# Glossary Terms

absolute value

The absolute value of a number is its distance from 0 on the number line. The absolute value of a number n is written as |n|.

accuracy

the degree to which a measure value agrees with the correct value for that measurement

The additive identity is the number 0; adding 0 to any number does not change its value.

The opposite of a number is its additive inverse. A number and it additive inverse add to 0.

amount of discount

The amount of discount is the amount resulting when a discount rate is multiplied by the original price of an item.

angle

An angle is formed by two rays that share a common endpoint. Each ray is called a side of the angle.

area

The area is a measure of the surface covered by a figure.

binomial

A binomial is a polynomial with exactly two terms.

coefficient

The coefficient of a term is the constant that multiplies the variable in a term.

coincident lines

Coincident lines are lines that have the same slope and same y-intercept.

complementary angles

Two angles are complementary if the sum of the measures of their angles is 90 degrees.

complex fraction

A complex fraction is a fraction in which the numerator or the denominator contains a fraction.

Composite Number

A composite number is a counting number that is not prime. A composite number has factors other than 1 and itself.

conditional equation

An equation that is true for one or more values of the variable and false for all other values of the variable is a conditional equation.

cone

A cone is a solid figure with one circular base and a vertex.

conjugate pair

A conjugate pair is two binomials of the form (a-b) , (a+b); the pair of binomials each have the same first term and the same last term, but one binomial is a sum and the other is a difference.

consistent system

A consistent system of equations is a system of equations with at least one solution.

constant

A constant is a number whose value always stays the same.

An equation that is false for all values of the variable is called a contradiction. A contradiction has no solution

counting numbers

The counting numbers are the numbers 1, 2, 3, …

cube

A cube is a rectangular solid whose length, width, and height are equal.

cylinder

A cylinder is a solid figure with two parallel circles of the same size at the top and bottom.

decimal

A decimal is another way of writing a fraction whose denominator is a power of ten.

decreasing linear function

a function with a negative slope: If f(x)=mx+b,  m<0.

degree of a constant

The degree of any constant is 0.

degree of a polynomial

The degree of a polynomial is the highest degree of all its terms.

degree of a term

The degree of a term is the exponent of its variable.

denominator

The denominator is the value on the bottom part of the fraction that indicates the number of equal parts into which the whole has been divided.

dependent equations

Two equations are dependent if all the solutions of one equation are also solutions of the other equation.

discount rate

The discount rate is the percent used to determine the amount of a discount, common in retail settings.

Divisible by a Number

If a number m is a multiple of n, then m is divisible by n.

equality symbol

The symbol “=” is called the equal sign.

equation

An equation is two expressions connected by an equal sign.

equilateral triangle

A triangle with all three sides of equal length is called an equilateral triangle.

equivalent decimals

Two decimals are equivalent if they convert to equivalent fractions.

equivalent fractions

Equivalent fractions are fractions that have the same value.

evaluate an expression

To evaluate an expression means to find the value of the expression when the variable is replaced by a given number.

expression

An expression is a number, a variable, or a combination of numbers and variables using operation symbols.

Factors

If $a\timesb=m$, then (a and b) are factors of m.

fraction

A fraction is written $$\frac{a}{b}$$, where $$b\ne 0$$ $$a$$ is the numerator and $$b$$ is the denominator. A fraction represents parts of a whole. The denominator $$b$$ is the number of equal parts the whole has been divided into, and the numerator $$a$$ indicates how many parts are included.

geoboard

A geoboard is a board with a grid of pegs on it.

graph of a linear equation

The graph of a linear equation Ax+By=C is a straight line. Every point on the line is a solution of the equation. Every solution of this equation is a point on this line.

horizontal line

A horizontal line is the graph of an equation of the form y=b. The line passes through the y-axis at (0,b).

hypotenuse

The side of the triangle opposite the 90° angle is called the hypotenuse.

identity

An equation that is true for any value of the variable is called an identity. The solution of an identity is all real numbers

inconsistent system

An inconsistent system of equations is a system of equations with no solution.

increasing linear function

a function with a positive slope: If f(x)=mx+b,  m>0.

independent equations

Two equations are independent if they have different solutions.

integers

The whole numbers and their opposites are called the integers: ...−3, −2, −1, 0, 1, 2, 3...

intercepts of a line

The points where a line crosses the x- axis and the y- axis are called the intercepts of the line

interest

Interest is the money that a bank pays its customers for keeping their money in the bank.

irrational number

An irrational number is a number that cannot be written as the ratio of two integers. Its decimal form does not stop and does not repeat.

irregular figure

An irregular figure is a figure that is not a standard geometric shape. Its area cannot be calculated using any of the standard area formulas.

isosceles triangle

A triangle with two sides of equal length is called an isosceles triangle

least common denominator

The least common denominator (LCD) of two fractions is the Least common multiple (LCM) of their denominators.

least common multiple

The least common multiple of two numbers is the smallest number that is a multiple of both numbers

legs of a right triangle

The sides of a right triangle adjacent to the right angle are called the legs.

like terms

Terms that are either constants or have the same variables raised to the same powers are called like terms.

linear equation

A linear equation is of the form Ax+By=C, where A and B are not both zero, is called a linear equation in two variables.

linear function

a function with a constant rate of change that is a polynomial of degree 1, and whose graph is a straight line

list price

The list price is the price a retailer sells an item for.

mark-up

A mark-up is a percentage of the original cost used to increase the price of an item.

the percent uncertainty in a quantity calculated by multiplication or division is the sum of the percent uncertainties in the items used to make the calculation

mixture problems

Mixture problems combine two or more items with different values together.

monomial

A monomial is a term of the form $a{x}^{m}$, where a is a constant and m is a whole number; a monomial has exactly one term.

multiple of a number

A number is a multiple of n if it is the product of a counting number and n.

multiplicative identity

The multiplicative identity is the number 1; multiplying 1 by any number does not change the value of the number.

multiplicative inverse

The reciprocal of a number is its multiplicative inverse. A number and its multiplicative inverse multiply to one.

negative slope

A negative slope of a line goes down as you read from left to right.

number line

A number line is used to visualize numbers. The numbers on the number line get larger as they go from left to right, and smaller as they go from right to left.

numerator

The numerator is the value on the top part of the fraction that indicates how many parts of the whole are included.

opposite

The opposite of a number is the number that is the same distance from zero on the number line but on the opposite side of zero: -a  means the opposite of the number. The notation -a is read “the opposite of a.”

ordered pair

An ordered pair (x,y) gives the coordinates of a point in a rectangular coordinate system.

origin

The origin is the point labeled 0 on a number line.

original cost

The original cost in a retail setting, is the price that a retailer pays for an item.

parallel lines

Lines in the same plane that do not intersect.

percent

A percent is a ratio whose denominator is 100.

percent uncertainty

the ratio of the uncertainty of a measurement to the measure value, express as a percentage

perimeter

The perimeter is a measure of the distance around a figure.

perpendicular lines

Lines in the same plane that form a right angle.

point–slope form

The point–slope form of an equation of a line with slope m and containing the point (x1,y1) is y-y1=m(x-x1)

polynomial

A polynomial is a monomial, or two or more monomials combined by addition or subtraction.

positive slope

A positive slope of a line goes up as you read from left to right.

precision

the degree to which repeated measurements agree with each other

prime factorization

The prime factorization of a number is the product of prime numbers that equals the number.

prime number

A prime number is a counting number greater than 1, whose only factors are 1 and itself.

principal

The principal is the original amount of money invested or borrowed for a period of time at a specific interest rate.

The x-axis and the y-axis divide a plane into four regions, called quadrants.

A radical sign is the symbol √m that denotes the positive square root.

rate of interest

The rate of interest is a percent of the principal, usually expressed as a percent per year.

rational number

A rational number is a number of the form p/q, where p and q are integers and q does not equal 0. A rational number can be written as the ratio of two integers. Its decimal form stops or repeats.

real number

A real number is a number that is either rational or irrational.

reciprocal

The reciprocal of $$\frac{a}{b}$$ is $$\frac{b}{a}$$. A number and its reciprocal multiply to one: $$\frac{a}{b}·\frac{b}{a}=1$$.

rectangle

A rectangle is a geometric figure that has four sides and four right angles.

rectangular coordinate system

A grid system is used in algebra to show a relationship between two variables; also called the xy-plane or the ‘coordinate plane’.

repeating decimal

A repeating decimal is a decimal in which the last digit or group of digits repeats endlessly.

right triangle

A right triangle is a triangle that has one 90° angle.

rise

The rise of a line is its vertical change.

run

The run of a line is its horizontal change.

scientific notation

A number is expressed in scientific notation when it is of the form $a\times{10^n}$ where $a\geq{1}$ and  $a<10$ and $n$ is an integer.

significant figures

the degree to which repeated measurements agree with each other

similar figures

A right triangle is a triangle that has one 90° angle.

simple interest

Simple interest is the interest earned according to the formula I=Prt.

simplified fraction

A fraction is considered simplified if there are no common factors in its numerator and denominator.

simplify an expression

To simplify an expression, do all operations in the expression.

slope formula

The slope of the line between two points (x1,y1) and (x2,y2) is $m=\frac{y2-y1}{x2-x1}$

slope of a line

The slope of a line is $m=\frac{rise}{run}$. The rise measures the vertical change and the run measures the horizontal change.

slope-intercept form of an equation of a line

The slope–intercept form of an equation of a line with slope m and y-intercept, (0,b) is, y=mx+b.

solution of an equation

A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.

solutions of a system of equations

Solutions of a system of equations are the values of the variables that make all the equations true. A solution of a system of two linear equations is represented by an ordered pair (x, y).

square and square root

If n^2=m, then m is the square of n and n is a square root of m.

standard form

A polynomial is in standard form when the terms of a polynomial are written in descending order of degrees.

supplementary angles

Two angles are supplementary if the sum of the measures of their angles is 180 degrees.

system of linear equations

When two or more linear equations are grouped together, they form a system of linear equations.

term

A term is a constant or the product of a constant and one or more variables.

trapezoid

A trapezoid is four-sided figure, a quadrilateral, with two sides that are parallel and two sides that are not.

triangle

A triangle is a geometric figure with three sides and three angles

trinomial

A trinomial is a polynomial with exactly three terms.

uncertainty

a quantitative measure of how much your measured values deviate from a standard or expected value

variable

A variable is a letter that represents a number whose value may change.

vertex of an angle

When two rays meet to form an angle, the common endpoint is called the vertex of the angle.

vertical line

A vertical line is the graph of an equation of the form x=a. The line passes through the x-axis at (a,0).

whole numbers

The whole numbers are the numbers 0, 1, 2, 3, ....

x-coordinate

The first number in an ordered pair (x,y).

x-intercept

The point (a,0) where the line crosses the x- axis; the x- intercept occurs when y is zero.

y-coordinate

The second number in an ordered pair (x,y)

y-intercept

The point (0,b) where the line crosses the y- axis; the y- intercept occurs when x is zero.