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Positives (-) and Negatives (-)PowerPoint Presentation

Positives (-) and Negatives (-)

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### Positives (-) and Negatives (-)

Negative Integer: A number denoting the spaces going left, a number denoting the amount of money you owe someone.

Positive Integer: A number representing spaces to the right on the number line; a number denoting the amount of money you have with you.

Negative plus Negative = Negative

( - ) + ( - ) = -

Ex: – 3 + (-4) = (go left on number line)

– 3 – 4 = – 7

Ex: – m + (– 5m) + (-4m) =

– m – 5m – 4m = – 10m

PositiveplusPositive = Positive

( + ) + ( + ) = +

Ex: 3+ 4 = (Right on the number line)

3 +4 = 7

Ex: m+5m+(4m) =

m+5m+4m = 10m

Positiveplus Negative = Bigger number sign

( + ) + ( - ) = + or-?

Ex: 3+ (-4 ) =

3 - 4 = – 1

Ex: – 3 + 4 = 1

Negative minus Negative = Bigger number sign

( - ) - ( - ) = - or + ?

Ex: – 3 - (-4) =

– 3 + 4 = 1

Ex: – 5 - (-4) =

– 5 + 4 = – 1

Ex: – m - (– 5m) - (-4m) =

– m + 5m + 4m =

– m + 9m = 8m

Positive minus Negative = Positive

( + ) - ( - ) = +

Ex: 3 - ( - 4 ) =

3 + 4 = 7

Ex: m- (-5m) - (-4m) =

m + 5m + 4m = 10m

Negative minusPositive = Negative

( - ) -( + ) = –

Ex: – 3 - ( 4 ) =

– 3 - 4 = – 7

Ex: – 5 - (+4) =

– 5 - 4= – 9

Ex: – m -(5m) -(4m) =

– m – 5m – 4m = –10m

Negative timesPositive = Negative

( - ) x( + ) = –

Ex: – 3 ( 4 ) =

( – 3)(4) = – 12

Ex: (-5)4 =

– 5 x 4 = – 20

Ex: (– m)5 =

( m)(-5)= –5m

Positive times Negative = Negative

( + )x ( - ) = –

Ex: (3 )( - 4 ) =

3( - 4 ) = – 12

Ex: (5) (-4) =

5(- 4)= – 20

Ex: (m)(-5)=

m(-5) = –5m

Positive timesPositive = Positive( + )x( + ) = +

Ex: (3 )( 4 ) =

3( 4 ) = 12

Ex: (5)(4) =

5(4)= 20

Ex: (m)(5) =

m(5) = 5m

This properties do extend to equations.

We use this whenever we are using the properties we have covered to solve for variables.

Ex: – 2(x+ 3) = 15

Distribute the –2

– 2(x)+(-2)(3)= 15

Use properties of signs

Now isolate the variable

– 2x – 6 = 15

+ 6 +6

Add to both sides of =

– 2x= 21

Divide by -2 both sides

x= -

Adding:(+) + (+)= positive

(-) + (-) = negative

(+) + (-) = Biggest number takes the sign.

Subtracting:(+) - (+)= (+)- = Biggest number takes sign

(-) - (-) = (-)+ = Biggest number takes sign

(+) - (-) = (+) + = positive

(-) – (+) = (-) - = negative

Multiplying:(+) ∙ (+)= positive

(-) ∙ (-) = positive

(+) ∙ (-) = Negative.

Dividing:(+) / (+)= Positive

(-) / (-) = Positive

(+) / (-) = Negative

(-) / (+) = Negative

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