Directed Numbers - The Concept of Negative Numbers

It is good idea to differentiate between what it means subtracting a number and adding its opposite. Negative numbers are numbers to the left of zero on the number line. To subtract, though, is to move left, by the amount to be subtracted, on the number line, if the number to be subtracted from is positive.

Positive numbers are numbers to the right of zero on the number line and negative numbers are to the left of zero on the number line. So it is good idea to think of a negative number as being the opposite of a positive number, as long as the numbers are the same distance from zero on either side of it.

To add to two numbers, move in the same direction; if adding positive numbers the movement is more to the right, but if both are negative numbers the movement is more to the left.

It is good idea to think of adding a positive number and its opposite being always zero. It is also good practice to enclose a negative numbers with a bracket, so that no two operators be next to each other.

Generally, to subtract a number is like to add its opposite and write up the balance as the answer.

For example, 5 -3 = 5 +(-3) = 2
or, (-5) - 3 = (-5) + (-3) = (-8)
or, (-8) - (-3) = (-8) + 3 = (-5) — here subtracting (-3) is like to add its opposite 3.
(or change direction and move 3 units to
right - informally)