Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{2}\right) -\left(\frac{2}{4}\right) +\left(\frac{-4}{-8}\right)\\= \frac{9}{2}- \frac{2}{4}+\frac{4}{8}\\=\frac{9}{2}-\frac{1}{2}+\frac{1}{2}\\=\frac{9-1+1}{2}\\=\frac{9}{2}\)
2. \(+\left(\frac{-7}{3}\right) -\left(\frac{10}{3}\right) -\left(\frac{-9}{-10}\right)\\= \frac{-7}{3}- \frac{10}{3}-\frac{9}{10}\\=\frac{-70}{30}-\frac{100}{30}-\frac{27}{30}\\=\frac{-70-100-27}{30}\\=\frac{-197}{30}\)
3. \(+\left(\frac{-2}{-3}\right) -\left(\frac{-10}{3}\right) +\left(\frac{-9}{8}\right)\\= \frac{2}{3}+ \frac{10}{3}-\frac{9}{8}\\=\frac{16}{24}+\frac{80}{24}-\frac{27}{24}\\=\frac{16+80-27}{24}\\=\frac{69}{24}\\=\frac{23}{8}\)
4. \(-\left(\frac{10}{9}\right) -\left(\frac{7}{-9}\right) -\left(\frac{-11}{-5}\right)\\= \frac{-10}{9}+ \frac{7}{9}-\frac{11}{5}\\=\frac{-50}{45}+\frac{35}{45}-\frac{99}{45}\\=\frac{-50+35-99}{45}\\=\frac{-114}{45}\\=\frac{-38}{15}\)
5. \(+\left(\frac{-2}{3}\right) +\left(\frac{-3}{2}\right) +\left(\frac{-2}{11}\right)\\= \frac{-2}{3}- \frac{3}{2}-\frac{2}{11}\\=\frac{-44}{66}-\frac{99}{66}-\frac{12}{66}\\=\frac{-44-99-12}{66}\\=\frac{-155}{66}\)
6. \(-\left(\frac{-7}{-4}\right) -\left(\frac{-10}{7}\right) +\left(\frac{-2}{6}\right)\\= \frac{-7}{4}+ \frac{10}{7}-\frac{2}{6}\\=\frac{-7}{4}+\frac{10}{7}-\frac{1}{3}\\=\frac{-147}{84}+\frac{120}{84}-\frac{28}{84}\\=\frac{-147+120-28}{84}\\=\frac{-55}{84}\)
7. \(+\left(\frac{4}{-7}\right) -\left(\frac{3}{-6}\right) +\left(\frac{-6}{-7}\right)\\= \frac{-4}{7}+ \frac{3}{6}+\frac{6}{7}\\=\frac{-4}{7}+\frac{1}{2}+\frac{6}{7}\\=\frac{-8}{14}+\frac{7}{14}+\frac{12}{14}\\=\frac{-8+7+12}{14}\\=\frac{11}{14}\)
8. \(+\left(\frac{7}{8}\right) -\left(\frac{5}{5}\right) -\left(\frac{3}{-12}\right)\\= \frac{7}{8}- \frac{5}{5}+\frac{3}{12}\\=\frac{7}{8}-\frac{1}{1}+\frac{1}{4}\\=\frac{7-1+1}{8}\\=\frac{7}{8}\)
9. \(-\left(\frac{3}{-4}\right) -\left(\frac{-8}{6}\right) +\left(\frac{3}{3}\right)\\= \frac{3}{4}+ \frac{8}{6}+\frac{3}{3}\\=\frac{3}{4}+\frac{4}{3}+\frac{1}{1}\\=\frac{9}{12}+\frac{16}{12}+\frac{12}{12}\\=\frac{9+16+12}{12}\\=\frac{37}{12}\)
10. \(+\left(\frac{10}{9}\right) -\left(\frac{4}{-4}\right) -\left(\frac{6}{11}\right)\\= \frac{10}{9}+ \frac{4}{4}-\frac{6}{11}\\=\frac{10}{9}+\frac{1}{1}-\frac{6}{11}\\=\frac{110}{99}+\frac{99}{99}-\frac{54}{99}\\=\frac{110+99-54}{99}\\=\frac{155}{99}\)
11. \(+\left(\frac{-7}{9}\right) -\left(\frac{9}{10}\right) -\left(\frac{6}{-3}\right)\\= \frac{-7}{9}- \frac{9}{10}+\frac{6}{3}\\=\frac{-7}{9}-\frac{9}{10}+\frac{2}{1}\\=\frac{-70}{90}-\frac{81}{90}+\frac{180}{90}\\=\frac{-70-81+180}{90}\\=\frac{29}{90}\)
12. \(+\left(\frac{10}{-7}\right) +\left(\frac{7}{-5}\right) -\left(\frac{4}{12}\right)\\= \frac{-10}{7}- \frac{7}{5}-\frac{4}{12}\\=\frac{-10}{7}-\frac{7}{5}-\frac{1}{3}\\=\frac{-150}{105}-\frac{147}{105}-\frac{35}{105}\\=\frac{-150-147-35}{105}\\=\frac{-332}{105}\)