Solve the Expression: Finding the Correct Sign in 0:4?4+0

To solve this problem, we will evaluate each part of the expression separately.

• Firstly, evaluate $0:4$ which is interpreted as $\frac{0}{4}$. Since dividing zero by any non-zero number results in zero, we get $\frac{0}{4} = 0$.
• Next, evaluate $4+0$. According to the property of addition, adding zero to any number does not change the number, thus $4+0 = 4$.

Now, we need to compare the two results: $0$ and $4$.

• Since $0$ is less than $4$, the correct inequality sign to use between them is $<$.

Thus, the correct sign for the expression $0:4?4+0$ is $<$.

Therefore, the solution to the problem is $0:4 < 4+0$.