Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{2}\right) -\left(\frac{2}{2}\right) -\left(\frac{8}{-8}\right)\\= \frac{-9}{2}- \frac{2}{2}+\frac{8}{8}\\=\frac{-9}{2}-\frac{1}{1}+\frac{1}{1}\\=\frac{-9-1+1}{2}\\=\frac{-9}{2}\)
2. \(-\left(\frac{6}{-5}\right) +\left(\frac{10}{7}\right) -\left(\frac{5}{-4}\right)\\= \frac{6}{5}+ \frac{10}{7}+\frac{5}{4}\\=\frac{168}{140}+\frac{200}{140}+\frac{175}{140}\\=\frac{168+200+175}{140}\\=\frac{543}{140}\)
3. \(-\left(\frac{-8}{9}\right) -\left(\frac{-10}{-4}\right) +\left(\frac{2}{-8}\right)\\= \frac{8}{9}- \frac{10}{4}-\frac{2}{8}\\=\frac{8}{9}-\frac{5}{2}-\frac{1}{4}\\=\frac{32}{36}-\frac{90}{36}-\frac{9}{36}\\=\frac{32-90-9}{36}\\=\frac{-67}{36}\)
4. \(-\left(\frac{-7}{2}\right) +\left(\frac{8}{10}\right) -\left(\frac{11}{-3}\right)\\= \frac{7}{2}+ \frac{8}{10}+\frac{11}{3}\\=\frac{7}{2}+\frac{4}{5}+\frac{11}{3}\\=\frac{105}{30}+\frac{24}{30}+\frac{110}{30}\\=\frac{105+24+110}{30}\\=\frac{239}{30}\)
5. \(-\left(\frac{-3}{2}\right) -\left(\frac{-8}{5}\right) +\left(\frac{4}{-9}\right)\\= \frac{3}{2}+ \frac{8}{5}-\frac{4}{9}\\=\frac{135}{90}+\frac{144}{90}-\frac{40}{90}\\=\frac{135+144-40}{90}\\=\frac{239}{90}\)
6. \(+\left(\frac{4}{3}\right) +\left(\frac{10}{-7}\right) -\left(\frac{-6}{-11}\right)\\= \frac{4}{3}- \frac{10}{7}-\frac{6}{11}\\=\frac{308}{231}-\frac{330}{231}-\frac{126}{231}\\=\frac{308-330-126}{231}\\=\frac{-148}{231}\)
7. \(+\left(\frac{2}{-5}\right) -\left(\frac{-2}{9}\right) -\left(\frac{-5}{11}\right)\\= \frac{-2}{5}+ \frac{2}{9}+\frac{5}{11}\\=\frac{-198}{495}+\frac{110}{495}+\frac{225}{495}\\=\frac{-198+110+225}{495}\\=\frac{137}{495}\)
8. \(+\left(\frac{-4}{7}\right) -\left(\frac{6}{-8}\right) +\left(\frac{-12}{10}\right)\\= \frac{-4}{7}+ \frac{6}{8}-\frac{12}{10}\\=\frac{-4}{7}+\frac{3}{4}-\frac{6}{5}\\=\frac{-80}{140}+\frac{105}{140}-\frac{168}{140}\\=\frac{-80+105-168}{140}\\=\frac{-143}{140}\)
9. \(-\left(\frac{9}{-2}\right) -\left(\frac{4}{10}\right) -\left(\frac{-6}{-10}\right)\\= \frac{9}{2}- \frac{4}{10}-\frac{6}{10}\\=\frac{9}{2}-\frac{2}{5}-\frac{3}{5}\\=\frac{45}{10}-\frac{4}{10}-\frac{6}{10}\\=\frac{45-4-6}{10}\\=\frac{35}{10}\\=\frac{7}{2}\)
10. \(-\left(\frac{-8}{9}\right) -\left(\frac{-9}{-4}\right) -\left(\frac{6}{-3}\right)\\= \frac{8}{9}- \frac{9}{4}+\frac{6}{3}\\=\frac{8}{9}-\frac{9}{4}+\frac{2}{1}\\=\frac{32}{36}-\frac{81}{36}+\frac{72}{36}\\=\frac{32-81+72}{36}\\=\frac{23}{36}\)
11. \(-\left(\frac{-6}{-7}\right) +\left(\frac{-7}{-4}\right) +\left(\frac{-2}{-9}\right)\\= \frac{-6}{7}+ \frac{7}{4}+\frac{2}{9}\\=\frac{-216}{252}+\frac{441}{252}+\frac{56}{252}\\=\frac{-216+441+56}{252}\\=\frac{281}{252}\)
12. \(-\left(\frac{3}{2}\right) -\left(\frac{-5}{-2}\right) +\left(\frac{-5}{7}\right)\\= \frac{-3}{2}- \frac{5}{2}-\frac{5}{7}\\=\frac{-21}{14}-\frac{35}{14}-\frac{10}{14}\\=\frac{-21-35-10}{14}\\=\frac{-66}{14}\\=\frac{-33}{7}\)