The rule of how to multiply negatives is simple:
|To multiply a negative number by any number, take the (positive) opposite of the negative number and multiply it by the other number, and take the opposite of that|
Negative by positive number
For a case where a negative number is multiplied by a positive, the rule above can be restated as: take the positive number, and the negative WITHOUT the minus sign, multiply them and add the inus sign to the product.
Example: multiply 5 and -3. Take 5 and -3 without the "-" sign: 5 and 3 Multiply them: 5*3 = 15. Add the minus sign: -15. Conclusion: Product of a negative and a positive is always a negative number.
Negative by negative number
When you have to multiply two negative numbers, such as (-5) * (-3), the rule above should be applied twice: (-5)*(-3) is the opposite of 5*(-3), which is the opposite of the opposite of 5*3. 5*3 is 15 Opposite of 15 s -15. Opposite of opposite of 15 is opposite of -15, and opposite of -15 is 15 again. Conclusion: Product of a negative multiplied by negative is always POSITIVE.
Here's a handy table: sign of result when we multiply
Examples: 2*3=6 2*(-3) = -6 (-2)*3 = -6 (-2)*(-3) = 6