Question

How can you use a number line to show that `3+(-3) = 0`?

Answer 1

Look below for explanation.

Explanation:

Numbers on a number line can be thought of as steps and the signs for each of these number as the respective direction of those steps.

For example,

If I define my positive sign as moving from left to right then negative sign represents movement from right to left.

Now the number `3` means `3` steps in the positive direction and similarly `-3` means `3` steps in the negative direction.

Now on the number line the starting position is usually called the origin which is `0`.

Hence, `3 + (-3)` means walking `3` steps in the positive direction (i.e. from `0` taking `3` steps we end up at point `3` on the number line) and `-3` means walking `3` steps in the negative direction from the previous position (i.e. from `3` taking `3` steps back in the opposite direction we end up at `0` on the number line.)