5}{3}\\=\frac{-18}{12}+\frac{15}{12}+\frac{20}{12}\\=\frac{-18+15+20}{12}\\=\frac{17}{12}\)
4. \(-\left(\frac{9}{-2}\right) -\left(\frac{-3}{-7}\right) -\left(\frac{-5}{10}\right)\\= \frac{9}{2}- \frac{3}{7}+\frac{5}{10}\\=\frac{9}{2}-\frac{3}{7}+\frac{1}{2}\\=\frac{63}{14}-\frac{6}{14}+\frac{7}{14}\\=\frac{63-6+7}{14}\\=\frac{64}{14}\\=\frac{32}{7}\)
5. \(-\left(\frac{5}{-6}\right) +\left(\frac{-2}{2}\right) +\left(\frac{4}{-4}\right)\\= \frac{5}{6}- \frac{2}{2}-\frac{4}{4}\\=\frac{5}{6}-\frac{1}{1}-\frac{1}{1}\\=\frac{5-1-1}{6}\\=\frac{3}{6}\\=\frac{1}{2}\)
6. \(+\left(\frac{-10}{7}\right) -\left(\frac{-7}{-9}\right) -\left(\frac{3}{-12}\right)\\= \frac{-10}{7}- \frac{7}{9}+\frac{3}{12}\\=\frac{-10}{7}-\frac{7}{9}+\frac{1}{4}\\=\frac{-360}{252}-\frac{196}{252}+\frac{63}{252}\\=\frac{-360-196+63}{252}\\=\frac{-493}{252}\)
7. \(-\left(\frac{3}{5}\right) +\left(\frac{-7}{8}\right) +\left(\frac{-8}{-6}\right)\\= \frac{-3}{5}- \frac{7}{8}+\frac{8}{6}\\=\frac{-3}{5}-\frac{7}{8}+\frac{4}{3}\\=\frac{-72}{120}-\frac{105}{120}+\frac{160}{120}\\=\frac{-72-105+160}{120}\\=\frac{-17}{120}\)
8. \(-\left(\frac{4}{-7}\right) +\left(\frac{2}{-3}\right) +\left(\frac{7}{11}\right)\\= \frac{4}{7}- \frac{2}{3}+\frac{7}{11}\\=\frac{132}{231}-\frac{154}{231}+\frac{147}{231}\\=\frac{132-154+147}{231}\\=\frac{125}{231}\)
9. \(+\left(\frac{-4}{-3}\right) +\left(\frac{9}{-3}\right) -\left(\frac{8}{8}\right)\\= \frac{4}{3}- \frac{9}{3}-\frac{8}{8}\\=\frac{4}{3}-\frac{3}{1}-\frac{1}{1}\\=\frac{4-3-1}{3}\\=\frac{0}{3}\\=\frac{0}{1}\)
10. \(+\left(\frac{-6}{5}\right) -\left(\frac{8}{-9}\right) -\left(\frac{9}{5}\right)\\= \frac{-6}{5}+ \frac{8}{9}-\frac{9}{5}\\=\frac{-54}{45}+\frac{40}{45}-\frac{81}{45}\\=\frac{-54+40-81}{45}\\=\frac{-95}{45}\\=\frac{-19}{9}\)
11. \(-\left(\frac{4}{7}\right) +\left(\frac{-4}{-7}\right) -\left(\frac{-3}{3}\right)\\= \frac{-4}{7}+ \frac{4}{7}+\frac{3}{3}\\=\frac{-4}{7}+\frac{4}{7}+\frac{1}{1}\\=\frac{-4+4+1}{7}\\=\frac{1}{7}\)
12. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-6}{-7}\right) -\left(\frac{-12}{-6}\right)\\= \frac{-6}{5}+ \frac{6}{7}-\frac{12}{6}\\=\frac{-6}{5}+\frac{6}{7}-\frac{2}{1}\\=\frac{-42}{35}+\frac{30}{35}-\frac{70}{35}\\=\frac{-42+30-70}{35}\\=\frac{-82}{35}\)