Find the value of the given expression:
$$\frac{1}{4}\times \frac{4}{3}÷\frac{5}{3}+\frac{1}{2}$$

Apply the BODMAS rule to solve the expression:
$$\frac{1}{4}\times \frac{4}{3}÷\frac{5}{3}+\frac{1}{2}$$

**Step 1: Perform the division operation ($÷$)**

$$\frac{4}{3}÷\frac{5}{3}=\frac{4}{3}\times \frac{3}{5}=\frac{4}{5}$$

Now substitute it back into the expression:

$$\frac{1}{4}\times \frac{4}{5}+\frac{1}{2}$$

**Step 2: Perform the multiplication operation ($\times$)**

$$\frac{1}{4}\times \frac{4}{5}=\frac{1}{5}$$

Now the expression is:

$$\frac{1}{5}+\frac{1}{2}$$

**Step 3: Perform the addition operation ($+$)**

$$\frac{1}{5}+\frac{1}{2}=0.2+0.5=0.7$$