ADDING INTEGERS (SAME SIGNS) SAME signs ADD and keep the sign 4 + 2 = 6 4 positives + 2 positives =...
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Transcript of ADDING INTEGERS (SAME SIGNS) SAME signs ADD and keep the sign 4 + 2 = 6 4 positives + 2 positives =...
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