Basic Mathematics for College Students

• Addition Property of 0 (Identity Property of Addition)

a 0 a and 0 aa

Here are several familiar properties of multiplication stated using variables.

• The Commutative Property of Multiplication

abba Changing the order when multiplying does not affect the answer.

• The Associative Property of Multiplication

(ab)ca(bc) Changing the grouping when multiplying does not affect the answer.

• Multiplication Property of 0

0 a 0 and a 0  0 The product of 0 and any number is 0.

• Multiplication Property of 1

1 aa and a 1 a

Here are two familiar properties of division stated using a variable.

• Division Properties

and provided a 0

Identify terms and coefficients of terms.

When we combine variables and numbers using arithmetic operations, the result is an
algebraic expression.

Algebraic Expressions

Variables and/or numbers can be combined with the operations of addition,

subtraction, multiplication, and division to create algebraic expressions.

The Language of Mathematics We often refer to algebraic expressionsas

simply expressions.

Here are some examples of algebraic expressions.

4 a 7

15 mn(2m)

This expression is a combination of the numbers 15 and 2, the

variables mand n, and the operation of multiplication.

This expression is a combination of the numbers 10 and 3, the

variable y, and the operations of subtraction and division.

10 y

3

This expression is a combination of the numbers 4 and 7, the

variable a, and the operations of multiplication and addition.

2

Any number divided by 1

is the number itself.

Any number (except 0)

divided by itself is 1.

a

a

 1

a

1

a

The product of 1 and any number is that

number.

When 0 is added to any number, the

result is the same number.

8.1 The Language of Algebra 639