1.1 Symbols and Sets of Numbers
Set. A collection of objects, called elements, enclosed in braces
{a,b,c}
Natural Numbers. {1,2,3,4...}
Whole Numbers. {0,1,2,3,4...}
Integers. {...,-3,-2,-1,0,1,2,3...}
Rational Numbers {real numbers that can be expressed as a quotient of integers}
Irrational Numbers. {real numbers that cannot be expressed as a quotient of integers}
Real Numbers. {all numbers that correspond to a point on the number line}
Number Line. A line used to picture numbers (please see test examples on page
23)
Absolute Value. The distance between a and 0 on the number line. Expressed as |a|
1.2 Introduction to Variable Expressions and Equations
Exponential Expression. A number raised to an exponent (please see text example, page 13). The base is the repeated factor and the exponent is the number of times that the base is a factor.
Order of Operations. Simplify expressions in the following order. If group symbols are present, simplify expressions within those first, starting with the innermost set. Also, simplify the numerator and the denominator of a fraction separately.
- Simplify exponential expressions.
- Multiply or divide in order from left to right
- Add or subtract in order from left to right.
Variable. A symbol used to represent a number.
Evaluate an Algebraic Expression. Substitute a given number for the variable and then simplify.
Equation. A mathematical statement that two expressions are equal.
Solution of an Equation. The value of the variable that makes the equation a true statement.
1.3 Adding Real Numbers
To Add 2 Numbers With the Same Sign (please see text examples, pages 23)
- Add their absolute values
- Use their common sign as the sign of the sum
To Add 2 Numbers With Different Signs (please see text examples, pages 23 and 24)
- Subtract their absolute values
- Use the sign of the number whose absolute value is larger as the sign of the sum
Opposites or Additive Inverses. Two numbers that are the same distance from 0 but lie on opposite sides of 0. The opposite of a is -a. (please see text examples, pages 25 and 26)
1.4 Subtracting Real Numbers
To Subtract Two Numbers. Add the first number to the opposite of the second number. EXAMPLE a-b=a+(-b) Please see text examples page R-31 and R-32)
1.5 Multiplying Real Numbers
Multiplying Real Numbers. The product of two numbers with he same sign is a positive number. The product of two numbers with different signs is a negative
number (please see text examples, page 41)
Products Involving Zero. The product of 0 and any number is 0 )please see text examples pages 41 and 42
1.6 Dividing Real Numbers
Quotient of Two Real Numbers. a/b = a*1/b
Dividing Real Numbers. The quotient of two numbers with the same sign is a positive number. The quotient of two numbers with different signs is a negative number (please see text examples pages
47 - 49)
1.7 Properties of Real Numbers
Commutative Properties