AlgebraSurvivalGuide - Glossary Flashcards
Absolute Value
the distance between a number and zero on the number line. Absolute Value is always positive because distance is always a positive number. Distance can never be a negative number in nature.
Additive Identity property
property that says when you add zero to any number or term, you get back the number or term you started with.
Associative property
property that says in addition and multiplication, the way ther terms are grouped makes no difference. In other words, a+(b+c)= (a+b) + c, and a(bc)=(ab)c.
Base
the bottom number in an exponential term. Example: in the exponential term X^7, the base is X, while the exponent is 7.
Binomial
a polynomial made up of two monomials.
Cancelling
the act of tidying up mathematical expressions.
Coefficient
the number that stands in front of the variable or variable string in a monomial. A coeffient may be position of negative. Example: in the monopial 5X^2Y, the coefficient is +5 in the monomial 5X^2Y, the coefficient is 5.
Commutative property:
property that says that in addtion and multiplication, the order of the terms makes no difference. In other words, a + b is the same as b + a, and ab is the same as ba.
Consecutive Integers
Integers that are one apart from one another. Example: 4,5 and 6 are consecutive integers.
Coordinate
a number which, by acting as a directional tool, helps you locate a point on the coordinate plane. Each pint on the coordinate plane has both an x-coordinate and a y-coordinate.
Coordinate plane
the x-y plane, used for graphing points, lines, and more.
Denominator:
the quality below a fraction bar is the denominator. (Compare with numberator)
Decending order:
a way of writing a polynomial so that its exponents decrease from left to right.
Distance:
the measure of the length of a line between two distinct points.
distributive property:
a property that says this: If you have a parenthesis containing a bunch of terms linked by addition or subtraction signs, any number or term that multiplies the parenthesis multiplies every term inside the parenthesis. That is: a(b+c)=ab+ac, and a(b-c)=ab-ac.
Equation
any mathematical expression that has an equal sign and quantities on both the left and right sides of the equal sign. An equaiton tells you that these tow quantities are equal.
Even numbers
the set of all numbers: {-∞…-6,-4,-2,0,2,4,6…+∞} (Compare with odd numbers.)
Exponent
a little number or term that sits on the right shoulder of another number or term called the base. The exponent tells you how many times the base is mulitplying itself. For example: int eh exponential term c^7, the exponent 7 tells you that X is multiplying itself 7 times.
Exponential term:
the base and the exponent, viewed as a whole.
Factor:
one of two or more terms which, multiplied together, give you some product. Examples: 3 and 5 are factors of 15 because 3×5=15; and x and x^3 are factors of x^4 because x times x^3 = x^4.
Facoring:
the act of splitting a methematical expression into its basic parts.
Fraction:
a term made up of a numberator and a denominator. When yo see a fraction, it mens that the numerator is eing divided b the denominator.
Greatest common factor:
the largest number or term that divides evenly into two or more numbers or terms.
Infinity:
a way of expressing that which is the ultimate in largeness or smallness. Positive infinity means that which is large beyong our ability to count it; neative infinity means that which is small beyond our ability to couont it. The symbol for infinity is this: ∞
integers:
the set of all whole numbers plus the negtive of the natural numbers: {-∞…-6,-4,-2,0,2,4,6…+∞}
Like terms:
terms that represent the same kinds of things. For example, 4X and 11X are like terms; 7p^2q and 5p^2q are like terms.
Line:
straight extension with no thickness. There is one and only one line between any two distinct points.
Linear equation:
an equation that represents a line. One type on linear equation is the slope-intercepts equation : y=mx +b
Mixed -sign rule:
the rule for combining numbers with different signs.
Monomial:
a term made up of either: a) a number, or b) a coefficient along with a vairable or a variable string. Ecamples of monomials are: 3, -3, 5x, 7x^3, -7x^3.
Multiplicative identity property:
property that says when you multple any number or tern by 1, you get back the number or term you started with.
Natural numbers:
the set of all counting numbers: {1,2,3,4…∞}
Negative exponent:
an exponent that has a negative sign.
Negative infinity:
a mathematical way of referring to that which is small beyond our ability to count it. The symbol for negative infinity isthis: -∞
Neighbor-sign rule:
the rule for dealing with two signs that are directly next ot each other. This rule tells you that the two signs merge to become one sign.
Number:
A symbol used to indicate how many of a certain quantity you’re dealing with.
Numerator:
the quantitiy above a fraction bar is the numerator. (Compare with denominator)
Odd numbers:
the set of all numbers: {-∞ …-5,-3,-1,1,3,5…+∞} Compare with even numbers.
Order of operations:
the set of rules that tells you which operation to perform before which other operation.
Origin:
the point on a coordinate plane where the x-axis and y-axis meet.
Percent:
a way of indicating how much of a quantity you’re dealing with. Percent means “out of one hundred,” so when you state a percent, you’re saying how many hundredths of something you have. Example: 12 percent means 12/100.
Perfect square
what you get when you square a number or a term.
Point:
a location on the coordinate plane. A point has no size.
Polynomial:
a string of two or more monomials.
Product:
what you get when you multiply numbers or terms together. Example: when you multiply 3 by 5, the product is 15.
Quadratic trinomial:
a trinomial in which the highest exponent is 2.
Radical:
the root of a number. In Algebra I, the tem radical means square root.
Rational numbers:
the set of numbers that can be written as an Integer divided by another integer. There’s one exception: any number divided by zero is not a rational numebr; it is undefined.
Real numbers:
Combine the rational numbers and Irrational numbers. Whe you put them together, you get the set of real numbers.
Reciprocal:
the flip of a fraction. For example: 4/3 is the reciprocal of 3/4; and 5x/3y is the reciprocal of 3y/5x.
Reflexive property:
a property that says that anything is equal to itself. That is a=a.
Same-sign rule:
rule that tells you how to combine a group of numbers that are either all positive or all negative.
Slope:
the measure of the steepness of a line on the corrdinate plane.
Square root:
Choose any number or term. The find the special number or term which, when multiplied by itself, gives you the numbeer or term you started with for example, start with 9. Since 3⋅3=9, 3 is the square root of 9. Or start with 25x^2. Since 5x ⋅5x = 25x^2, 5x is the square root of 25x^2.
Squaring:
the act of multiplying a number or term by itself. Example: if you square 7, you get 49.
Symmetric property:
property that says the left and right sides of an equation are interchangeable. In other words, if it’s true that a=b, then it’s also true that b=a.
Transitive property:
property by which you discover that two quqntities are equal because both of them are equal to a third quantity. Here’s an example with b acting as the third quantity. If a=b and b=c, then a=c.
Trinomial:
a string of three monomials.
Variable:
a letter that stands for a nystery quantity whose value you want to discover. In general algebraic rule and principles, variables stand for any number whatsoever.
Variable string:
two or more varibales multipled together. Examples of variable string are: xyz and a^4bc^3.
Whole numbers:
the set of all natural numbers, plus zero: {0,1,2,3,4,5…∞}
X-axis:
the axis that runs horizontally (left to right) on the coordinate plane.
y-coordinate:
the coordinate of a point that tells you how far that point stands above or below the origin.
y-intercept:
point where a line crosses the y-axis.
