Question

How can you use a number line to show that $3+\left( -3 \right)=0$ ?

Answer 1

Hint: To solve such questions, one needs to have imagination and a basic idea of how a number line looks. We can use the number line to add and subtract whole numbers, which can be either positive or negative.

Complete step by step solution:
Given the expression: $3+\left( -3 \right)=0$
We have to show that this expression holds true with the help of a number line.
Now, let us imagine that the number line can be thought of as a one way path and the respective signs of those numbers as the direction of movement on that path.

If we have positive numbers, then we move towards the right-hand side of the number line, and if the number is a negative number then we move towards the left of the number line.
We always start from the base or the origin position which by default is taken as $0$ .
Now, for the given expression $3+\left( -3 \right)=0$ , we have to take $3$ steps towards the right or the positive direction and then, similarly $-3$ which means $3$ steps towards the left or the negative direction on the number line.
Hence, taking $3$ steps from the origin in the positive direction, we reach the number $3$ on the number line, and then by taking $3$ steps in the negative direction from the previous position, we again reach the origin or the place where we eventually started from.
Therefore, the given expression $3+\left( -3 \right)=0$ is true.

Note: A number line can prove to be very useful to tell which numbers are greater or lesser and to add or subtract small problem statements. A number on the left of the number line is less than the number on the right of the number line.