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65 terms

Real Numbers, Operations and Properties of Real Numbers

Commutative Property of Addition

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

(negative)(negative) = POSITIVE

(positive)(negative) = NEGATIVE

(negative)(positive) = NEGATIVE

Dividing Real Numbers

(positive)/(positive) = POSITIVE

(negative)/(negative) = POSITIVE

(positive)/(negative) = NEGATIVE

(negative)/(positive) = NEGATIVE

(negative)/(negative) = POSITIVE

(positive)/(negative) = NEGATIVE

(negative)/(positive) = NEGATIVE

When is a quotient undefined?

When the denominator is zero.

a/0 = undefined

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)

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

Natural Numbers, Whole Number, Integers, Rational Numbers and Irrational Numbers

Associative Property of Addition

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?

Addition

"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?

Addition

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 addition

add, sum, plus, more than

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?

Quadrant 1

The ordered pair (-2,5) is found in what quadrant of the rectangular coordinate system?

Quadrant 2

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?

Quadrant 4

The point (-5, -1) lies in which quadrant?

Quadrant 3

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

Plottin x and y intercepts

The slope-intercept method