Respuesta :

let's convert the mixed fractions to "improper" firstly, and then let's make them the same denominator by multiply each other by "the other's denominator", so

[tex]\bf \stackrel{mixed}{2\frac{5}{8}}\implies \cfrac{2\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{21}{8}} \\\\\\ \stackrel{mixed}{2\frac{2}{3}}\implies \cfrac{2\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{8}{3}}\\\\ -------------------------------\\\\ \cfrac{21}{8}\cdot \cfrac{3}{3}\implies \boxed{\cfrac{63}{24}}\qquad \qquad \qquad \qquad \qquad \qquad \cfrac{8}{3}\cdot \cfrac{8}{8}\implies \boxed{\cfrac{64}{24}}[/tex]

so, which one do you think is greater?
Amphitrite1040
Hey there! 

[tex]2[/tex] and [tex] \frac{5}{8} [/tex] equals [tex] 2\frac{5}{8} [/tex]

[tex]2[/tex] and [tex] \frac{2}{3} [/tex] equals [tex]2 \frac{2}{3} [/tex]

So, now that we got that out of the way, let's set up our problems to answer your question, shall we? 

[tex] 2\frac{5}{8} = \frac{21}{8} = 2.625\\ \\ \\ 2\frac{2}{3} = \frac{8}{3} = 2.67 [/tex]

[tex] 2\frac{5}{8} \ \textless \ 2\frac{2}{3} [/tex]

The greatest (aka the biggest one) is [tex] 2\frac{2}{3} [/tex]

Good luck on your assignment and enjoy your day!

[tex]~LoveYourselfFirst:)[/tex]