Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-8}{-7}\right) -\left(\frac{5}{-10}\right) +\left(\frac{10}{-11}\right)\\= \frac{-8}{7}+ \frac{5}{10}-\frac{10}{11}\\=\frac{-8}{7}+\frac{1}{2}-\frac{10}{11}\\=\frac{-176}{154}+\frac{77}{154}-\frac{140}{154}\\=\frac{-176+77-140}{154}\\=\frac{-239}{154}\)
2. \(-\left(\frac{-9}{4}\right) -\left(\frac{-4}{4}\right) +\left(\frac{5}{-4}\right)\\= \frac{9}{4}+ \frac{4}{4}-\frac{5}{4}\\=\frac{9}{4}+\frac{1}{1}-\frac{5}{4}\\=\frac{9+1-5}{4}\\=\frac{5}{4}\)
3. \(+\left(\frac{5}{-4}\right) +\left(\frac{-4}{-2}\right) -\left(\frac{3}{2}\right)\\= \frac{-5}{4}+ \frac{4}{2}-\frac{3}{2}\\=\frac{-5}{4}+\frac{2}{1}-\frac{3}{2}\\=\frac{-5+2-3}{4}\\=\frac{-6}{4}\\=\frac{-3}{2}\)
4. \(+\left(\frac{-7}{-9}\right) +\left(\frac{2}{6}\right) +\left(\frac{-12}{11}\right)\\= \frac{7}{9}+ \frac{2}{6}-\frac{12}{11}\\=\frac{7}{9}+\frac{1}{3}-\frac{12}{11}\\=\frac{77}{99}+\frac{33}{99}-\frac{108}{99}\\=\frac{77+33-108}{99}\\=\frac{2}{99}\)
5. \(-\left(\frac{-2}{-5}\right) -\left(\frac{-9}{6}\right) -\left(\frac{-6}{8}\right)\\= \frac{-2}{5}+ \frac{9}{6}+\frac{6}{8}\\=\frac{-2}{5}+\frac{3}{2}+\frac{3}{4}\\=\frac{-8}{20}+\frac{30}{20}+\frac{15}{20}\\=\frac{-8+30+15}{20}\\=\frac{37}{20}\)
6. \(-\left(\frac{2}{-3}\right) -\left(\frac{8}{-8}\right) -\left(\frac{10}{-10}\right)\\= \frac{2}{3}+ \frac{8}{8}+\frac{10}{10}\\=\frac{2}{3}+\frac{1}{1}+\frac{1}{1}\\=\frac{2+1+1}{3}\\=\frac{4}{3}\)
7. \(-\left(\frac{7}{5}\right) -\left(\frac{-5}{3}\right) +\left(\frac{5}{-12}\right)\\= \frac{-7}{5}+ \frac{5}{3}-\frac{5}{12}\\=\frac{-84}{60}+\frac{100}{60}-\frac{25}{60}\\=\frac{-84+100-25}{60}\\=\frac{-9}{60}\\=\frac{-3}{20}\)
8. \(-\left(\frac{10}{-3}\right) +\left(\frac{-10}{9}\right) +\left(\frac{-3}{8}\right)\\= \frac{10}{3}- \frac{10}{9}-\frac{3}{8}\\=\frac{240}{72}-\frac{80}{72}-\frac{27}{72}\\=\frac{240-80-27}{72}\\=\frac{133}{72}\)
9. \(+\left(\frac{-10}{9}\right) +\left(\frac{3}{8}\right) +\left(\frac{-7}{12}\right)\\= \frac{-10}{9}+ \frac{3}{8}-\frac{7}{12}\\=\frac{-80}{72}+\frac{27}{72}-\frac{42}{72}\\=\frac{-80+27-42}{72}\\=\frac{-95}{72}\)
10. \(-\left(\frac{-6}{5}\right) +\left(\frac{10}{3}\right) +\left(\frac{-7}{4}\right)\\= \frac{6}{5}+ \frac{10}{3}-\frac{7}{4}\\=\frac{72}{60}+\frac{200}{60}-\frac{105}{60}\\=\frac{72+200-105}{60}\\=\frac{167}{60}\)
11. \(+\left(\frac{-9}{-7}\right) -\left(\frac{6}{-3}\right) -\left(\frac{-8}{11}\right)\\= \frac{9}{7}+ \frac{6}{3}+\frac{8}{11}\\=\frac{9}{7}+\frac{2}{1}+\frac{8}{11}\\=\frac{99}{77}+\frac{154}{77}+\frac{56}{77}\\=\frac{99+154+56}{77}\\=\frac{309}{77}\)
12. \(-\left(\frac{-8}{-9}\right) +\left(\frac{-3}{9}\right) +\left(\frac{-5}{10}\right)\\= \frac{-8}{9}- \frac{3}{9}-\frac{5}{10}\\=\frac{-8}{9}-\frac{1}{3}-\frac{1}{2}\\=\frac{-16}{18}-\frac{6}{18}-\frac{9}{18}\\=\frac{-16-6-9}{18}\\=\frac{-31}{18}\)