Question

What's is 1 1/2 + 2 + 2 1/2 + 2 3/4

Answer 1

Starting from the expression:

`1(1)/(2)+2+2(1)/(2)+2(3)/(4)`

Separate the integer part of the sum form the fractionary part:

`\begin{gathered} 1(1)/(2)=1+(1)/(2) \\ 2(1)/(2)=2+(1)/(2) \\ 2(3)/(4)=2+(3)/(4) \end{gathered}`

Then:

`\begin{gathered} 1(1)/(2)+2+2(1)/(2)+2(3)/(4)=1+(1)/(2)+2+2+(1)/(2)+2+(3)/(4) \\ =1+2+2+2+(1)/(2)+(1)/(2)+(3)/(4) \\ =7+(1)/(2)+(1)/(2)+(3)/(4) \end{gathered}`

Notice that in order to sum two fractions, they must have the same denominator. Add 1/2 and 1/2:

`\begin{gathered} =7+(2)/(2)+(3)/(4) \\ =7+1+(3)/(4) \\ =8+(3)/(4) \\ =8(3)/(4) \end{gathered}`

Therefore:

`1(1)/(2)+2+2(1)/(2)+2(3)/(4)=8(3)/(4)`