To place each number on the number line, let’s examine where each one falls based on its value.

1. 1/2: This is a positive fraction just less than 1. Place it halfway between 0 and 1.

2. 4 1/2: This is a mixed number, 4 plus 1/2. It lies halfway between 4 and 5, so place it in the middle of 4 and 5 on the positive side.

3. -3/4: This is a negative fraction close to -1, but slightly to the right of it. Place it between -1 and 0, closer to -1.

4. -4 1/2: This is a negative mixed number, -4 and an additional -1/2. Place it halfway between -4 and -5, on the negative side.

Let me know if you have questions or need further clarification on any steps!

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Here are 5 related questions for deeper understanding:

1. How would you locate $-1 \frac{1}{4}$ on a number line?
2. What’s the position of $\frac{3}{4}$ relative to $-3/4$ on the number line?
3. How can you identify the exact halfway point between two numbers on a number line?
4. Where would $-0.5$ be placed on the number line compared to $-3/4$?
5. What strategies help in estimating fractions' placement on a number line?

Tip: To place fractions or mixed numbers on a number line, convert them to decimals if possible; it makes visual placement easier!