1. **State the problem:** Given that $$\left|\frac{ab}{|ab|}\right| = 1,$$ find the value of $$\left|\frac{a}{|a|}\right| + \left|\frac{b}{b}\right| + \left|\frac{ab}{ab}\right|.$$\n\n2. **Analyze the given condition:** The expression $$\left|\frac{ab}{|ab|}\right| = 1$$ means the absolute value of the fraction is 1. Since $$|ab|$$ is the magnitude of $$ab$$, dividing $$ab$$ by its magnitude gives a complex number or real number on the unit circle with magnitude 1. So this condition is always true for any nonzero $$a$$ and $$b$$.\n\n3. **Evaluate each term in the sum:**\n- $$\left|\frac{a}{|a|}\right|$$: Since $$|a|$$ is the magnitude of $$a$$, dividing $$a$$ by $$|a|$$ gives a number on the unit circle with magnitude 1. Taking the absolute value again gives $$1$$.\n- $$\left|\frac{b}{b}\right|$$: Simplify the fraction first. $$\frac{b}{b} = 1$$ (assuming $$b \neq 0$$). Then $$|1| = 1$$.\n- $$\left|\frac{ab}{ab}\right|$$: Similarly, $$\frac{ab}{ab} = 1$$ (assuming $$ab \neq 0$$). Then $$|1| = 1$$.\n\n4. **Sum the values:**\n$$\left|\frac{a}{|a|}\right| + \left|\frac{b}{b}\right| + \left|\frac{ab}{ab}\right| = 1 + 1 + 1 = 3.$$\n\n5. **Final answer:** The value is $$3$$.\n\n**Note:** The problem's answer choices include 3, so the correct choice is the one containing 3.\n