Reviewing The Properties of Multiplication

A Negative Times a Negative

Work Time

A Negative Times a Negative

The rule “a negative times a negative equals a positive” can be represented by the equation (−a) ⋅ (−b) = ab. The following proof shows that this equation is true.

  • Work on the table and justify each step using the properties of operations for addition or multiplication to prove that if the values for a and b are positive, then both (−a) and (−b) are negative and ab is positive.

HANDOUT: Multiplying a Negative by a Negative

Hint:

  • The addition property of equality states that you can add any quantity to both sides of an equation without changing the equation.
  • The multiplication property of equality states that you can multiply both sides of an equation by any quantity without changing the equation.
  • The addition property of zero states thata + 0 =a . You can rewrite this equation asa + ( −a ) = 0 .