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

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Presentation transcript:

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

2-3: Multiplying/Dividing Rational Numbers Identity Property of Multiplication For every real number n, 1 ● n = n and n ● 1 = n I N E NGLISH : Multiplying any number by 1 does not affect the number Examples: 1 ● (-5) = -5-5 ● 1 = -5 Multiplication Property of Zero For every real number n, 0 ● n = 0 and n ● 0 = 0 I N E NGLISH : Anything multiplied by 0 is 0 Examples: 0 ● 35 = 035 ● 0 = 0

2-3: Multiplying/Dividing Rational Numbers Multiplication Property of -1 For every real number n, -1 ● n = -n and -1 ● -n = n I N E NGLISH : Multiplying any number by -1 flips the sign Examples: -1 ● (-5) = 5-1 ● 5 = -5

2-3: Multiplying/Dividing Rational Numbers This leads us to two rules Multiplying numbers with the same sign = positive + ● +- ● Multiplying numbers with different signs = negative + ● -- ● + - -

2-3: Multiplying/Dividing Rational Numbers Example 1: Multiplying numbers Simplify -9(-4) = 36Negative ● Negative = Positive 5(- 2 / 3 ) = - 10 / 3 Positive ● Negative = Negative Y OUR T URN 4(-6) -10(-5) -4.9(-8) - 2 / 3 ( 3 / 4 ) ½

2-3: Multiplying/Dividing Rational Numbers Example 2: Evaluating Expressions Evaluate -2xy for x = -20 and y = -3 -2xy = -2(-20)(-3)Substitute using ( ) = 40(-3)Multiply left  right = -120 Y OUR T URN Evaluate for c = -8 and d = -7 -(cd) (-2)(-3)(cd) c(-d)

2-3: Multiplying/Dividing Rational Numbers Example 3: Simplifying Exponential Expressions PARENTHESIS MATTER!!! -3 4 Means -1 ● 3 4 -(3)(3)(3)(3) = -81 (-3) 4 (-3)(-3)(-3)(-3) = 81 Y OUR T URN -4 3 (-2) 4 (-0.3) 2 -(¾) / 16

2-3: Multiplying/Dividing Rational Numbers The rules for signs when dividing are the same as the rules for multiplication Dividing numbers with the same sign = positive + ● +- ● Dividing numbers with different signs = negative + ● -- ● + - -

2-3: Multiplying/Dividing Rational Numbers Example 4: Dividing numbers Simplify 12 ÷ (-4) = -3Positive ÷ Negative = Negative -12 ÷ (-4) = 3Negative ÷ Negative = Positive Y OUR T URN -42 ÷ 7 -8 ÷ (-2) 8 ÷ (-8) -39 ÷ (-3)

2-3: Multiplying/Dividing Rational Numbers Example 5: Evaluating Expressions Evaluate –x / y ÷ z for x = -20, y = 6 and z = -1 -x / y ÷ z -(-20) / (6) ÷ (-1)use ( ) 20 / (6) ÷ (-1)-(-20) = (-12)Multiply/Divide -17Add Y OUR T URN Evaluate for x = -8, y = -5 and z = -1 3x ÷ (2z) + y ÷ 10 3z 2 – 4y ÷ x /

2-3: Multiplying/Dividing Rational Numbers Inverse Property of Multiplication For every nonzero real number a, there is a multiplicative inverse 1 / a such that a( 1 / a ) = 1 I N E NGLISH : 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 Numbers Example 6: Division Using the Reciprocal Evaluate x / y for x = - 3 / 4 and y = - 5 / 2 x / y = x ÷ yRewrite for viewing ease = - 3 / 4 ÷ - 5 / 2 Substitute = - 3 / 4 (- 2 / 5 )Rewrite as multiplication = 3 / 10 Y OUR T URN Evaluate x / y for x = 8 and y = - 4 / 5 -10

2-3: Multiplying/Dividing Rational Numbers Assignment Worksheet #2-3 1 – 47, odds