Transcript Document

•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.
•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 {}.
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 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 are very helpful
to solve problems using mental math strategies
Solve: 18 + 13 + 16 + 27 + 22 + 24
Rewrite the problem by grouping numbers that
can be formed easily. (Associative property)
(18 + 22) + (16 + 24) + (13 + 27)
This process may change the order in which the
original problem was introduced. (Commutative
property)
(40) + (40) + (40) = 120
Commutative and associative properties are very helpful
to solve problems using mental math strategies
Solve: 4  7  25
4  25  7
(4  25)  7
(100)  7 = 700
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)