Chapter 1

Words

Definition and Example

Associative Property

The property that states that for three or more numbers, their sum or product is always the same, regardless of their grouping.

Example : 2 + 3 + 8 = (2 + 3) + 8 = 2 + (3 + 8)

2 • 3 • 8  (2 • 3) • 8  2 • (3 • 8)

 

base (in numeration)

when a number is raised to a power, the number that is used as a factor is the base.

Example: 35 to the fifth power =

3 • 3 • 3 • 3 • 3; 3 is the base.

 

Commutative Property

The property that states that two or more numbers can be added (or multiplied) in any order without changing the sum (product).

Example: 8 + 20 = 20 + 8 or 6 • 12 = 12 • 6

 

Distributive Property

The property that states if you multiply a sum by a number, you will get the same result if you multiply each addend by that number and then add the products.

Example: 5(20 + 1) = 5 • 20 + 5 • 1

 

exponent

The number that indicates how many times the base is used as a factor.

Example : 2 to the third power = 2 • 2 • 2 = 8; 3 is the exponent

order of operations

A rule for evaluating expressions: first perform the operations in parentheses, then compute powers and roots, then perform all multiplication and division from left to right, and then perform all addition and subtraction from left to right.