OAR key terms

A comparison of two quantities that shows how many times one contains the other, often written as a fraction or with a colon. Ratios appear in scale drawings, mixtures, and gear problems.

An equation stating that two ratios are equal, such as 3/4 = 6/8. You can solve for an unknown value by cross-multiplying the two fractions.

A ratio that compares a number to 100. For example, 25 percent means 25 out of every 100, which is the same as the decimal 0.25.

The arithmetic average of a data set, found by adding all the values and dividing by the number of values. Extreme values can pull the mean up or down.

The middle value in a list of numbers ordered from least to greatest. If the list has an even number of values, average the two middle ones.

The standard sequence for evaluating a math expression: parentheses first, then exponents, then multiplication and division left to right, and finally addition and subtraction left to right.

A number that tells how many times a base is multiplied by itself. In 2 to the third power, the exponent 3 means 2 times 2 times 2.

A number that produces the original number when multiplied by itself. The square root of 49 is 7 because 7 times 7 equals 49.

The amount of flat surface inside a two-dimensional shape, measured in square units. For a rectangle, multiply length by width.

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

A ratio that compares two quantities with different units, such as miles per hour or dollars per gallon. Rates are useful in travel, work, and cost problems.

A number from 0 to 1 that expresses how likely an event is. Find it by dividing the number of favorable outcomes by the total number of possible outcomes.

A rule for right triangles: the square of the hypotenuse equals the sum of the squares of the other two sides, written a squared plus b squared equals c squared.

Changing a measurement from one unit to another, such as inches to feet, by multiplying by a ratio that equals one, like 1 foot over 12 inches.

The central point that a passage makes about its topic. It is broader than any single detail and is often stated in the opening or closing paragraph.

A fact, example, statistic, or reason that explains or proves the main idea of a passage. Details answer questions like who, what, when, and why.

A conclusion a reader draws from evidence in the text combined with reasonable background knowledge, even though the author does not state it directly.

The author's attitude toward the subject, shown through word choice and details. A passage might sound respectful, sarcastic, urgent, or amused.

The reason a writer created a text, such as to inform, persuade, entertain, or explain a process. Purpose shapes the style and structure of a passage.

A hint in the surrounding words or sentences that helps a reader work out the meaning of an unfamiliar word without using a dictionary.

A fact is a statement that can be proven true or false with evidence. An opinion expresses a belief, feeling, or judgment that cannot be verified.

A short restatement of a passage's main points in your own words. A good summary leaves out minor details and repeated examples.

A word or phrase such as however, therefore, or meanwhile that shows how one idea connects to another or signals a shift in the passage.

A slant or preference in a text that unfairly favors one side. Bias often appears through loaded language, selective facts, or omitted viewpoints.

A push or pull on an object that can change its speed, direction, or shape. Force is measured in newtons or pounds.

The amount of matter in an object, which stays the same no matter where the object is. Mass is different from weight.

The force that gravity exerts on an object's mass. On Earth, weight equals mass multiplied by the acceleration due to gravity.

A resistance force that opposes motion when two surfaces slide or roll against each other. Friction converts some motion energy into heat.

A turning or twisting force. Torque equals the applied force multiplied by the distance from the pivot point to where the force acts.

A rigid bar that turns around a fixed point called the fulcrum. Levers can multiply force, increase speed, or change the direction of a force.

A wheel with a rope or belt wrapped around it. A single pulley changes the direction of a force, and combined pulleys can reduce the effort needed to lift a load.

A flat, sloped surface that lets a load be raised with less force over a longer distance. Ramps are common examples.

The ratio of a machine's output force to the input force. A value greater than one means the machine multiplies the force you apply.

Force spread over a given area, measured in pounds per square inch or pascals. The same force on a smaller area produces greater pressure.

The mass of a substance per unit of volume. An object with lower density than water will float in it.

The upward force that a fluid exerts on an object placed in it. Buoyancy equals the weight of the fluid the object pushes aside.

Speed in a stated direction. A change in velocity can mean a change in speed, a change in direction, or both.

The rate at which velocity changes over time. Accelerating includes speeding up, slowing down, and changing direction.

In physics, work is force applied over a distance in the direction of the force. It is measured in joules.

The rate at which work is done or energy is transferred. Power is measured in watts or horsepower.