Praxis Middle School Math key terms

A number that can be written as a fraction of two integers with a nonzero denominator; its decimal form either terminates or repeats a pattern forever.

A real number that cannot be written as a fraction of two integers; its decimal form never ends and never repeats, such as pi or the square root of two.

A whole number that may be positive, negative, or zero, with no fractional or decimal part; the integers include negative two, negative one, zero, one, and two.

The distance from a number to zero on the number line, which is never negative; the absolute value of both 6 and negative 6 is 6.

The process of writing a whole number greater than one as a product of prime numbers; each such number has only one prime factorization except for the order of factors.

The largest whole number that divides each number in a set without a remainder; for 24 and 36, the greatest common factor is 12.

The smallest positive number that is a multiple of every number in a set; for 6 and 8, the least common multiple is 24.

The agreed sequence for simplifying expressions: grouping symbols first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.

A raised number that tells how many times a base is used as a factor; in 2 to the fifth power, the exponent 5 means multiply five 2s.

A value that gives a specified number when multiplied by itself; 7 is a square root of 49 because 7 times 7 equals 49.

A compact way to write very large or very small numbers as a number between 1 and 10 multiplied by a power of ten, such as 3.5 times 10 to the fourth.

A relationship in which two quantities are related by a constant multiplier; its graph is a straight line that passes through the origin.

A ratio that compares a number to 100; 40 percent means 40 out of 100, and percents often describe parts of a whole or rates of change.

A letter or symbol that represents an unknown or changing number in an expression or equation, such as x in x plus 8 equals 15.

The numerical factor that multiplies a variable in an algebraic term; in 9x the coefficient is 9, and in negative 4y squared it is negative 4.

An equation whose graph is a straight line and whose variable terms have degree at most one, such as y equals 2x plus 3.

The steepness of a line, found by dividing the vertical change between two points by the horizontal change; a positive slope rises from left to right.

The point where a graph crosses the vertical axis; in the slope-intercept form y equals mx plus b, the value b gives the y-intercept.

A rule that assigns exactly one output value to each input value; if a single input has two different outputs, the relation is not a function.

Two or more equations that share the same variables and are solved together; the solution makes all the equations true at the same time.

An equation in which the highest power of the variable is two, usually written as ax squared plus bx plus c equals zero; its graph is a parabola.

An algebraic expression made from terms with whole-number exponents, where no variable is in a denominator; 3x squared minus 5x plus 2 is an example.

The rule that in a right triangle the square of the hypotenuse equals the sum of the squares of the legs; it is written a squared plus b squared equals c squared.

Figures that have the same shape but not necessarily the same size; their corresponding angles are equal and corresponding side lengths share a constant ratio.

Having exactly the same size and shape; one congruent figure can be moved onto the other without changing any side lengths or angle measures.

A movement or resizing of a figure on a coordinate plane, such as a translation, rotation, reflection, or dilation; translations, rotations, and reflections preserve size and shape.

The constant ratio used to enlarge or reduce a figure; a factor greater than one enlarges, a factor between zero and one reduces, and a negative factor also flips it.

The distance around a circle, equal to pi times the diameter or two times pi times the radius; it is the circle's perimeter.

The number of square units needed to cover a flat two-dimensional region; for a rectangle it is length times width, and for a triangle it is half the base times height.

The amount of space inside a three-dimensional solid, measured in cubic units; for a rectangular prism it equals length times width times height.

The sum of a set of values divided by the number of values; it is a measure of center affected by every value, including outliers.

The middle value in an ordered data set, or the average of the two middle values when the set has an even number of items.

The difference between the third quartile and the first quartile of a data set; it measures the spread of the middle half of the data.

A graph that plots ordered pairs as points to show the relationship between two variables; patterns can suggest positive, negative, or no association.

A number from 0 to 1 that expresses how likely an event is, often found by dividing favorable outcomes by all equally likely outcomes.

The complete set of all possible outcomes for a probability experiment; for one roll of a standard die, it is the numbers 1 through 6.

A sample selected so that every member of a population has an equal chance of being chosen, which helps reduce bias in conclusions.

Using mathematics such as equations, graphs, or functions to describe a real-world situation, then interpreting and checking the results in that context.

Finding a value close enough to an exact answer for a purpose, often by rounding numbers or using compatible numbers to simplify calculations.

Explaining why a mathematical statement is true by using definitions, properties, and logical steps rather than only giving an answer.