escrevendo a razao 1 sobre 2 + 5 sobre 3 sobre 0,5+2 na forma irredutivel obtemos.
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![\dfrac{1}{2}+ \dfrac{5}{3}+ \dfrac{3}{0,5+2}\\\\\\\\\
\dfrac{1}{2}+ \dfrac{5}{3}+ \dfrac{3}{2,5}\\\\\\\\\
Lembrando:2,5= \frac{25}{10}= \frac{5}{2}\\\\\\\\
\dfrac{1}{2}+ \dfrac{5}{3}+ \dfrac{3}{ \dfrac{5}{2} }\\\\\\\\\
\dfrac{1}{2}+ \dfrac{5}{3}+ 3\times \dfrac{2}{5} \\\\\\\\\
\dfrac{1}{2}+ \dfrac{5}{3}+ \dfrac{6}{5} \\\\\\\\\
\dfrac{15+50+36}{30}\\\\\\
\dfrac{101}{30}\Leftarrow~~Forma~~irredutivel](https://tex.z-dn.net/?f=+%5Cdfrac%7B1%7D%7B2%7D%2B+%5Cdfrac%7B5%7D%7B3%7D%2B+%5Cdfrac%7B3%7D%7B0%2C5%2B2%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A+%5Cdfrac%7B1%7D%7B2%7D%2B+%5Cdfrac%7B5%7D%7B3%7D%2B+%5Cdfrac%7B3%7D%7B2%2C5%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%0ALembrando%3A2%2C5%3D+%5Cfrac%7B25%7D%7B10%7D%3D+%5Cfrac%7B5%7D%7B2%7D%5C%5C%5C%5C%5C%5C%5C%5C+%0A++++%5Cdfrac%7B1%7D%7B2%7D%2B+%5Cdfrac%7B5%7D%7B3%7D%2B+%5Cdfrac%7B3%7D%7B+%5Cdfrac%7B5%7D%7B2%7D+%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A+%5Cdfrac%7B1%7D%7B2%7D%2B+%5Cdfrac%7B5%7D%7B3%7D%2B+3%5Ctimes+%5Cdfrac%7B2%7D%7B5%7D+%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cdfrac%7B1%7D%7B2%7D%2B+%5Cdfrac%7B5%7D%7B3%7D%2B++%5Cdfrac%7B6%7D%7B5%7D+%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A+%5Cdfrac%7B15%2B50%2B36%7D%7B30%7D%5C%5C%5C%5C%5C%5C+++%0A+%5Cdfrac%7B101%7D%7B30%7D%5CLeftarrow%7E%7EForma%7E%7Eirredutivel%0A%0A%0A%0A++++++++ "\dfrac{1}{2}+ \dfrac{5}{3}+ \dfrac{3}{0,5+2}\\\\\\\\\
\dfrac{1}{2}+ \dfrac{5}{3}+ \dfrac{3}{2,5}\\\\\\\\\
Lembrando:2,5= \frac{25}{10}= \frac{5}{2}\\\\\\\\
\dfrac{1}{2}+ \dfrac{5}{3}+ \dfrac{3}{ \dfrac{5}{2} }\\\\\\\\\
\dfrac{1}{2}+ \dfrac{5}{3}+ 3\times \dfrac{2}{5} \\\\\\\\\
\dfrac{1}{2}+ \dfrac{5}{3}+ \dfrac{6}{5} \\\\\\\\\
\dfrac{15+50+36}{30}\\\\\\
\dfrac{101}{30}\Leftarrow~~Forma~~irredutivel")
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Solução!
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Bons estudos!
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