65 terms

# Elementary Algebra Flash Cards - Chapter 1

Real Numbers, Operations and Properties of Real Numbers
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a + b = b + a
Natural Numbers
Counting Numbers
Whole Numbers
Counting Numbers and Zero
Integers
Whole Numbers and their opposites
Rational Numbers
Quotient of Intergers a/b, where "b" does not equal zero.
Absolute Value
measurement of distance of how far a value is from zero. The absolute value of a number is always positive.
Multiplying Real Numbers
(positive)(positive) = POSITIVE
(negative)(negative) = POSITIVE
(positive)(negative) = NEGATIVE
(negative)(positive) = NEGATIVE
Dividing Real Numbers
(positive)/(positive) = POSITIVE
(negative)/(negative) = POSITIVE
(positive)/(negative) = NEGATIVE
(negative)/(positive) = NEGATIVE
When is a quotient undefined?
When the denominator is zero.

a/0 = undefined
State the Order of Operations
1. Grouping Symbols (Parenthesis, Brackets, Absolute Value)
2. Simplify Exponents
3. Multiply OR Divide (FROM LEFT TO RIGHT)
4. Add OR Subtract (FROM LEFT TO RIGHT)
Real Numbers
The set of numbers that include:
Natural Numbers, Whole Number, Integers, Rational Numbers and Irrational Numbers
a +(b + c) = (a + b) + c
Inequality Symbols
Symbolize that algebraic quantities are not equal.

>,<,
Composite Numbers
natural numbers, excluding 1, which are not prime
Prime Numbers
Natural Numbers that have exactly two factors, one and itself
Commutative Property of Multiplication
(a)(b) = (b)(a)
Associative Property of Multiplication
a (b c) = (a b) c
Distributive Property
a(b +c) = ab + ac
In the fraction a/b, "a" represents the....?
Numerator
In the fraction a/b, "b" represents the...?
Denominator
Finding the prime factorization of a natural number means to...?
Express a natural number as a product of all prime numbers
"Sum" is a key word for which operation?
"Product" is a key word for which operation?
Multiplication
"Difference" is a key word for which operation
Subtraction
"Quotient" is a key word for which operation
Division
"Twice" is a key word for which operation?
Multiplication
The key word "is" means what?
Equals
"Of" is a key word for which operation?
Multiplication
"More than" is a phrase that represents which operation?
The reciprocal of a fraction is...
To rewrite the fraction to where what was the numerator becomes the denominator and what was the denominator becomes the numerator
To add fractions the denominators must be....
THE SAME
To subtract fractions the denominators must be...
THE SAME
To multiply fractions you...
multiply the numerators straight across and multiply the denominators straight across
To divide fractions you...
multiply by the reciprocal of the divisor
Key words for subtraction
subtract, minus, difference, less than
Key words for multiplication
multiply, times, product, of
Key words for division
divide, quotient, ratio, into
How do you clear the fractions in an equation when solving?
Multiply both sides of the equation by the LCD
The rectangular coordinate system has how many quadrants
four
The vertical axis in the rectangular coordinate system is called
The "y" axis
The horizontal axis in the rectangular coordinate system is called
The "x" axis
Ordered pairs represent
points
The point where the x and y axis intersect is called the
Origin
The equation of a vertical line is:
x = any real number
The equation of a horizontal line is:
y = any real number
Slope of a line
change in y coordinate/change in x coordinate
Formula to find the slope of a line when you know two points on the line
y2-y1/x2-x1
Formula for the point slope equation
y - y1 = m(x - x1)
Slope intercept equation of a line
y = mx + b
When discussing linear equations, the variable "m" represents
The slope
In the slope intercept equation y = mx + b, "b" represents
The y-coordinate of the y-intercept
What is a "y-intercept"
The point where the graph, intersects the y-axis
Whis a an "x" intercept?
The point where the graph, intersects the x-axis
To find the x-intercept algebraically, you should
In your equation, let y = 0. Then solve your equation for "x". Write intercept as the ordered pair (x, 0)
The ordered pair (3,2) is found in what quadrant of the rectangular coordinate system?
The ordered pair (-2,5) is found in what quadrant of the rectangular coordinate system?
If the x coordinate of a point if positive and the y coordinate of that same point is negative, the point lies in which quadrant of the rectangular coordinate system?
The point (-5, -1) lies in which quadrant?
Standard Equation of a Line
Ax + By = C
Slopes of parallel lines are:
The same
Slopes of perpendicular lines are:
Opposite Reciprocals
The slope of a vertical line is
Undefined
The slope of a horizontal line is:
Zero
The three methods used to graph a line are:
The T-chart Method
Plottin x and y intercepts
The slope-intercept method