FAST Grade 7 Math key terms

A number that can be written as a fraction with an integer numerator and a nonzero integer denominator. Its decimal form either ends or repeats in a pattern. Includes integers, fractions, and terminating or repeating decimals.

A whole number that can be positive, negative, or zero, with no fractional or decimal part. Examples include -7, 0, and 12. Integers are a subset of rational numbers.

The distance a number is from zero on a number line, always zero or positive. Written with vertical bars, so |-5| equals 5. It measures size without regard to sign.

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. Also called the additive inverse.

The number you add to a given number to get a sum of zero. For any number a, the additive inverse is -a. Subtracting a number is the same as adding its additive inverse.

A small raised number that tells how many times a base is used as a factor. In 3^4, the exponent 4 means multiply four factors of 3. It is not the same as multiplying base times exponent.

In an expression written with an exponent, the base is the number or variable being repeatedly multiplied. In 5^3 the base is 5, and it is used as a factor three times.

The result of raising a base to an exponent, or the whole expression such as 2^5. It can also mean the number of times a base is used as a factor.

A way to write very large or very small numbers as a product of a number between 1 and 10 and a power of ten, such as 4.2 x 10^6. Useful for comparing magnitudes quickly.

A decimal in which one or more digits repeat forever in a fixed pattern, shown with a bar over the repeating block. For example, 0.333... equals 1/3. Any repeating or terminating decimal is rational.

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 with a denominator that is a power of ten.

A comparison of two quantities by division, often written as a to b, a:b, or a/b. Ratios can compare part to part or part to whole, and order matters.

A ratio that compares two quantities measured in different units, such as miles per hour or dollars per pound. A rate often describes how one quantity changes relative to another.

A rate in which the second quantity is one unit, found by dividing. For example, 150 miles in 3 hours gives a unit rate of 50 miles per hour. Useful for comparing prices and speeds.

An equation stating that two ratios are equal, such as 3/4 = 9/12. Proportions can be solved by cross multiplying or by finding a scale factor between the ratios.

A relationship between two quantities in which one is a constant multiple of the other, so the graph is a straight line through the origin. The equation has the form y = kx.

The fixed number k that relates two proportional quantities in y = kx. It equals the ratio y/x for every pair of corresponding values and is the unit rate of the relationship.

A ratio that compares a number to 100, written with the percent symbol. For example, 35% means 35 out of every 100, or 35/100, which equals 0.35 as a decimal.

The amount a quantity grows, expressed as a percent of the original amount. Found by dividing the change by the original value and multiplying by 100. Percent decrease uses the same method.

A measure of how far an estimate or measurement is from an accepted value, written as a percent. Divide the absolute value of the difference by the accepted value, then multiply by 100.

The amount added to a wholesale or cost price to set a selling price, often given as a percent of cost. Selling price equals cost plus markup.

An amount subtracted from a regular price, usually stated as a percent of that price. Sale price equals the original price minus the discount amount.

Money paid for borrowing or earned on a deposit, calculated only on the original principal using I = prt, where r is the annual rate as a decimal and t is time in years.

A mathematical phrase that combines numbers, variables, and operations but has no equals sign. For example, 4x + 7. Expressions can be simplified or evaluated but not solved.

A letter or symbol that stands for an unknown or changing number in an expression or equation. For example, in 3n + 2, the variable n represents a number.

The number that multiplies a variable in a term. In 7x, the coefficient is 7; in -y, it is -1. Coefficients can be fractions or decimals.

A term in an expression that contains no variable, so its value never changes. In 5x - 9, the constant term is -9, including its sign.

Terms that have exactly the same variable factors, so they can be combined by adding their coefficients. For example, 3x and -8x are like terms, but 3x and 3x^2 are not.

An expression in which every variable appears to the first power only, with no variables multiplied together. It can be written as ax + b, and its graph is a straight line.

The rule that multiplying a sum or difference by a number gives the same result as multiplying each part separately, as in a(b + c) = ab + ac. Used to expand or factor expressions.

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

A statement comparing two expressions that are not necessarily equal, using symbols such as <, >, <=, or >=. Its solutions form a range of values, often graphed on a number line.

An operation that undoes another, such as addition and subtraction, or multiplication and division. Solving equations uses inverse operations to isolate the variable.

A value or set of values for the variable that makes an equation or inequality true. Checking a solution means substituting it back into the original statement.

A drawing in which every length is a fixed fraction of the corresponding real length, so the drawing keeps the same shape. Maps and floor plans are common examples.

The ratio comparing a length in a drawing or scaled copy to the corresponding length in the original. Multiplying actual lengths by the scale factor gives the new lengths.

The distance around a circle, equal to pi times the diameter, or 2 times pi times the radius. It is the circle's perimeter and is measured in linear units.

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

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

The amount of surface inside a circle, calculated as pi times the radius squared, or A = pi r^2. The result is in square units.

The total area of all the faces or surfaces of a three-dimensional figure, measured in square units. For a prism it is the sum of the areas of its rectangular faces.

The amount of space a three-dimensional figure occupies, measured in cubic units. For prisms and cylinders it equals the area of the base times the height.

A flat pattern that folds into a three-dimensional figure, showing every face. Nets help you find surface area by adding the areas of the flat pieces.

Two angles whose measures add to 180 degrees. They can be adjacent or separate. Angles on a straight line are supplementary.

Two angles whose measures add to 90 degrees. They need not be next to each other. Angles forming a right angle are complementary.

The pair of opposite angles formed when two lines cross. Vertical angles are always equal in measure and share only a vertex, not a side.

The entire group being studied or described in a statistical question. Because measuring everyone is often impractical, data is usually collected from a sample.

A part of a population selected to provide information about the whole group. Conclusions about the population are only as trustworthy as the sample is representative.

A sample chosen so that every member of the population has an equal chance of being selected. Random sampling reduces bias and supports valid inferences.

A sample whose characteristics closely match those of the whole population. It allows results to be generalized to the population with reasonable confidence.

A sample that systematically favors some members of the population over others, so results do not reflect the whole group. Convenience sampling often produces this problem.

The 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 ordered from least to greatest. If there is an even number of values, it is the mean of the two middle values. It resists the pull of outliers.

The average distance between each data value and the mean. Find each distance, take its absolute value, then average those distances. It describes how spread out data are.

A data value that is far away from most of the other values in a set. Outliers pull the mean toward them but usually affect the median much less.

A number from 0 to 1 describing how likely an event is. For equally likely outcomes it equals the number of favorable outcomes divided by the total number of outcomes.

The set of all possible outcomes of a probability experiment. For rolling one number cube, the sample space contains the six results 1 through 6.

The probability predicted by analyzing equally likely outcomes, such as 1/6 for each face of a number cube. It is based on reasoning rather than on actually running trials.

The probability estimated from the results of an actual experiment, equal to the number of times an event occurred divided by the number of trials. It tends to approach theoretical probability as trials increase.

An event made up of two or more simple events, such as rolling an even number or flipping two coins. Its probability may be found with organized lists, tables, or tree diagrams.