Transcript Whole Number Operations and Their Properties

Whole Number Operations
and Their Properties
Commutative Property of Addition and
Multiplication
Addition and Multiplication are commutative:
switching the order of two numbers being added
or multiplied does not change the result. When
adding numbers, it doesn't matter which number
comes first, the sum will be the same. Another
way to look at it is, buying two things in different
order still will cost the same.
Examples:
100 + 8 = 8 + 100
100 × 8 = 8 × 100
Associative Property
Addition and multiplication are associative: the
order that numbers are grouped in addition and
multiplication does not affect the result.
Examples:
(2 + 10) + 6 = 2 + (10 + 6) = 18
2 × (10 × 6) = (2 × 10) × 6 =120
Distributive Property
The Distributive Property is an algebra property
which is used to multiply a single term and two or
more terms inside a set of parentheses.
Examples:
10 × (50 + 3) = (10 × 50) + (10 × 3)
3 × (12+99) = (3 × 12) + (3 × 99)
The Zero Property of Addition
Adding 0 to a number leaves it unchanged.
We call 0 the additive identity.
Example:
88 + 0 = 88
The Zero Property of Multiplication
Multiplying any number by 0 gives 0.
Example:
88 × 0 = 0
0 × 1003 = 0
The Multiplicative Identity
We call 1 the multiplicative identity. Multiplying any
number by 1 leaves the number unchanged.
Example:
88 × 1 = 88
AdditiveInverse
Property
• The additive inverse of a number is
the number’s opposite.
• Ex: 5 + -5 = 0 In this example -5 is
the additive inverse of 5.
Multiplicative Inverse
Property
• The multiplicative inverse of a
number is the reciprocal of the
number.
• Ex: 3 · 1/3 = 1 In this example,
notice that the product of a number
and it’s multiplicative inverse is
always 1.
Closure Property
• A set of numbers is closed under an
operation if the result of the
operation on any two numbers in the
set is also a number in the set.