2.32.3

Multiply and Divide IntegersMultiply and Divide Integers

ReviewReview

-12+8-12+8 0-(-9)0-(-9) -7+(-4)-7+(-4) 2-(-4)2-(-4) -6-(-9)-(4)+13-6-(-9)-(4)+13 Write the sum of y and negative fiveWrite the sum of y and negative five True, sometimes true or false: True, sometimes true or false:

The difference between a number and The difference between a number and its additive inverse is zeroits additive inverse is zero

The sum of a negative number and a The sum of a negative number and a negative number is a negative numbernegative number is a negative number

Multiplying Multiplying

Steps for Multiplying IntegersSteps for Multiplying Integers 1. Multiply the numbers and ignore 1. Multiply the numbers and ignore

their signstheir signs 2. If both have the same signs 2. If both have the same signs

(positive-positive or negative-(positive-positive or negative-negative) then the answer is a negative) then the answer is a positive number.positive number.

3. If they opposite signs (one 3. If they opposite signs (one negative and one positive) then the negative and one positive) then the answer is negative.answer is negative.

ExamplesExamples -7(4) = -28-7(4) = -28 3(-2) = -63(-2) = -6 4(5) = 204(5) = 20 (-6)(-1) = 6(-6)(-1) = 6

PropertiesProperties

Multiplicative property of zeroMultiplicative property of zero

A*0 = 0A*0 = 0

Multiplicative property of oneMultiplicative property of one

a*1 = aa*1 = a

Commutative property Commutative property

a*b = b*a 2*3 = 3*2a*b = b*a 2*3 = 3*2

Associative Property of MultiplicationAssociative Property of Multiplication

(a*b)*c = a*(b*c)(a*b)*c = a*(b*c)

DivisionDivision

Same rules as multiplicationSame rules as multiplication 1. Divide the numbers and ignore 1. Divide the numbers and ignore

their signstheir signs 2. If both have the same signs 2. If both have the same signs

(positive-positive or negative-(positive-positive or negative-negative) then the answer is a negative) then the answer is a positive number.positive number.

3. If they opposite signs (one 3. If they opposite signs (one negative and one positive) then the negative and one positive) then the answer is negative.answer is negative.

PropertiesProperties

Top = numeratorTop = numerator Bottom = denominatorBottom = denominator a / 1 = aa / 1 = a 0 / a = 00 / a = 0

Zero cannot be in the denominatorZero cannot be in the denominator a/0 = undefineda/0 = undefined b/a is okay as long as a does not b/a is okay as long as a does not

equal 0equal 0

examplesexamples

-2 / -2 = 1-2 / -2 = 1 50 / -10 = 550 / -10 = 5

Try itTry it

(-38)(51) (-38)(51) -1938-1938 -7(-8)(9)(-2)-7(-8)(9)(-2) -1008-1008 Is -3 a solution to 12 = -4aIs -3 a solution to 12 = -4a Yes’mYes’m What is zero divided by -17What is zero divided by -17 ZeroZero 84/-684/-6 -14-14 Is -3 a solution to: -6/y = -2Is -3 a solution to: -6/y = -2 No!No! The daily high temperatures for one week in The daily high temperatures for one week in

winter were: winter were: -7, -8, 0, -1, -6, -11, -2 -7, -8, 0, -1, -6, -11, -2 -5-5

2.3 homework2.3 homework

1 thru 119 EOO1 thru 119 EOO

20, 36, 48, 60, 80, 84, 90, 100, 20, 36, 48, 60, 80, 84, 90, 100, 108, 112108, 112