Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{-2}\right) -\left(\frac{-10}{-7}\right) +\left(\frac{5}{-9}\right)\\= \frac{3}{2}- \frac{10}{7}-\frac{5}{9}\\=\frac{189}{126}-\frac{180}{126}-\frac{70}{126}\\=\frac{189-180-70}{126}\\=\frac{-61}{126}\)
2. \(-\left(\frac{-9}{5}\right) -\left(\frac{-6}{-9}\right) -\left(\frac{4}{-8}\right)\\= \frac{9}{5}- \frac{6}{9}+\frac{4}{8}\\=\frac{9}{5}-\frac{2}{3}+\frac{1}{2}\\=\frac{54}{30}-\frac{20}{30}+\frac{15}{30}\\=\frac{54-20+15}{30}\\=\frac{49}{30}\)
3. \(-\left(\frac{-2}{9}\right) +\left(\frac{5}{-4}\right) +\left(\frac{7}{8}\right)\\= \frac{2}{9}- \frac{5}{4}+\frac{7}{8}\\=\frac{16}{72}-\frac{90}{72}+\frac{63}{72}\\=\frac{16-90+63}{72}\\=\frac{-11}{72}\)
4. \(-\left(\frac{-10}{9}\right) +\left(\frac{-9}{5}\right) +\left(\frac{-12}{7}\right)\\= \frac{10}{9}- \frac{9}{5}-\frac{12}{7}\\=\frac{350}{315}-\frac{567}{315}-\frac{540}{315}\\=\frac{350-567-540}{315}\\=\frac{-757}{315}\)
5. \(+\left(\frac{-7}{-8}\right) -\left(\frac{-4}{5}\right) -\left(\frac{-12}{5}\right)\\= \frac{7}{8}+ \frac{4}{5}+\frac{12}{5}\\=\frac{35}{40}+\frac{32}{40}+\frac{96}{40}\\=\frac{35+32+96}{40}\\=\frac{163}{40}\)
6. \(+\left(\frac{9}{8}\right) -\left(\frac{7}{-3}\right) +\left(\frac{-2}{4}\right)\\= \frac{9}{8}+ \frac{7}{3}-\frac{2}{4}\\=\frac{9}{8}+\frac{7}{3}-\frac{1}{2}\\=\frac{27}{24}+\frac{56}{24}-\frac{12}{24}\\=\frac{27+56-12}{24}\\=\frac{71}{24}\)
7. \(+\left(\frac{-2}{5}\right) +\left(\frac{5}{5}\right) -\left(\frac{12}{12}\right)\\= \frac{-2}{5}+ \frac{5}{5}-\frac{12}{12}\\=\frac{-2}{5}+\frac{1}{1}-\frac{1}{1}\\=\frac{-2+1-1}{5}\\=\frac{-2}{5}\)
8. \(+\left(\frac{-8}{-5}\right) +\left(\frac{7}{-6}\right) -\left(\frac{-6}{-9}\right)\\= \frac{8}{5}- \frac{7}{6}-\frac{6}{9}\\=\frac{8}{5}-\frac{7}{6}-\frac{2}{3}\\=\frac{48}{30}-\frac{35}{30}-\frac{20}{30}\\=\frac{48-35-20}{30}\\=\frac{-7}{30}\)
9. \(-\left(\frac{-10}{7}\right) -\left(\frac{10}{-5}\right) +\left(\frac{-9}{-7}\right)\\= \frac{10}{7}+ \frac{10}{5}+\frac{9}{7}\\=\frac{10}{7}+\frac{2}{1}+\frac{9}{7}\\=\frac{10+2+9}{7}\\=\frac{21}{7}\\=\frac{3}{1}\)
10. \(-\left(\frac{-5}{3}\right) -\left(\frac{-2}{-7}\right) +\left(\frac{8}{-3}\right)\\= \frac{5}{3}- \frac{2}{7}-\frac{8}{3}\\=\frac{35}{21}-\frac{6}{21}-\frac{56}{21}\\=\frac{35-6-56}{21}\\=\frac{-27}{21}\\=\frac{-9}{7}\)
11. \(+\left(\frac{-9}{-5}\right) +\left(\frac{-5}{-3}\right) +\left(\frac{-12}{-6}\right)\\= \frac{9}{5}+ \frac{5}{3}+\frac{12}{6}\\=\frac{9}{5}+\frac{5}{3}+\frac{2}{1}\\=\frac{27}{15}+\frac{25}{15}+\frac{30}{15}\\=\frac{27+25+30}{15}\\=\frac{82}{15}\)
12. \(-\left(\frac{8}{3}\right) +\left(\frac{-9}{-2}\right) -\left(\frac{3}{-12}\right)\\= \frac{-8}{3}+ \frac{9}{2}+\frac{3}{12}\\=\frac{-8}{3}+\frac{9}{2}+\frac{1}{4}\\=\frac{-32}{12}+\frac{54}{12}+\frac{3}{12}\\=\frac{-32+54+3}{12}\\=\frac{25}{12}\)