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Commutative and
Associative Properties
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Commutative Property of Addition: The order in which
the terms of a sum are added does not change the sum.
a+b=b+a
5+7=7+5
12= 12
Commutative Property of Multiplication: The order in
which the terms of a product are multiplied does not
change the product.
ab = ba
4(5) = 5(4)
Associative Property of Addition: The order in which the
terms of a sum are grouped does not change the sum.
(a + b) + c = a + (b + c)
(2 + 3) + 4 = 2 + (3 + 4)
5+4=2+7
9=9
The Associative Property is particularly useful when
you are combining integers.
Example:
-15 + 9 + (-4)=
-15 + (-4) + 9=
-19 + 9 =
-10
Changing it this way allows for the
negatives to be added together first.
Associative Property of Multiplication: The order in
which the terms of a product are grouped does not
change the product.
1
Identify the property of -5 + 3 = 3 + (-5)
A
B
C
D
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
2
Identify the property of a + (b + c) = (a + c) + b
A
B
C
D
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
Discuss why using the associative property would be
useful with the following problems:
1. 4 + 3 + (-4)
2. -9 x 3 x 0
3. -5 x 7 x -2
4. -8 + 1 + (-6)
Combining Like Terms
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An Expression - contains numbers, variables and at
least one operation.
Like terms: terms in an expression that have the
same variable raised to the same power
Examples:
LIKE TERMS
NOT LIKE TERMS
2
6x and 2x
6x and 2x
5y and 8y
5x and 8y
2
4x and 7x
2
2
2
4x y and 7xy
4
Identify all of the terms like 2x
A
B
C
D
E
5x
2
3x
5y
12y
2
5
Identify all of the terms like 8y
A
B
C
D
E
9y
2
4y
7y
8
-18x
If two or more like terms are being added or
subtracted, they can be combined.
To combine like terms add/subtract the coefficient
but leave the variable alone.
7x +8x =15x
9v-2v = 7v
Sometimes there are constant terms that can be
combined.
9 + 2f + 6 =
9 + 2f + 6 =
2f + 15
Sometimes there will be both coeffients and constants to
be combined.
3g + 7 + 8g - 2
11g + 5
Notice that the sign before a given term goes with the
number.
9
8x + 3x = 11x
A
B
True
False
10 7x + 7y = 14xy
A
B
True
False
12
9x + 5y = 14xy
A
B
True
False
15
-6 + y + 8 = 2y
A
B
True
False
19 -4x - 6 + 2x - 14
A
B
C
D
-22x
-2x - 20
-6x +20
22x