Reviewing The Properties of Multiplication

Explain and Justify Proofs

Work Time

Explain and Justify Proofs

The rule “a positive times a negative equals a negative” can be represented by the equation a ⋅ (−b) = −(ab). One way to prove that the rule is true is to prove that the equation is true—which we do in the following proof.

  • Work on the handout 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 (−b) and −(ab) are negative.

HANDOUT: Explaining and Justifying Proofs

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 .