Lesson 1-6 Multiplying and Dividing Real Numbers Pages

Objective The learner will multiply and divide real numbers.

Properties Identity Property of Multiplication For every real number n, 1 x n = n 1 x 5 = 5 1 x (-5) = -5 Multiplication Property of Zero For every real number n, n x 0 = 0 35 x 0 = x 0 = 0 Multiplication Property of -1 For every real number n, -1 x n = -n -1 x 5 = x (-5) = 5

When to Multiply??? x * ab a(b)

Rules for Multiplication The product of two numbers with the same sign is positive. 5 * 2 = 10 -5(-2) = 10 The product of two numbers with different signs is negative. 3(-6) = * 6 = -18 Note: NO PE!! Odd number of negatives, the product is negative. Even number – Positive!!

Example #1 Simplify each expression. a.-9 (-4) = 36 (same signs) b.5(-2/3) = -10/3 (different signs) = -3 1/3 (change to mixed number)

Now you try: Simplify each expression. a.4(-6) b.-10(-5)(-2) c.-4.9(-8) d.-2/3(3/4)

Example #2 You can evaluate expressions involving multiplication. To simplify expressions with three or more negative numbers be careful to account for all of the negative signs. Evaluate -2xy for x = -20 and y = -3 -2xy = -2(-20)(-3) (substitute) = 40(-3) (multiply) = -120

Now you try: Evaluate each expression for c = -8 and d = -7 a.–(cd) b.(-2)(-3)(cd) c.c(-d)

Example #3

Now you try:

Example #4

Now you try:

Multiplication Review The product of two positive integers is _______ The product of two negative integers is________ The product of a positive & a negative integer is _________ If there is even number of negative integers, the product will be ___________ If there is an odd number of negative integers, the product will be __________

Rules for Division Dividing Numbers with the Same Sign The quotient of two numbers with the same sign is positive. 6 ÷ 3 = 2 and -6 ÷ -3 = 2 Dividing Numbers with Different Signs The quotient of two numbers with different signs is negative. -6 ÷ 3 = -2 and 6 ÷ (-3) = -2 Note: The rules are the same for multiplication AND division!!

Example #5 Simplify each expression. a.12 (-4) = -3 (different signs) b.-12 (-4) = 3 (same signs)

Now you try: Simplify each expression: a b.-8 (-2) c.8 (-8) d.-39 (-3)

Example #6 Evaluate –x /-4 + 2y z for x = -20, y = 6, and z = -1 -(-20) + 2(6) (-1) (substitute) (-12) (divide & mult.) -17 (add)

Now you try: Evaluate each expression for x = 8, y = -5, and z = -3. a.3x 2z + y 10 b.2z + x 2y c. 3z² - 4y x

Inverse Property of Multiplication: For every nonzero real number a, there is a multiplicative inverse 1/a such that a(1/a) = 1. Examples: 5(1/5) = 1 -5(1/-5) = 1 The multiplicative inverse, or reciprocal, of a nonzero rational number a/b is b/a. Zero does not have a reciprocal. Division by zero is undefined.

Example #7 Evaluate x/y for x = -3/4 and y = -5/2 x = x y(rewrite the expression) y = -3/4 (-5/2) (substitute) = -3/4(-2/5) (multiply by reciprocal) = 6/20 = 3/10 (simplify)

Now you try: Evaluate x÷y for x = 8 and y = -4/5

Division Review The quotient of two positive integers is _______ The quotient of two negative integers is________ The quotient of a positive & a negative integer is _________