Commutative and Associative Property of Multiplication

Contributed by:

Diego Mon, Jan 24, 2022 07:29 AM UTC

Learn about the properties of Multiplication.

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 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 {}.

4. Commutative Properties
CommutativeProperty
Property
ofaddition
addition--(Order)
(Order)
For
Forany numbersaaand
anynumbers andbb, ,aa++bb==bb++a.a.
45
45++55==55++45
45
50
50==50
50
CommutativeProperty
Property
For
Forany numbersaaand
anynumbers andbb, ,aabb==bba.a.
ofmultiplication
multiplication--
(order)
6688==8866
48
48==48
48

5. Associative Properties
AssociativeProperty
Propertyof
of For
Forany numbersa,a,b,b,and
anynumbers andc,c,
addition--(grouping
(grouping
symbols) (a++b)
(a b)++cc==aa++(b
(b++c).
c).
(2
(2++4)
4)++55==22++(4
(4++5)
5)
(6)
(6)++55 == 22++(9)
(9)
11
11==11
11
AssociativeProperty
Propertyof
of For
Forany numbersa,a,b,b,and
anynumbers andc,c,
multiplication--
(groupingsymbols)
symbols) (ab)cc==aa(bc).
(ab) (bc).
(2
(23)
3)55==22(3
(35)
5)
(6)
(6)55 == 22(15)
(15)
30
30 == 30
30

6. Commutative and Associative Properties
• Commutative and Associative properties are very helpful
to solve problems using mental math strategies.
Rewritethe
theproblem
problemby
bygrouping
groupingnumbers
numbersthat
thatcan
canbe
beformed
formedeasily.
easily.
(Associativeproperty)
property) This
Thisprocess
processmay
maychange
changethe
theorder
orderin
inwhich
whichthe
the
originalproblem
problemwas
wasintroduced.
introduced.(Commutative
(Commutativeproperty)
property)
Evaluate:
Evaluate:18
18++13
13++16
16++27
27++22
22++24
24
(18
(18++22)
22)++(16
(16++24)
24)++(13
(13++27)
27)
(40)
(40)++(40)
(40)++(40)
(40)==120
120

7. Commutative and Associative Properties
• Commutative and Associative properties are very helpful
to solve problems using mental math strategies.
Rewritethe
theproblem
problembybychanging
changingthe
theorder
orderin
inwhich
whichthe
theoriginal
original
problemwas
wasintroduced.
introduced.(Commutative
(Commutativeproperty)
property) Group
Groupnumbers
numbersthat
that
canbe
beformed
formedeasily.
easily.(Associative
(Associativeproperty)
property)
Evaluate:
Evaluate:447725
25
4425
2577
(4
(425)
25)77
(100)
(100)77==700
700

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