16A Commutative and Associative Properties

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1-6A Commutative and Associative Properties
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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Properties of Addition
Commutative Property The order in which
numbers are added does not change the sum.
x y y x
9 4 4 9
Associative Property The way numbers are
grouped when added does not change the sum.
(2 5) 10 2 (5 10)
(a b) c a (b c)
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Properties of Multiplication
Commutative Property The order in which
numbers are multiplied does not change the
product.
y x x y
9(4) 4(9)
Associative Property The way numbers are
grouped when multiplied does not change the
product.
(2 5) 10 2 (5 10)
(a b) c a (b c)
(ab)c a(bc)
Property of Negative One The product of a
number and 1 is the opposite of the number.
Items inside parentheses are read as the
quantity of
x(1) -x
16 (1) 16
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Name the property shown by the statement.
12 36 36 12
Example 1
commutative
Example 2
associative
Example 3
commutative
Example 4
commutative
Example 5
property of negative one
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Name the property shown by the statement.
Example 6
(4 5) 6 (5 4) 6
commutative
(9 6) 5 9 (6 5)
Example 7
associative
Example 8
commutative
Example 9
associative
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Simplify.
If you override the left to right rule, you must
show the step/s which gives support to your
thinking!
You must follow the rules for the order of
operations.
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Simplify the expression and indicate the
properties used.
Write the problem.
Commutative
Substitution
Substitution
If you override the left to right rule, you must
show the step/s which gives support to your
thinking!
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Simplify the expression and indicate the
properties used.
Example 10
Example 11
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Example 10 Simplify the expression and indicate
the properties used.
Write the problem.
-3
Commutative
Substitution
36
Substitution
If you alter the left to right rule, you must
show the step which gives support to your
thinking!
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Example 11 Simplify the expression and indicate
the properties used.
Write the problem.
Distributive
Substitution
Commutative
Associative
Distributive
Substitution
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Write and algebraic expression for the verbal
expression. Then simplify the expression and
indicate the properties used. Example 12 four
times the sum of a and b increased by twice the
sum of a and 2b Example 13 5 times the
difference of x squared and y plus 8 times the
sum of 3x and 2y
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Example 12 Write and algebraic expression for
the verbal expression. Then simplify the
expression and indicate the properties used. four
times the sum of a and b increased by twice the
sum of a and 2b
Write the problem.
Distributive
Substitution
Commutative
Associative
Distributive
Substitution
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Example 13 Write and algebraic expression for
the verbal expression. Then simplify the
expression and indicate the properties used. 5
times the difference of x squared and y plus 8
times the sum of 3x and 2y
Write the problem.
Distributive
Substitution
Commutative
Associative
Distributive
Substitution
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Homework

• 1-A10 Page 36-37 11-21 odd, 24-40, 48-55.