6th Grade Math Textbook, Fundamentals

Think

“order”

Think

“grouping”

Think

“same number”

130 Chapter 5

5-12

Properties of Rational Numbers

Objective To identify properties of addition and multiplication of rational numbers

• To use the properties to compute mentally with rational numbers

Properties can help you compute. Let a, b, and crepresent any rational numbers.

Commutative Property of Addition

Changing the orderof the addends

does notchange the sum.

abba

Example:^23 ^144132

Commutative Property of Multiplication

Changing the orderof the factors

does notchange the product.

abba

Example:  75 () 81 () 81  75

Associative Property of Addition

Changing the groupingof the addends

does notchange the sum.

(ab)ca(bc)

Example: ( 32  31 )  51  32 (^13  51 )

Associative Property of Multiplication

Changing the groupingof the factors

does notchange the product.

(ab)ca(bc)

Example: (^34 • 95 ) 53 ^34 ( 95 •^35 )

Identity Property of Addition

The additive identity elementis 0.

Adding 0 to any number does not

change the value of the number.

a 0 aand 0aa

Examples:^38  0 ^38 and 0^3883

Identity Property of Multiplication

The multiplicative identity elementis 1.

Multiplying 1 and any number does not

change the value of the number.

a• 1aand 1• aa

Examples:• 101 1  101 and 1• 101  101

Inverse Property of Addition

The additive inverse, or opposite, of a

is a.

a(a) 0 and aa 0

Examples:^12 ( 21 )0 and ^12  21 0

The multiplicative inverse, or

reciprocal, ofais , a0.

a()1 and ()a 1

Examples:9() 91 1 and () 919  1

1

a

1

a

1

a

Inverse Property of Multiplication

Zero Property of Multiplication

The product of 0 and any number is 0.

a• 00 and 0• a 0

()0, when band d^0

Examples: (^0) () 125 0 and () 125 0  0
c
d
0
b
The product of 1 and any number is the
additive inverse of the number.
a• (1) (a)
Example:(^49 1) ^4949 and  94 are opposites.
Multiplicative Property of  1