Praxis Core Math key terms

A whole number that can be positive, negative, or zero, with no fractional or decimal part, such as -7, 0, or 42. Integers exclude fractions like 1/2 and decimals like 3.5.

A number that can be written as a fraction of two integers, with a nonzero denominator. This includes terminating decimals and repeating decimals, but excludes numbers like the square root of 2.

A real number that cannot be expressed as a fraction of two integers. Its decimal form neither terminates nor repeats. Common examples are pi and the square root of 2.

The distance of a number from zero on the number line, always zero or positive. Written with vertical bars, so the absolute value of -5 is 5 and of 5 is also 5.

A horizontal line with evenly spaced tick marks representing numbers, increasing left to right. It visually shows order, distance, and the position of negatives, positives, and zero.

A whole number greater than 1 whose only positive divisors are 1 and itself, such as 2, 3, 5, 7, and 11. The number 1 is not prime, and 2 is the only even prime.

A whole number that divides another number evenly with no remainder. For example, 1, 2, 3, 4, 6, and 12 are all factors of 12 because each divides 12 exactly.

The result of multiplying a given whole number by any integer. Multiples of 6 include 6, 12, 18, 24, and so on; every number is a multiple of itself and of 1.

The smallest positive number that is a multiple of two or more given numbers. For 4 and 6, the multiples overlap first at 12, so the least common multiple is 12.

The largest whole number that divides two or more given numbers evenly. For 18 and 24, the shared factors are 1, 2, 3, and 6, so the greatest common factor is 6.

A ratio comparing a number to 100, meaning per hundred. For example, 35 percent equals 35/100 or 0.35, and finding a percent of a quantity means multiplying by that decimal.

A comparison of two quantities by division, often written with a colon or as a fraction. A ratio of 3 to 4 means for every 3 of one item there are 4 of another.

An equation stating that two ratios are equal, such as 3/4 = 9/12. Proportions are solved by cross-multiplying to find an unknown value in one of the ratios.

A rate expressed as an amount per one unit of another quantity, such as 60 miles per hour or 3 dollars per pound. It is found by dividing the first quantity by the second.

A way of writing very large or very small numbers as a number between 1 and 10 multiplied by a power of 10, such as 4.5 times 10 to the sixth power.

A number that, when multiplied by itself, produces a given number. The square root of 49 is 7 because 7 times 7 equals 49; positive numbers have two square roots, one positive and one negative.

A small raised number showing how many times a base is used as a factor. In 2 to the fifth power, the exponent 5 means multiply five factors of 2, giving 32.

A letter or symbol that stands for an unknown or changing number in an expression or equation. In 3x + 5, the variable x represents a value that can vary.

A combination of numbers, variables, and operation symbols without an equals sign, such as 4x - 7. It can be simplified or evaluated but not solved for a specific value.

A mathematical statement that two expressions are equal, joined by an equals sign. Solving an equation means finding the value or values of the variable that make the statement true.

An equation in which every variable appears to the first power only, so its graph is a straight line. An example is 2x + 3 = 11, which has exactly one solution for x.

A statement comparing two expressions that are not necessarily equal, using symbols such as less than, greater than, or their or-equal-to forms. Its solution is a range of values rather than a single number.

A measure of how steep a line is, calculated as the change in y divided by the change in x between two points. A positive slope rises left to right; a negative slope falls.

The point where a graph crosses the vertical y-axis, occurring where x equals zero. In the equation y = mx + b, the value b gives the y-intercept.

A rule that assigns exactly one output value to each input value. For example, doubling a number is a function, but a rule giving two different outputs for one input is not.

An equation containing a variable raised to the second power as its highest term, often written as ax squared plus bx plus c equals zero. It can have zero, one, or two real solutions.

Two or more equations containing the same variables that must be satisfied at the same time. The solution is the set of values making every equation in the system true simultaneously.

The total distance around the outside of a two-dimensional shape, found by adding the lengths of all its sides. Perimeter is measured in linear units such as inches or centimeters.

The amount of surface a two-dimensional shape covers, measured in square units. Common formulas include length times width for rectangles and one-half base times height for triangles.

The amount of space a three-dimensional solid occupies, measured in cubic units. For a rectangular box, it equals length times width times height.

The distance around a circle, calculated as pi times the diameter, or two times pi times the radius. It plays the same role for circles that perimeter plays for polygons.

The distance from the center of a circle to any point on its edge. It is exactly half the diameter, and many circle formulas use it, including area equals pi times radius squared.

A rule stating that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. It is used to find a missing side length.

A triangle containing one angle of exactly 90 degrees. The side opposite the right angle is the longest side, called the hypotenuse, and the other two sides are the legs.

Shapes with the same shape but possibly different sizes, having equal corresponding angles and proportional corresponding side lengths. Their scale factor relates every pair of matching sides.

The arithmetic average of a data set, found by adding all values and dividing by how many there are. It is affected strongly by very large or very small values.

The middle value of a data set arranged in order. If there is an even number of values, the median is the mean of the two middle values.

The value that appears most often in a data set. A set may have one mode, several modes, or no mode if every value occurs the same number of times.

A number from 0 to 1 describing how likely an event is, where 0 means impossible and 1 means certain. For equally likely outcomes, it equals favorable outcomes divided by total outcomes.

The difference between the largest and smallest values in a data set, found by subtracting the minimum from the maximum. It measures how spread out the data are.