**
Readings for Session 10 – **
Properties of Addition and Standard Algorithm

**
Properties for Addition
of Whole Numbers**

**
Commutative Property of
Multiplication:**

General Property:
*ab* =
*ba*

Numeric Example:
3
× 5 = 15 = 5
× 3

Algebraic Example:
(3*x*)(4*x*)
= (4*x*)(3*x*)

**
Associative Property of
Multiplication:**

General Property: (*ab*)*c*
= *a*(*bc*)

Numeric Example:
(2
× 6)
× 8
= 12
× 8

=
96

= 2 ×
48

= 2
× (6
×
8)

Algebraic Example:
2
∙ (3*x*)
= (2
∙ 3)*x*

=
6*x*

Notice that in this case, regrouping allows us to simplify the
expression.

*Example:*
We show how the associative and commutative properties
for multiplication of whole numbers are used to simplify an
algebraic expression.

(3*x*)(4*x*)
= 3(*x *
∙
4)*x*
Associative Property of Multiplication

=
3(4
∙
*x*)
*x*
Commutative Property of Multiplication

=
(3
∙ 4)(*x*
∙
*x*)
Associative Property of Multiplication

=
12*x*^{2}

**
Identity Property for
Multiplication:**

General Property: 1
∙
*
a*
= *a *
∙* *
1
= *a*

Numeric Example:
1
∙ 5
= 5
∙ 1
= 5

Algebraic Example:
1(4*x*) = (4*x*)
∙
1 = 4*x*

**
Distributive Properties
of Multiplication:**

General Property:
*a*(*b
*+ *c*) =
*ab* +
*ac*
or
*a*(*b
*– *c*) =
*ab* –
*ac*

Numeric Example:
4(145) = 4(100 + 40 + 5)

=
4(100) + 4(40) + 4(5)

=
400
+ 160
+ 20

=
580

Algebraic Example:
5(3*x* + 9)
= 5(3*x*)
+ 5(9)

=
(5
∙
3)*x* + 5(9)

=
15*x*
+ 45

Note that the Associative Property of Multiplication is used in
the second step.

*Example:*
The distributive property allows us to more easily perform
computations mentally.

7(29) = 7(30 – 1)

=
7(30) – 7(1)

=
210 – 7

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