What is the value of 2.6+0.5(1(3)/(4))-(3)/(2) (3)/(5) 1(39)/(40) 1(29)/(40) (19)/(40)

## Step 1: Simplify the Expression<br />### Begin by simplifying the expression inside the parentheses. Convert $1\frac{3}{4}$ to an improper fraction: $1\frac{3}{4} = \frac{7}{4}$. Then multiply by $0.5$: $0.5 \times \frac{7}{4} = \frac{7}{8}$.<br />## Step 2: Perform Addition and Subtraction<br />### Add $2.6$ and $\frac{7}{8}$, then subtract $\frac{3}{2}$. Convert $2.6$ to a fraction: $2.6 = \frac{26}{10} = \frac{13}{5}$. Find a common denominator for $\frac{13}{5}$, $\frac{7}{8}$, and $\frac{3}{2}$, which is $40$. Convert each fraction: $\frac{13}{5} = \frac{104}{40}$, $\frac{7}{8} = \frac{35}{40}$, and $\frac{3}{2} = \frac{60}{40}$. Now perform the operations: $\frac{104}{40} + \frac{35}{40} - \frac{60}{40} = \frac{79}{40}$.<br />## Step 3: Convert to Mixed Number<br />### Convert $\frac{79}{40}$ to a mixed number: $1\frac{39}{40}$.