Positive and negative numbers are two broad classes of numbers that are used in math and also everyday transactions, like managing money or measuring weight.
- A positive number has a value greater than zero. Its sign is positive, but it is usually written without a plus sign in front of it (e.g., 4, 51 rather than +4, +51).
- A negative number has a value less than zero. Its sign is considered to be negative and it is written with a minus sign in front of it (e.g., -2, -23).
- The sum of a positive number and its equal negative number is zero.
- Zero is neither a positive nor negative number.
There are rules for adding, subtracting, multiplying, and dividing positive and negative numbers. Generally, it’s easier to perform operations on negative numbers if they are enclosed in brackets to keep them separate. Number lines can make positive and numbers easier to understand, too.
Addition and Subtraction of Positive and Negative Numbers
Adding positive and negative numbers is simple when both numbers have the same sign. Simply find the sum of the numbers and keep the sign. For example:
- 3 + 2 = 5
- (-4) + (-2) = -6
Find the sum of a positive and negative number by subtracting the number with the smaller value from the one with the larger value. The sign is that of the larger number.
- (-7) + 2 = -5
- 4 + (-8) = 4 – 8 = -4
- (-3) + 8 = 5
- 10 + (-2) = 10 – 2 = 8
- (-5) + 4 = -1
The rules for subtraction are similar to those of addition. For two positive numbers, if the first number is larger than the second, then the result is another positive number.
- 12 – 10 = 2
- 4 -3 = 1
If you subtract a large positive number from a smaller positive number, you get a negative number.
- 5 – 6 = -1
- 2 – 4 = -2
An easy way to do this is to subtract the smaller number from the larger number and change the sign of the answer to a minus.
When you subtract a positive number from a negative number, it’s the same as adding a negative number. In other words, it makes the negative number more negative.
- (-4) – 3 = (-4) + (-3) = -7
- (-10) – 12 = (-10) + (-12) = -24
Subtracting a negative number from a positive number cancels out the negative signs and becomes simple addition. It makes the positive number more positive.
- 4 – (-3) = 4 + 3 = 7
- 5 – (-2) = 5 + 2 = 7
When you subtract a negative number from another negative number, once again the negative signs cancel each other to become a plus sign. The answer has the sign of the larger number.
- (-2) – (-7) = (-2) + 7 = 5
- (-5) – (-3) = (-5) + 3 = -2
Multiplication and Division of Positive and Negative Numbers
The rules for multiplication and division are simple:
- If both numbers are positive, the result is positive.
- If both numbers are negative, the result is positive. (Basically, the two negative values cancel each other out).
- If one number is positive and the other is negative, the result is negative.
- If you are multiplying or dividing multiple numbers with signs, add up how many positive numbers there are and how many negative numbers there are. The sign in excess is the sign of the answer.
- Multiplying any number (positive or negative) by zero gives an answer of 0.
- Zero divided by any numbers is 0.
- Any number divided by zero is infinity.
Here are some examples. These examples use integers (whole numbers), but the same rules apply to decimals and fractions.
- 4 x 5 = 20
- (-2) x (-3) = 6
- (-6) x 3 = -18
- 7 x (-2) = -14
- 2 x (-3) x 4 = -24
- (-2) x 2 x (-3) = 12
- 12 / 2 = 6
- (-10) / 5 = -2
- 14 / (-7) = -2
- (-6) / (-2) = 3