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

Multiply: | Positive | Negative |

Positive | + | - |

Negative | - | + |

Examples: 2*3=6 2*(-3) = -6 (-2)*3 = -6 (-2)*(-3) = 6