Question

Which is greater? 2 and5/8 or 2 and 2/3

Answer 1

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


`\bf \stackrel{mixed}{2(5)/(8)}\implies \cfrac{2\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{21}{8}} \\\\\\ \stackrel{mixed}{2(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}}`

so, which one do you think is greater?

Answer 2

Hey there!


`2` and
`(5)/(8)` equals
`2(5)/(8)`


`2` and
`(2)/(3)` equals
`2 (2)/(3)`

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


`2(5)/(8) = (21)/(8) = 2.625\\ \\ \\ 2(2)/(3) = (8)/(3) = 2.67`


`2(5)/(8) \ \textless \ 2(2)/(3)`

The greatest (aka the biggest one) is
`2(2)/(3)`

Good luck on your assignment and enjoy your day!


`~LoveYourselfFirst:)`