same signs

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Transcript same signs

ADDING INTEGERS
(SAME SIGNS)
• SAME signs
keep the sign
4 +
2
4 positives
+ 2 positives
ADD and
=
6
=
6 positives
ADDING INTEGERS
(SAME SIGNS)
• SAME signs
keep the sign
-4
4 negatives
+ - 2
+
add and
= -6
2 negatives =
6 negatives
ADDING INTEGERS
(DIFFERENT SIGNS)
• DIFFERENT signs
SUBTRACT
and keep the sign of the larger number
4
+ - 2
4 positives +
= 2
2 negatives =
2 positives
ADDING INTEGERS
(DIFFERENT SIGNS)
• DIFFERENT signs
SUBTRACT
and keep the sign of the larger number
-4
+
4 negatives +
2
= -2
2 positives =
2 negatives
SUBTRACTING INTEGERS
(KFC & follow Rules for addition)
Problem
8 - 10
KFC
follow addition rules
8 + - 10
K – keep the first number
F – flip the subtraction to an addition sign
C – 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 sign
B. 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
axb=bxa
MULTIPLYING INTEGERS
4x2
4 groups of 2
=
=
2 x 4
2 groups of 4
=
8
=
8
4 x -2
4 groups of - 2 = - 8
What would
-2 x 4
-8
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!!
-7 x 2
-14
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 ( -6 + 6 )
-5 (0)
(-5)(-6) + (-5)( 6)
=0
So we know
that -5 (-6 + 6)
equals 0
?
+
-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.
4x2=8
inverse
4 x (– 2 )= (-8) inverse
8 ÷ 2 =4
(-8) ÷ (-2) = 4
Dividing Integers
(-5) x 3 =(-15) inverse
2 x (-3) = (-6) inverse
(-15) ÷ 3 = -5
(-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