Question

What is the value of n in the equation 2/3 (n-5/6) = 2 1/2A.) 1 2/3B.) 5C.) 4 7/12D.) 1 17/18

Answer 1

`(2)/(3)(n-(5)/(6))=2(1)/(2)`

In this case it is convinient to transform first 2 1/2 into an improper fraction

`2(1)/(2)=(4)/(2)+(1)/(2)=(5)/(2)`

And the equation becomes in

`(2)/(3)(n-(5)/(6))=(5)/(2)`

Since all the denominators are divisible by 6, it is convinient to multipy all the equation by

`\begin{gathered} (6*2)/(3)(n-(5)/(6))=(5*6)/(2) \\ 4(n-(5)/(6))=15 \\ 4n-(4*5)/(6)=15 \\ 4n-(10)/(3)=15 \\ 12n-10=45 \\ 12n=55 \\ n=(55)/(12) \\ n=4\text{ }(7)/(12) \end{gathered}`

Then, the answer ic C.) 4 7/12