Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{6}{-5}\right) -\left(\frac{-2}{6}\right) -\left(\frac{10}{-9}\right)\\= \frac{6}{5}+ \frac{2}{6}+\frac{10}{9}\\=\frac{6}{5}+\frac{1}{3}+\frac{10}{9}\\=\frac{54}{45}+\frac{15}{45}+\frac{50}{45}\\=\frac{54+15+50}{45}\\=\frac{119}{45}\)
2. \(-\left(\frac{-5}{8}\right) -\left(\frac{7}{-3}\right) +\left(\frac{2}{-12}\right)\\= \frac{5}{8}+ \frac{7}{3}-\frac{2}{12}\\=\frac{5}{8}+\frac{7}{3}-\frac{1}{6}\\=\frac{15}{24}+\frac{56}{24}-\frac{4}{24}\\=\frac{15+56-4}{24}\\=\frac{67}{24}\)
3. \(+\left(\frac{-2}{-3}\right) -\left(\frac{-10}{-8}\right) -\left(\frac{-7}{3}\right)\\= \frac{2}{3}- \frac{10}{8}+\frac{7}{3}\\=\frac{2}{3}-\frac{5}{4}+\frac{7}{3}\\=\frac{8}{12}-\frac{15}{12}+\frac{28}{12}\\=\frac{8-15+28}{12}\\=\frac{21}{12}\\=\frac{7}{4}\)
4. \(-\left(\frac{-9}{7}\right) -\left(\frac{8}{4}\right) +\left(\frac{-11}{8}\right)\\= \frac{9}{7}- \frac{8}{4}-\frac{11}{8}\\=\frac{9}{7}-\frac{2}{1}-\frac{11}{8}\\=\frac{72}{56}-\frac{112}{56}-\frac{77}{56}\\=\frac{72-112-77}{56}\\=\frac{-117}{56}\)
5. \(+\left(\frac{-5}{-9}\right) -\left(\frac{10}{9}\right) -\left(\frac{-7}{-4}\right)\\= \frac{5}{9}- \frac{10}{9}-\frac{7}{4}\\=\frac{20}{36}-\frac{40}{36}-\frac{63}{36}\\=\frac{20-40-63}{36}\\=\frac{-83}{36}\)
6. \(+\left(\frac{8}{-7}\right) +\left(\frac{3}{-6}\right) -\left(\frac{-5}{12}\right)\\= \frac{-8}{7}- \frac{3}{6}+\frac{5}{12}\\=\frac{-8}{7}-\frac{1}{2}+\frac{5}{12}\\=\frac{-96}{84}-\frac{42}{84}+\frac{35}{84}\\=\frac{-96-42+35}{84}\\=\frac{-103}{84}\)
7. \(+\left(\frac{-5}{6}\right) +\left(\frac{3}{2}\right) +\left(\frac{-12}{4}\right)\\= \frac{-5}{6}+ \frac{3}{2}-\frac{12}{4}\\=\frac{-5}{6}+\frac{3}{2}-\frac{3}{1}\\=\frac{-5+3-3}{6}\\=\frac{-5}{6}\)
8. \(+\left(\frac{-10}{-7}\right) -\left(\frac{10}{-2}\right) +\left(\frac{-10}{3}\right)\\= \frac{10}{7}+ \frac{10}{2}-\frac{10}{3}\\=\frac{10}{7}+\frac{5}{1}-\frac{10}{3}\\=\frac{30}{21}+\frac{105}{21}-\frac{70}{21}\\=\frac{30+105-70}{21}\\=\frac{65}{21}\)
9. \(+\left(\frac{4}{9}\right) +\left(\frac{-9}{-5}\right) -\left(\frac{5}{7}\right)\\= \frac{4}{9}+ \frac{9}{5}-\frac{5}{7}\\=\frac{140}{315}+\frac{567}{315}-\frac{225}{315}\\=\frac{140+567-225}{315}\\=\frac{482}{315}\)
10. \(-\left(\frac{5}{-4}\right) -\left(\frac{-5}{-9}\right) +\left(\frac{5}{-4}\right)\\= \frac{5}{4}- \frac{5}{9}-\frac{5}{4}\\=\frac{45}{36}-\frac{20}{36}-\frac{45}{36}\\=\frac{45-20-45}{36}\\=\frac{-20}{36}\\=\frac{-5}{9}\)
11. \(+\left(\frac{-6}{5}\right) +\left(\frac{10}{4}\right) -\left(\frac{8}{-6}\right)\\= \frac{-6}{5}+ \frac{10}{4}+\frac{8}{6}\\=\frac{-6}{5}+\frac{5}{2}+\frac{4}{3}\\=\frac{-36}{30}+\frac{75}{30}+\frac{40}{30}\\=\frac{-36+75+40}{30}\\=\frac{79}{30}\)
12. \(+\left(\frac{4}{-5}\right) +\left(\frac{-8}{9}\right) -\left(\frac{9}{10}\right)\\= \frac{-4}{5}- \frac{8}{9}-\frac{9}{10}\\=\frac{-72}{90}-\frac{80}{90}-\frac{81}{90}\\=\frac{-72-80-81}{90}\\=\frac{-233}{90}\)