Lesson HOW TO add and subtract negatives

Negative numbers start with the minus sign. Example: -5, -2.345. When you look at a number line like this:

negative numbers would be to the LEFT of zero. -1, -3, and -2.5 are all negative numbers.

Why negative numbers were invented?

Negative numbers were invented to be able to solve problems similar to this one:
5-10 = ?
Negative numbers are creations of our imagination and, therefore, we humans had to invent rules for them: how to add, subtract, and modify them. To be useful, the rules have to make sense. This lesson discusses addition and subtraction of negative numbers.

Rule 1: Opposite

The opposite of a positive number is the same number, but with the sign '-'. Example: the opposite of 2 is -2.
The opposite of a negative number is the same number without the minus sign. Example: the opposite of -2 is 2.

Rule 2: Subtracting a bigger positive number from a positive

If you subtract a bigger positive number, from a smaller positive number, you will get a negative number that is the opposite of the difference between the bigger and the smaller number.

Example: subtract 5 from 3 (3-5). 5 is the bigger number, 3 is the smaller number. According tot he above rule, 3-5 is the opposite of the difference between the bigger number (5) and smaller number (3). That difference, 5-3, is 2. The opposite of it is -2. So, we have

3-5=-2

Rule 3: Adding a positive and a negative

To add a positive number and a negative number, subtract the opposite of the negative number, from the positive number.

Visualising this: think of the effect of adding positive numbers as shiiiifting the point on a number line to the right. Adding negative numbers shifts the point to the left:
Adding a positive, 2+(+1): (shift to the right)
Adding a negative, 2+ (-1): (shift to the left)
Example: 3+(-2) = 3-(+2) = 3-2

Rule 4: Adding two negatives

To add two negative numbers, add their opposites and take the opposite of the sum. The opposites of those negative numbers would be regular positive numbers, and you know how to deal with adding positives together. Once you have the sum of positives, take the opposite of it (you would get a negative number).
Example: -5+(-3) = -(5+3) = -8.

Rule 5: subtracting a number

Simply remember that subtracting a negative number is the same as adding its opposite.

Example: 2-(-1) = 2+(+1) = 3.

Please play with a few solvers here to see how these rules are applied.