Download Commutative and Associative Property

Integrated Algebra
Commutative and Associative
Name__________________________
Exercise #1: Add the following numbers without using a calculator. Hint: Although order of
operations tells us we should add from left to right, think about an easier way to sum these
numbers. Show how you summed them.
3+9+4+2+7+1+6+8
Addition and multiplication have two very important properties with very technical names. The next
exercise will review these properties.
Exercise #2: Fill in the missing blanks for each property.
(a) Commutative Property of Addition:
8+4 gives the same sum as _________________. Both sums equal _________.
(b) Commutative Property of Multiplication:
6 x 3 gives the same product as _______________. Both products equal __________.
(c) Associative Property of Addition:
The sum (3+5) + 9 gives the same result as the sum _______________________.
Both sums are equal to ___________________
(d) Associative Property of Multiplication:
The product (2 ● 5) ● 7 gives the same result as the product ____________________.
Both products are equal to _________________
The Commutative Property and Associative Property essentially give us permission to rewrite
addition and multiplication problems in different orders than what are normally given.
Exercise #3: Give an example that shows that subtraction is not commutative.
TWO properties of the Real Number System?
PROPERTY
COMMUTATIVE
ASSOCIATIVE
What is it?
Examples/Information
Change Order: changing the order of
multiplication or addition problem
does not change the answer.
Multiplication and addition problems
can be regrouped with parentheses.
Grouping does not change the answer.
Rewrite each expression using both properties:
1) 2 + 1
_________________________ (Commutative)
2) (1 + 2) + 3 ____________________________ (associative)
3) Use the associative property to rewrite the following. You do NOT need to simplify these
(a) 2+(3+4)=
(b) 5x(3x7) =
4)Use the commutative property to rewrite the following. You do NOT need to simplify these
(a) 6+8+7 =
(b) 12x + 3x +7x =
Properties Practice- Flow Diagrams
Fill in each circle with the appropriate symbol:
C+ for the commutative property of addition
Cx for the commutative property of multiplication
A+ for the associative property of addition
Ax for the associative property of multiplication
1) The following portion of a flow diagram shows that the expression ab + cd is equivalent to
the expression dc + ba. Fill in each circle with the appropriate symbol from above.
ab + cd
ba + cd
ba + dc
dc + ba
2) Fill in the following flow diagram using the symbols from above.
z + (x + y)
(z + x) + y
y + (z + x)
3) Fill in the following flow diagram using the symbols from above.
5 ( a + y (2x)) + ( x + 4)
(x + 4) + 5 ( a + (2x) y)
5 ( a + (2x) y) + (x + 4)
5 ( a + 2 (xy)) + (x+4)
Commutative and Associative Properties Homework
Name_________________
1) Are the following everyday activities commutative? Answer yes or no.
a) Putting on socks, putting
on shoes?
b) Putting on a ring, putting
on a watch?
2) Explain why the following statement are
equivalent: x  (a  7)  x  (7  a)
4)
c) Washing dishes, drying
dishes?
3) Explain why the following statements are
equivalent : x  ( y  9)  ( x  y )  9
Complete the flow diagram with one of the following symbols:
C+ for the commutative property of addition
Cx for the commutative property of multiplication
A+ for the associative property of addition
Ax for the associative property of multiplication
D is for the Distributive property (will do more tomorrow)
4( x  3)  ab( x  3)
D
4x  12  abx  ab3
4x  12  abx  3ab
4x  abx  12  3ab