1. Ch 2.5 Objective: To multiply integers.

2. Properties Commutative Property: a * b = b * a Two numbers can be multiplied in either order and the result is always the same. For example: 4 * 6 = 6 * 4 Associative Property: (a * b) * c = a * (b * c) Three numbers can be multiplied in any order and the result will always be the same. For example: (1 * 2) * 3 = 1 * (2 * 3)

3. More Properties Identity Property: 1 * a = a The product of 1 and a number will always be the number. For example: 1 * 11 = 11 Inverse Property: a * (1/a) = 1 The product of a number and its reciprocal will always equal one. For example: 10 * (1/10) = 1

4. Property & Definition Zero Product Property: a * 0 = 0 The product of zero and any number will always equal zero. For example: 5 * _____ = 0 Reciprocal: The reciprocal of a number is 1 divided by the number. For example: Reciprocal of a is 1/a. Reciprocal of 1/a is a.

5. Rules for Multiplying Integers Same Sign (+) Evaluate 2 numbers at a time. If they have the same sign, the result is always positive. For example: 4 * 5 = 20 -4 (– 5) = 20 Opposite Signs (-) Evaluate 2 numbers at a time. If they have opposite signs, the result is always negative. For example: 4 (–7) = -28-4 (7) = -28

6. Odd # of Negatives = Negative Even # of Negatives = Positive Simplify. 1) 2) 3) 4) 5) 6) 7) 8) -24 +36 -42 +30 -40 +40 24 (-2) = -48 20 2 = +40

7. Review Simplify the following. 1) -6(7) = 2) 6(-7) = 3) (6) -7 = 4) (-6) -7 = 5) (-9) -5 = 6) -9(-5) = 7) (+9) -5 = 8) +9(-5) = -42 -13 -14 +45 +4 -45

8. Simplify the following. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) -81 +81 -64 16 25 3 54 -36 1

9. Simplify the following. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)