ADDING INTEGERS(SAME SIGNS)

•SAME signs ADD and keep the sign 4 + 2 = 6

4 positives + 2 positives = 6 positives

ADDING INTEGERS(SAME SIGNS)

•SAME signs add and keep the sign

- 4 + - 2 = - 6

4 negatives + 2 negatives = 6 negatives

ADDING INTEGERS(DIFFERENT SIGNS)

• DIFFERENT signs SUBTRACT and keep the sign of the larger number

4 + - 2 = 2

4 positives + 2 negatives = 2 positives

ADDING INTEGERS(DIFFERENT SIGNS)

• DIFFERENT signs SUBTRACT and keep the sign of the larger number

- 4 + 2 = -2

4 negatives + 2 positives = 2 negatives

SUBTRACTING INTEGERS(KFC & follow Rules for

addition)Problem KFC follow addition rules 8 - 10 8 + - 10

K – keep the first numberF – flip the subtraction to an addition signC – change the second number to its

opposite****then******

FOLLOW RULES FOR ADDITION!!!!

Steps 1. Is it an addition or subtraction problem?

A. Addition (go to step 2)B. Subtraction (go to step 3)

2. Addition – are the signs the same?A. Yes – add and keep the signB. No – subtract and keep the sign of the larger

number

3. Subtraction – KFC –Keep the first number; Flip to an addition problem; Change the last number to its opposite – then go back to step 2

MULTIPLYING INTEGERS

Multiplying is REPEATED ADDITION

Commutative Property of Multiplication - the order in which numbers are multiplied does not matter a x b = b x a

MULTIPLYING INTEGERS

4 x 2 = 2 x 4

4 groups of 2 = 2 groups

of 4

8 8

=

=

4 x -2

4 groups of - 2 = - 8

- 8

What would

-2 x 4 be?(HINT: use the commutative

property)

-2 x 4

Use the commutative property to turn the problem around to 4 x -2

- 8

Use grouping to model these!!

-14-7 x 2

3 x -4 -12

What about a negative times a negative?

-3 x - 2 means the opposite of 3 groups of - 2.

The OPPOSITE would be

Another way to look at negative times a negative using the Distributive Property…..

-5 (- 6 + 6)

-5 (0)

= 0

So we know that -5 (-6 + 6)

equals 0

-5 ( -6 + 6 )

(-5)(-6) + (-5)( 6)

? + -30

= 0

For the problem to equal zero, the

negative times a negative must equal

a positive!

Multiplying Integers Rules

• If the signs are the same (+ x + or - x -); multiply and the answer is positive

• If the signs are different ( + x – or - x +); multiply and the answer is negative

Dividing Integers

Division is the inverse operation of multiplication.

4 x 2 = 8 inverse 8 ÷ 2 = 4

4 x (– 2 )= (-8) inverse (-8) ÷ (-2) = 4

Dividing Integers

(-5) x 3 =(-15) inverse (-15) 3 = -5

2 x (-3) = (-6) inverse (-6) ÷ (-3) = 2

÷

Rules for Division

Same as Multiplication:

• If the signs are the same (+ x + or - x -); multiply and the answer is positive

• If the signs are different ( + x – or - x +); multiply and the answer is negative