In the first chapter entry on representing directed numbers, Is it Positive or Negative?, we discussed how numbers move along a number line. Remember, as we move to the right along the number line, the numbers get bigger or grow. So when we see a positive number, the plus sign is an operator telling us that the total is getting bigger and moving to the right along the number line.
The first number in an expression tells us the starting point on our number line. The operator (something like + or -) and the next number tell us how many places to move along the number line. When we are adding positive integers, we move to the right along the number line.
Here is an example of adding integers.
Think: Start at $5$5, then move $3$3 spaces to the right along the number line.
Now let's look at an example that uses negative numbers:
What about when the negative number has a bigger size than the positive number?
Think: Start at $-15$−15, then move $7$7 spaces to the right along the number line.
Or, we could rearrange the number sentence as $7-15$7−15.
Check out this applet and see how numbers move along a number line when we add them:
Understand addition and subtraction of fractions, decimals, and integers