Commutative and
Associative Properties
Commutative and Associative Properties
• Commutative Property means changing the order
in which you add or subtract numbers does not
change the sum or product.
• Associative Property means changing the
grouping of numbers when adding or multiplying
does not change their sum or product.
• Grouping symbols are typically parentheses (),but
can include brackets [] or Braces {}.
Commutative Properties
Commutative Property
of addition - (Order)
For any numbers a and b , a + b = b + a.
45 + 5 = 5 + 45
50 = 50
Commutative Property
of multiplication (order)
For any numbers a and b , a  b = b  a.
68=86
48 = 48
Associative Properties
Associative Property of
addition - (grouping
symbols)
For any numbers a, b, and c,
(a + b) + c = a + (b + c).
(2 + 4) + 5 = 2 + (4 + 5)
(6) + 5 = 2 + (9)
11 = 11
Associative Property of
multiplication (grouping symbols)
For any numbers a, b, and c,
(ab) c = a (bc).
(2  3)  5 = 2  (3  5)
(6)  5 = 2  (15)
30 = 30
Commutative and Associative Properties
• Commutative and Associative properties are very helpful
to solve problems using mental math strategies.
Rewrite the problem by grouping numbers that can be formed easily.
(Associative property) This process may change the order in which the
original problem was introduced. (Commutative property)
Evaluate: 18 + 13 + 16 + 27 + 22 + 24
(18 + 22) + (16 + 24) + (13 + 27)
(40) + (40) + (40) = 120
Commutative and Associative Properties
• Commutative and Associative properties are very helpful
to solve problems using mental math strategies.
Rewrite the problem by changing the order in which the original
problem was introduced. (Commutative property) Group numbers that
can be formed easily. (Associative property)
Evaluate: 4  7  25
4  25  7
(4  25)  7
(100)  7 = 700