Question

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

Answer 1

Starting from the expression:

$1\frac{1}{2}+2+2\frac{1}{2}+2\frac{3}{4}$

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

$\begin{gathered} 1\frac{1}{2}=1+\frac{1}{2} \\ 2\frac{1}{2}=2+\frac{1}{2} \\ 2\frac{3}{4}=2+\frac{3}{4} \end{gathered}$

Then:

$\begin{gathered} 1\frac{1}{2}+2+2\frac{1}{2}+2\frac{3}{4}=1+\frac{1}{2}+2+2+\frac{1}{2}+2+\frac{3}{4} \\ =1+2+2+2+\frac{1}{2}+\frac{1}{2}+\frac{3}{4} \\ =7+\frac{1}{2}+\frac{1}{2}+\frac{3}{4} \end{gathered}$

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

$\begin{gathered} =7+\frac{2}{2}+\frac{3}{4} \\ =7+1+\frac{3}{4} \\ =8+\frac{3}{4} \\ =8\frac{3}{4} \end{gathered}$

Therefore:

$1\frac{1}{2}+2+2\frac{1}{2}+2\frac{3}{4}=8\frac{3}{4}$