## 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 that*a*+ 0 =*a*. You can rewrite this equation as*a*+ ( −*a*) = 0 .