Grade 7 Mathematics key terms

A rate in which the second quantity is one unit, found by dividing the first quantity by the second. For example, 150 miles in 3 hours gives a unit rate of 50 miles per hour.

A ratio that compares two quantities measured in different units, such as dollars per pound or words per minute. Rates often describe how one quantity changes relative to another.

A comparison of two quantities by division, often written as a to b, a:b, or a/b. It tells how many times as large one quantity is compared with another.

Ratios that describe the same comparison even though the numbers differ, such as 2:3 and 8:12. Multiplying or dividing both quantities by the same nonzero number produces an equivalent ratio.

An equation stating that two ratios are equal, such as 3/4 = 9/12. Solving a proportion means finding a missing value that keeps the two ratios equivalent.

The results of multiplying the numerator of one ratio by the denominator of the other in a proportion. In a true proportion the cross products are equal, which allows you to solve for a missing value.

A relationship between two quantities in which their ratio stays constant, so the graph is a straight line through the origin. Doubling one quantity doubles the other.

The fixed ratio between two proportional quantities, usually written k in the equation y = kx. It equals the unit rate and appears as the steepness of the graph.

The point (0, 0) where the x-axis and y-axis of a coordinate plane meet. A graph of a proportional relationship always passes through this point.

A ratio that compares a number to 100, written with the symbol %. For example, 35% means 35 out of every 100, or 35/100.

The amount a quantity grows, expressed as a percent of its original value. It is found by dividing the increase by the original amount and multiplying by 100.

The amount a quantity shrinks, expressed as a percent of its original value. It is found by dividing the decrease by the original amount and multiplying by 100.

Any number that can be written as a fraction a/b where a and b are integers and b is not zero. This includes integers, terminating decimals, and repeating decimals.

A whole number that may be positive, negative, or zero, such as -4, 0, or 7. Integers have no fractional or decimal part.

Two numbers that are the same distance from zero on a number line but on opposite sides, such as 6 and -6. Their sum is always zero.

The distance of a number from zero on the number line, always zero or positive. It is written with vertical bars, as in |-8| = 8.

A straight line on which every point represents a number, arranged in order with zero in the middle. It is used to compare, order, and locate positive and negative numbers.

The number you add to a given number to get a sum of zero, also called its opposite. The additive inverse of -5 is 5.

A decimal in which one or more digits repeat without end, such as 0.333... or 0.272727... . A repeating decimal represents a rational number and can be written as a fraction.

A decimal that ends after a finite number of digits, such as 0.75 or 3.125. Every terminating decimal can be written as a fraction, so it is a rational number.

A mathematical phrase made of numbers, variables, and operations without an equals sign, such as 4x + 7. An expression can be simplified or evaluated but not solved.

A mathematical sentence stating that two expressions are equal, such as 3x + 2 = 14. Solving an equation means finding the value of the variable that makes it true.

A letter or symbol that stands for an unknown or changing number. In 5n, the variable n represents a quantity that can take different values.

The number that multiplies a variable in a term. In the expression 7x + 3, the coefficient of x is 7.

A single number, variable, or product of numbers and variables separated by plus or minus signs in an expression. In 4x + 2y - 9, the terms are 4x, 2y, and -9.

Terms that have the same variable factors raised to the same powers, such as 3x and 8x. They can be combined by adding or subtracting their coefficients.

A value of the variable that makes an equation or inequality true. Substituting it back into the original statement should produce a correct numerical sentence.

A mathematical statement comparing two expressions using <, >, ≤, or ≥. Its solutions form a range of values, often shown on a number line.

The rule that multiplying a sum by a number gives the same result as multiplying each addend separately, as in a(b + c) = ab + ac. It is used to expand and simplify expressions.

Two angles that share a common vertex and a common side but do not overlap. Their measures can be added when they form a larger angle together.

Two angles whose measures add up to 90 degrees. If one is known, the other is found by subtracting it from 90.

Two angles whose measures add up to 180 degrees. They often appear as two angles forming a straight line.

The pair of opposite angles formed when two lines cross. Vertical angles are always equal in measure.

The distance around a circle, calculated as C = 2πr or C = πd. It is the circle's perimeter.

The distance from the center of a circle to any point on the circle. It is half the diameter and is used in both circumference and area formulas.

The distance across a circle through its center, equal to twice the radius. It relates to circumference by C = πd.

The amount of space inside a circle, calculated as A = πr². The radius is squared, so doubling the radius makes the area four times as large.

A drawing in which every length is a fixed fraction of the corresponding real length. The scale lets you convert between measurements on the drawing and actual measurements.

The ratio that compares a length in a drawing or scaled copy to the corresponding length in the original. It tells how many times larger or smaller the copy is.

The entire group of items or people being studied in a statistical question. Information about a population is often estimated from a sample.

A part of a population selected to be studied. Data from a sample is used to draw conclusions about the whole population.

A sample in which every member of the population has an equal chance of being chosen. Random sampling helps reduce bias so results better represent the population.

A conclusion about a population drawn from data collected in a sample. Its reliability depends on how representative and how large the sample is.

The sum of a data set divided by the number of values, also called the average. It describes the balance point of the data.

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

The average distance between each data value and the mean. It measures how spread out the data are, with larger values indicating greater variability.

A description of how spread out or clustered a set of data values is. Measures such as range and mean absolute deviation quantify it.

The difference between the greatest and least values in a data set. It is a simple measure of how spread out the data are.

A number from 0 to 1 describing how likely an event is, where 0 means impossible and 1 means certain. It can be found by comparing favorable outcomes to all equally likely outcomes.

A single possible result of an experiment or random event, such as rolling a 4 on a number cube. A collection of outcomes forms an event.

The set of all possible outcomes of an experiment. For rolling a standard number cube, the sample space is 1, 2, 3, 4, 5, and 6.

The probability calculated from the number of favorable outcomes divided by the total number of equally likely outcomes, without running an experiment. It predicts what should happen in theory.

The probability found by actually performing an experiment and dividing the number of times an event occurs by the total number of trials. It may differ from theoretical probability.