Negative & Positive Number Rules

Examine the many uses of negative numbers to understand them better.
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Whole numbers, decimals and fractions can all be positive or negative. A negative number is any number less than zero and a positive number is any number greater than zero. Zero is neither positive or negative. You can add, subtract, multiply and divide both positive and negative numbers by combining negatives, positives or a combination of the two.

Adding Numbers

When adding a positive to a positive or a negative to a negative, add them together and give them the same sign. For instance, 5 + 5 is equal to 10, while -5 + -7 is -12. When adding a positive number and negative number together, use subtraction by taking the absolute value — the numbers without their signs — and subtract the smaller from the larger. Then give the answer the sign of the larger number. For instance, -7 + 4 means you take 7, subtract 4 and give the answer a negative sign since the absolute value of -7 is greater than 4.


To subtract, switch the sign of the number being subtracted to its opposite and follow the rules for adding. In 12 - 9, take 9 and convert it to negative then add them together, resulting in 12 + (-9). Add the two new values together to get 3. When subtracting a negative from a negative, such as -6 - -4, switch -4 to positive 4 and add the values together to have -6 + 4, giving -2 following the addition rules. To subtract a positive and negative number, 12 - -9, switch the -9 to 9 and add the values to get 21.


When multiplying a positive and positive number together or negative and negative together, keep the same sign. When you multiply a positive and a negative number together, the result is always negative. Any number multiplied by zero becomes zero and is neither positive or negative.


In division, rules vary slightly from multiplication. A positive number divided by a positive is always positive and a negative divided by a positive or vice-versa is always negative. When dividing a negative by a negative, you divide the absolute values by each other. You cannot divide by zero.

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