Essential Question: What are the rules for multiplying and dividing real numbers?

2-3: Multiplying/Dividing Rational NumbersIdentity Property of Multiplication

For every real number n, 1 ● n = n and n ● 1 = nIN ENGLISH: Multiplying any number by 1 does not

affect the numberExamples:

1 ● (-5) = -5 -5 ● 1 = -5

Multiplication Property of ZeroFor every real number n, 0 ● n = 0 and n ● 0 = 0IN ENGLISH: Anything multiplied by 0 is 0Examples:

0 ● 35 = 0 35 ● 0 = 0

2-3: Multiplying/Dividing Rational NumbersMultiplication Property of -1

For every real number n, -1 ● n = -n and -1 ● -n = nIN ENGLISH: Multiplying any number by -1 flips the

signExamples:

-1 ● (-5) = 5 -1 ● 5 = -5

2-3: Multiplying/Dividing Rational NumbersThis leads us to two rules

Multiplying numbers with the same sign = positive + ● + - ● -

+ +Multiplying numbers with different signs =

negative + ● - - ● +

- -

2-3: Multiplying/Dividing Rational NumbersExample 1: Multiplying numbers

Simplify -9(-4) = 36 Negative ● Negative = Positive 5(-2/3) = -10/3 Positive ● Negative = Negative

YOUR TURN4(-6)-10(-5)-4.9(-8)-2/3(3/4)

-2450

39.2

-½

2-3: Multiplying/Dividing Rational NumbersExample 2: Evaluating Expressions

Evaluate -2xy for x = -20 and y = -3-2xy = -2(-20)(-3) Substitute using ( )

= 40(-3) Multiply left right = -120

YOUR TURNEvaluate for c = -8 and d = -7-(cd)(-2)(-3)(cd)c(-d)

-56336

-56

2-3: Multiplying/Dividing Rational NumbersExample 3: Simplifying Exponential Expressions

PARENTHESIS MATTER!!!-34 Means -1 ● 34

-(3)(3)(3)(3) = -81(-3)4

(-3)(-3)(-3)(-3) = 81YOUR TURN

-43

(-2)4

(-0.3)2

-(¾)2

-6416

0.09

-9/16

2-3: Multiplying/Dividing Rational NumbersThe rules for signs when dividing are the same

as the rules for multiplicationDividing numbers with the same sign = positive

+ ● + - ● - + +

Dividing numbers with different signs = negative + ● - - ● +

- -

2-3: Multiplying/Dividing Rational NumbersExample 4: Dividing numbers

Simplify 12 ÷ (-4) = -3 Positive ÷ Negative = Negative -12 ÷ (-4) = 3 Negative ÷ Negative = Positive

YOUR TURN-42 ÷ 7-8 ÷ (-2)8 ÷ (-8)-39 ÷ (-3)

-64

-1

13

2-3: Multiplying/Dividing Rational NumbersExample 5: Evaluating Expressions

Evaluate –x/-4 + 2y ÷ z for x = -20, y = 6 and z = -1 -x/-4 + 2y ÷ z -(-20)/-4 + 2(6) ÷ (-1) use ( ) 20/-4 + 2(6) ÷ (-1) -(-20) = 20 -5 + (-12) Multiply/Divide -17 Add

YOUR TURNEvaluate for x = -8, y = -5 and z = -13x ÷ (2z) + y ÷ 10

3z2 – 4y ÷ x

-4.5

-1/5

29.5

2

2

z x

y

2-3: Multiplying/Dividing Rational NumbersInverse Property of Multiplication

For every nonzero real number a, there is a multiplicative inverse 1/a such that a(1/a) = 1

IN ENGLISH: Multiplying any number by it’s reciprocal equals 1

Examples: 5(1/5) = 1 -5(-1/5) = 1

Why we need to know this Dividing using fractions isn’t possible, so instead, we

multiply by the reciprocal.

2-3: Multiplying/Dividing Rational NumbersExample 6: Division Using the Reciprocal

Evaluate x/y for x = -3/4 and y = -5/2

x/y = x ÷ y Rewrite for viewing ease

= -3/4 ÷ -5/2 Substitute

= -3/4(-2/5) Rewrite as multiplication

= 3/10

YOUR TURNEvaluate x/y for x = 8 and y = -4/5

-10

2-3: Multiplying/Dividing Rational NumbersAssignment

Worksheet #2-31 – 47, odds