# Review of Chapter 1

**Operations Involving Fractions
**

**Order of Operations
**The acronym PEMA is commonly used to help students remember the order of
operations.

P = parentheses or any grouping symbols

E = exponents

M = multiplications or divisions (evaluate in the order in which they occur, working from left to right)

A = additions or subtractions

Example: Simplify 5[(3 +1)^{2} ÷ 8×
2]

**Exponents
**

**Types of Numbers**

**· REAL NUMBER** = Any number on the number line.

Examples:

**·** **NATURAL NUMBERS** = 1, 2, 3, 4, 5, 6, ...

Examples:

**· WHOLE NUMBERS** = 0, 1, 2, 3, 4, 5, 6, ...**
**Examples:

**· INTEGERS **= ..., -4, -3, -2, -1, 0, 1, 2, 3, 4,
...

Examples:

**· RATIONAL NUMBER** = Any number that can be written
in the form a/b where a,b are integers and b≠0.

Notes: (a) Terminating decimals are rational numbers.

(b) Repeating decimals are rational numbers.

Examples:

**·** **IRRATIONAL NUMBER** = Any real number that is not
rational.

Note: Decimals that are simultaneously nonterminating and nonrepeating are
irrational numbers.

Examples:

NOTE: The rational numbers together with the irrational numbers comprise the real numbers.

**Absolute Value
**The absolute value of a number is the distance between the number and 0 on a
number line.

1. |7|

2. |-3|

3. -|-2 + 5|

**Important Division Facts
·**
is undefined. Examples:
and
are
undefined.

**·**Example:

**Addition and Subtraction of Real Numbers**

Example: Simplify [-4 - (-6)] - (-1 - 5) + (3 - 9)

**Properties of the Real Number System
**Let a,b,c be real numbers.

**· COMMUTATIVE PROPERTY:**

a + b = b + a

ab = ba

The commutative property states that the order in which
two numbers are added or multiplied does not

affect the result.

Example: 2(7) = 7(2)

**·** **ASSOCIATIVE PROPERTY:
**(a + b) + c = a + (b + c)

(ab)c = a(bc)

The associative property states that when adding or
multiplying three numbers, the same result is obtained

whether the first two numbers are grouped together or the last two numbers are
grouped together.

Example: (2 + 3) + 4 = 2 + (3 + 4)

**· DISTRIBUTIVE PROPERTY:**

a(b + c) = ab + ac

a(b - c) = ab - ac

Examples: Use the distributive property to rewrite each expression.

1. 3(x + 5)

2. 4(3a - b)

3. -2(4k - 7)

4. -(-3 + 2z)

**Important Definitions
**1. A term is a number (constant), a variable, a product, or a quotient.

Examples: 5, x, 4x

^{3}y, and are examples of terms. 3x - y + 7 has 3 terms (3x, -y, and 7).

2. The numerical part of a term is called its coefficient.

Example: The coefficients of the terms of 3x - y + 7 are 3, -1, and 7.

3. Like terms are terms that have the same variables with
the same exponents.

Examples: 4x^{3} and -7x^{3} are like terms. 8y^{2} and 3y are unlike terms.

**Simplifying Expressions by Combining Like Terms**

1. 7x^{2} + 2x^{2} - 8y^{2} + 3x

2. 4 - 3(x - 5) + 2x

3. -(5y + 2) + 2(3 - y) - 8