Determine o valor da seguinte expressão numérica:
(6/5 - 3/10 - 1/15) + (11/15 - 1/2)
Obs: quero entender passo a passo e quero saber se posso usar a regra de cancelamento nesse caso
Respostas
respondido por:
3
Bom dia Josiane!
Solução!
![\left ( \dfrac{6}{5}- \dfrac{3}{10}- \dfrac{1}{15} \right )+\left ( \dfrac{11}{15}- \dfrac{1}{2} \right )\\\\\\\
\left ( \dfrac{6}{5}- \dfrac{3}{10}- \dfrac{1}{15} + \dfrac{11}{15}- \dfrac{1}{2} \right )](https://tex.z-dn.net/?f=%5Cleft+%28+%5Cdfrac%7B6%7D%7B5%7D-+%5Cdfrac%7B3%7D%7B10%7D-+%5Cdfrac%7B1%7D%7B15%7D+++%5Cright+%29%2B%5Cleft+%28+%5Cdfrac%7B11%7D%7B15%7D-+%5Cdfrac%7B1%7D%7B2%7D++%5Cright+%29%5C%5C%5C%5C%5C%5C%5C%0A%5Cleft+%28+%5Cdfrac%7B6%7D%7B5%7D-+%5Cdfrac%7B3%7D%7B10%7D-+%5Cdfrac%7B1%7D%7B15%7D++%2B+%5Cdfrac%7B11%7D%7B15%7D-+%5Cdfrac%7B1%7D%7B2%7D++%5Cright+%29 "\left ( \dfrac{6}{5}- \dfrac{3}{10}- \dfrac{1}{15} \right )+\left ( \dfrac{11}{15}- \dfrac{1}{2} \right )\\\\\\\
\left ( \dfrac{6}{5}- \dfrac{3}{10}- \dfrac{1}{15} + \dfrac{11}{15}- \dfrac{1}{2} \right )")
Veja que a operação matemática tem frações,obrigatoriamente precisamos fazer o MMC dos denominadores.
![5~~10~~15~~2|2\\
5~~~5~~~15~1|3\\
5~~~5~~~5~~1|5\\
1~~~1~~~1~~1\\\\\\\
MMC=2\times3\times5=30](https://tex.z-dn.net/?f=5%7E%7E10%7E%7E15%7E%7E2%7C2%5C%5C%0A5%7E%7E%7E5%7E%7E%7E15%7E1%7C3%5C%5C%0A5%7E%7E%7E5%7E%7E%7E5%7E%7E1%7C5%5C%5C%0A1%7E%7E%7E1%7E%7E%7E1%7E%7E1%5C%5C%5C%5C%5C%5C%5C%0AMMC%3D2%5Ctimes3%5Ctimes5%3D30 "5~~10~~15~~2|2\\
5~~~5~~~15~1|3\\
5~~~5~~~5~~1|5\\
1~~~1~~~1~~1\\\\\\\
MMC=2\times3\times5=30")
Com o MMC pronto divide pelo denominador e multiplica pelo numerador.
![[tex]\left( \dfrac{6}{5}- \dfrac{3}{10}- \dfrac{1}{15} + \dfrac{11}{15}- \dfrac{1}{2} \right )\\\\\\\\ \left( \dfrac{36-9-2+22-15}{30} \right )\\\\\\\\ \left( \dfrac{36+22-9-2-15}{30} \right )\\\\\\\\ \left( \dfrac{58-26}{30} \right )\\\\\\\\ \left( \dfrac{32}{30} \right )\\\\\\\\ Simplificando~~a~~fra\c~\~cao~~por~~2~~chegamos~~ao resultado~~de:\\\\\\\\ \left( \dfrac{32:2}{30:2} \right )=\left( \dfrac{16}{15} \right )\\\\\\\\\ \boxed{Resposta: \dfrac{16}{15}}](https://tex.z-dn.net/?f=%5Btex%5D%5Cleft%28+%5Cdfrac%7B6%7D%7B5%7D-+%5Cdfrac%7B3%7D%7B10%7D-+%5Cdfrac%7B1%7D%7B15%7D+%2B+%5Cdfrac%7B11%7D%7B15%7D-+%5Cdfrac%7B1%7D%7B2%7D+%5Cright+%29%5C%5C%5C%5C%5C%5C%5C%5C+%5Cleft%28+%5Cdfrac%7B36-9-2%2B22-15%7D%7B30%7D+%5Cright+%29%5C%5C%5C%5C%5C%5C%5C%5C+%5Cleft%28+%5Cdfrac%7B36%2B22-9-2-15%7D%7B30%7D+%5Cright+%29%5C%5C%5C%5C%5C%5C%5C%5C+%5Cleft%28+%5Cdfrac%7B58-26%7D%7B30%7D+%5Cright+%29%5C%5C%5C%5C%5C%5C%5C%5C+%5Cleft%28+%5Cdfrac%7B32%7D%7B30%7D+%5Cright+%29%5C%5C%5C%5C%5C%5C%5C%5C+Simplificando%7E%7Ea%7E%7Efra%5Cc%7E%5C%7Ecao%7E%7Epor%7E%7E2%7E%7Echegamos%7E%7Eao+resultado%7E%7Ede%3A%5C%5C%5C%5C%5C%5C%5C%5C+%5Cleft%28+%5Cdfrac%7B32%3A2%7D%7B30%3A2%7D+%5Cright+%29%3D%5Cleft%28+%5Cdfrac%7B16%7D%7B15%7D+%5Cright+%29%5C%5C%5C%5C%5C%5C%5C%5C%5C+%5Cboxed%7BResposta%3A+%5Cdfrac%7B16%7D%7B15%7D%7D+ "[tex]\left( \dfrac{6}{5}- \dfrac{3}{10}- \dfrac{1}{15} + \dfrac{11}{15}- \dfrac{1}{2} \right )\\\\\\\\ \left( \dfrac{36-9-2+22-15}{30} \right )\\\\\\\\ \left( \dfrac{36+22-9-2-15}{30} \right )\\\\\\\\ \left( \dfrac{58-26}{30} \right )\\\\\\\\ \left( \dfrac{32}{30} \right )\\\\\\\\ Simplificando~~a~~fra\c~\~cao~~por~~2~~chegamos~~ao resultado~~de:\\\\\\\\ \left( \dfrac{32:2}{30:2} \right )=\left( \dfrac{16}{15} \right )\\\\\\\\\ \boxed{Resposta: \dfrac{16}{15}}")
Bom dia!
Bons estudos!
Solução!
Veja que a operação matemática tem frações,obrigatoriamente precisamos fazer o MMC dos denominadores.
Com o MMC pronto divide pelo denominador e multiplica pelo numerador.
Bom dia!
Bons estudos!
josianecomunica:
Grata, JBK. Agora vou ver todo o processo :)
Ok! Bons estudos! Qualquer dívida é comente aqui!
apertei a estrelinha errada... vc foi genial, JBK
Esta tudo bem!
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