Algebra I SECTION 2 4 MULTIPLYING AND DIVIDING

Algebra I SECTION 2. 4 MULTIPLYING AND DIVIDING REAL NUMBERS OBJECTIVES: MULTIPLY AND DIVIDE POSITIVE AND NEGATIVE NUMBERS AND DEFINE THE PROPERTIES OF ZERO.

Warm-up Find each sum or difference. 1. -23 + (-51) 2. -17 – (-17) 3. -18 + (-83) 4. -32 – (-5) Let q = 8, r = -2, and s = -5. Evaluate each expression. 5. q – r 6. -q – r 7. -r – (-s) 8. s – (-r)

Basic Mathematical Operations + · ÷ ^ √

Rules for Multiplying Two Signed Numbers Multiplying Two Numbers With Like Signs 1. Find the product of the absolute values of the numbers. 2. Write the product as a positive number. (+) · (+) = (+) (-) · (-) = (+) Multiplying Two Numbers With Unlike Signs 1. Find the product of the absolute values of the numbers. 2. Write the product as a negative number. (+) · (-) = (-) · (+) = (-)

Rules for Dividing Two Signed Numbers Dividing Two Numbers With Like Signs 1. Find the quotient of the absolute values of the numbers. 2. Write the quotient as a positive number. (+) ÷ (+) = (+) (-) ÷ (-) = (+) Multiplying Two Numbers With Unlike Signs 1. Find the quotient of the absolute values of the numbers. 2. Write the quotient as a negative number. (+) ÷ (-) = (-) ÷ (+) = (-)

Example: Find each product. a. (-15)(2) b. (-6. 1)(-9) c. (8. 3)(-4) Practice: P 75 Try this after Example 1 Example: Find each quotient a. b. (-3. 8) ÷ 19 c. Practice: P 75 Try this after Example 2

Identity Property for Multiplication For all real numbers a, a · 1 = a and 1 · a = a Multiplicative Inverse Property For every nonzero real number a, there is exactly one number such that The number is called the reciprocal or multiplicative inverse of a.

Example: Find each quotient by using reciprocals. a. -54 ÷ 9 b. c. Practice: P 76 Try this after Example 3

Properties of Zero Let a represent any real number 1. The product of any real number and zero is zero. a · 0 = 0 and 0 · a = 0 2. Zero divided by any nonzero real number is zero. = 0, where a ≠ 0 3. Division by zero is undefined (Division by zero is not possible)

Example: Find each quotient by using reciprocals. a. b. c. 6. 05 ÷ 0 Practice: P 77 Try this after Example 4 If Time: P 77 #s 6 -17 Homework: P 78 #18 – 63 all