Solve Nested Division Expression: 3:(4:(5:12)) Using Colon Notation

The colon symbol means division, just like ÷. So $3:4$ is the same as $3 ÷ 4$ or $\frac{3}{4}$. It's commonly used in some countries and textbooks.

Order of operations requires us to solve parentheses first! In nested expressions like this, start with the innermost parentheses and work your way outward, just like peeling an onion.

To divide by a number, multiply by its reciprocal. For example: $a:b = a ÷ b = a × \frac{1}{b}$. So $3:4 = 3 × \frac{1}{4} = \frac{3}{4}$.

Yes! Simplifying as you go makes the problem easier. In this problem, we simplified $\frac{3×5}{4×3×4}$ by canceling the 3s to get $\frac{5}{16}$.

Try rewriting each step clearly. Start with the deepest parentheses, solve that first, then substitute the result back. Take your time - nested operations require careful, step-by-step work!

Work backwards! If $3:(4:(5:12)) = \frac{5}{16}$, then $4:(5:12)$ should equal $3 ÷ \frac{5}{16} = \frac{48}{5}$. Check each step to verify your answer!