Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{7}\right) +\left(\frac{8}{-8}\right) +\left(\frac{11}{-8}\right)\\= \frac{9}{7}- \frac{8}{8}-\frac{11}{8}\\=\frac{9}{7}-\frac{1}{1}-\frac{11}{8}\\=\frac{72}{56}-\frac{56}{56}-\frac{77}{56}\\=\frac{72-56-77}{56}\\=\frac{-61}{56}\)
2. \(+\left(\frac{4}{-3}\right) -\left(\frac{8}{-7}\right) +\left(\frac{9}{8}\right)\\= \frac{-4}{3}+ \frac{8}{7}+\frac{9}{8}\\=\frac{-224}{168}+\frac{192}{168}+\frac{189}{168}\\=\frac{-224+192+189}{168}\\=\frac{157}{168}\)
3. \(+\left(\frac{-10}{-3}\right) -\left(\frac{3}{4}\right) -\left(\frac{3}{-6}\right)\\= \frac{10}{3}- \frac{3}{4}+\frac{3}{6}\\=\frac{10}{3}-\frac{3}{4}+\frac{1}{2}\\=\frac{40}{12}-\frac{9}{12}+\frac{6}{12}\\=\frac{40-9+6}{12}\\=\frac{37}{12}\)
4. \(-\left(\frac{-8}{-7}\right) -\left(\frac{5}{6}\right) -\left(\frac{7}{9}\right)\\= \frac{-8}{7}- \frac{5}{6}-\frac{7}{9}\\=\frac{-144}{126}-\frac{105}{126}-\frac{98}{126}\\=\frac{-144-105-98}{126}\\=\frac{-347}{126}\)
5. \(+\left(\frac{-9}{-7}\right) -\left(\frac{-4}{-9}\right) -\left(\frac{-11}{5}\right)\\= \frac{9}{7}- \frac{4}{9}+\frac{11}{5}\\=\frac{405}{315}-\frac{140}{315}+\frac{693}{315}\\=\frac{405-140+693}{315}\\=\frac{958}{315}\)
6. \(+\left(\frac{3}{-4}\right) +\left(\frac{-9}{9}\right) -\left(\frac{9}{-8}\right)\\= \frac{-3}{4}- \frac{9}{9}+\frac{9}{8}\\=\frac{-3}{4}-\frac{1}{1}+\frac{9}{8}\\=\frac{-6}{8}-\frac{8}{8}+\frac{9}{8}\\=\frac{-6-8+9}{8}\\=\frac{-5}{8}\)
7. \(+\left(\frac{6}{-5}\right) -\left(\frac{4}{-7}\right) -\left(\frac{-3}{-5}\right)\\= \frac{-6}{5}+ \frac{4}{7}-\frac{3}{5}\\=\frac{-42}{35}+\frac{20}{35}-\frac{21}{35}\\=\frac{-42+20-21}{35}\\=\frac{-43}{35}\)
8. \(+\left(\frac{-5}{6}\right) -\left(\frac{5}{-10}\right) +\left(\frac{2}{9}\right)\\= \frac{-5}{6}+ \frac{5}{10}+\frac{2}{9}\\=\frac{-5}{6}+\frac{1}{2}+\frac{2}{9}\\=\frac{-15}{18}+\frac{9}{18}+\frac{4}{18}\\=\frac{-15+9+4}{18}\\=\frac{-2}{18}\\=\frac{-1}{9}\)
9. \(+\left(\frac{-2}{9}\right) -\left(\frac{7}{3}\right) +\left(\frac{12}{10}\right)\\= \frac{-2}{9}- \frac{7}{3}+\frac{12}{10}\\=\frac{-2}{9}-\frac{7}{3}+\frac{6}{5}\\=\frac{-10}{45}-\frac{105}{45}+\frac{54}{45}\\=\frac{-10-105+54}{45}\\=\frac{-61}{45}\)
10. \(+\left(\frac{-8}{5}\right) -\left(\frac{6}{4}\right) +\left(\frac{11}{10}\right)\\= \frac{-8}{5}- \frac{6}{4}+\frac{11}{10}\\=\frac{-8}{5}-\frac{3}{2}+\frac{11}{10}\\=\frac{-16}{10}-\frac{15}{10}+\frac{11}{10}\\=\frac{-16-15+11}{10}\\=\frac{-20}{10}\\=\frac{-2}{1}\)
11. \(+\left(\frac{-8}{-3}\right) -\left(\frac{-2}{-8}\right) -\left(\frac{-5}{2}\right)\\= \frac{8}{3}- \frac{2}{8}+\frac{5}{2}\\=\frac{8}{3}-\frac{1}{4}+\frac{5}{2}\\=\frac{32}{12}-\frac{3}{12}+\frac{30}{12}\\=\frac{32-3+30}{12}\\=\frac{59}{12}\)
12. \(+\left(\frac{7}{-8}\right) -\left(\frac{7}{-7}\right) +\left(\frac{4}{9}\right)\\= \frac{-7}{8}+ \frac{7}{7}+\frac{4}{9}\\=\frac{-7}{8}+\frac{1}{1}+\frac{4}{9}\\=\frac{-63}{72}+\frac{72}{72}+\frac{32}{72}\\=\frac{-63+72+32}{72}\\=\frac{41}{72}\)