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### Pre-Algebra Chapter 1

Algebraic Expressions and Integers

Section 1-1 Variables and Expressions

is a letter or a symbol that replaces a number.

- Variable

- Variableexpression

is a mathematical phrase that uses variable, numbers and operation symbols.

- Numerical expression

is a mathematical phrase that uses numbers and operation symbols.

Examples

Identify each expression as a numerical expression or a variable expression. For a variable expression, name the variable.

- 7 x 3
- 8 + m
- x + y
- 27/9
- 5m
- k

1-2 The Order of Operations

Remember order of operation by the following saying:

Please Excuse My Dear Aunt Sally

Examples

Simplify the following numerical expressions using the order of operations.

a. 8-2(2)

b. 12/3-1(2)+1

c. 20-3[(5+2)-1]

1-4 Integers and Absolute Value

- Numbers that are the same distance from zero on a number line but in opposite directions are called opposites.
- Integers are the set of whole numbers and their opposites.
- A number’s distance from zero on a number line is called its absolute value.

1-5 Adding Integers

When adding opposites, the sum is zero

Rules for Adding Integers

- The sum of two positive integers is positive. The sum of two negative integers is negative.

- Same Signs:

- Different Signs:

To add two integers with signs, find the difference of their absolute values. The sum has the sign of the integer with the greater absolute value.

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