Commutative and Associative Properties

1
Commutative and Associative Properties
2
Commutative and Associative Properties

• Properties refer to rules that indicate a
  standard procedure or method to be followed.
• A proof is a demonstration of the truth of a
  statement in mathematics.
• Properties or rules in mathematics are the result
  from testing the truth or validity of something
  by experiment or trial to establish a proof.
• Therefore every mathematical problem from the
  easiest to the more complex can be solved by
  following step by step procedures that are
  identified as mathematical properties.

3
Commutative and Associative Properties

• Commutative Property changing the order in
  which you add or subtract numbers does not change
  the sum or product.
• Associative Property 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 .

4
Commutative and Associative Properties
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
5
Commutative and Associative Properties
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
6
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)
Solve 18 13 16 27 22 24
(18 22) (16 24) (13 27)
(40) (40) (40) 120
7
Commutative and Associative Properties
Commutative and associative properties are very
helpful to solve problems using mental math
strategies
Solve 4 ? 7 ? 25
Rewrite the problem by changing the order in
which the original problem was introduced.
(Commutative property)
4 ? 25 ? 7
Group numbers that can be formed easily.
(Associative property)
(4 ? 25) ? 7
(100) ? 7 700