NG Navy Exam key terms

The number that produces 1 when multiplied by a given number; for a fraction, swap numerator and denominator. For example, the reciprocal of 3/4 is 4/3, and of 5 is 1/5. Used when dividing by fractions.

The amount a value grows, expressed as a share of the original value: divide the change by the original amount, then multiply by 100. A price rising from 40 to 50 is a 25 percent increase, not 10.

The amount a value shrinks, expressed as a share of the original value: divide the drop by the original amount, then multiply by 100. Always divide by the starting figure, never by the ending figure, or the answer is wrong.

A comparison of two quantities by division, often written with a colon such as 3:5 or as a fraction. It states how many of one item there are for each of another, not the actual counts.

An equation stating that two ratios are equal, such as 3/4 = x/12. Solving usually means cross-multiplying: multiply the numerator of each side by the opposite denominator, then isolate the unknown.

A ratio comparing quantities with different units, such as miles per hour or cost per gallon. Word problems often give a rate and ask for a total, requiring multiplication by the time or quantity involved.

The sum of a set of values divided by how many values there are. To find a missing value when the average is known, multiply the average by the count, then subtract the known values.

An average in which some values count more than others. Multiply each value by its weight, add those products, then divide by the total of the weights. Used for mixed grades or blended prices.

Changing a measurement from one unit to another by multiplying by a fraction equal to 1, such as 12 inches over 1 foot. Arrange the fraction so unwanted units cancel, leaving the desired unit.

A problem where two or more people or machines finish a job at different speeds. Add their individual per-hour fractions of the job, then take the reciprocal of the sum to get combined time.

The top number of a fraction, showing how many equal parts are being counted. In 5/8 the numerator is 5. It is the dividend when the fraction is treated as a division problem.

The bottom number of a fraction, showing the total number of equal parts in the whole. In 5/8 the denominator is 8. Fractions must share a denominator before they can be added or subtracted.

A fraction whose numerator is equal to or larger than its denominator, such as 9/4. It can be rewritten as a mixed number (2 1/4) by dividing and expressing the remainder as a fraction.

A whole number combined with a proper fraction, such as 3 1/2. To multiply or divide, first convert it to an improper fraction by multiplying the whole number by the denominator and adding the numerator.

The smallest number that both denominators divide into evenly. It is the least common multiple of the denominators and lets you add or subtract fractions without changing their values.

The largest number that divides evenly into two or more numbers. Dividing a fraction's numerator and denominator by it reduces the fraction to lowest terms, as 18/24 becomes 3/4.

A small raised number showing how many times the base is used as a factor. In 2^5 the exponent is 5, meaning 2 x 2 x 2 x 2 x 2. Any nonzero number to the zero power equals 1.

A number that, multiplied by itself, gives the original value. The square root of 81 is 9 because 9 x 9 = 81. Perfect squares such as 25, 36, and 144 have whole-number roots.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a^2 + b^2 = c^2. Used to find a missing side length or a diagonal distance.

The longest side of a right triangle, opposite the 90-degree angle. It is the side isolated in the Pythagorean theorem and is always longer than either leg of the triangle.

The total distance around the outside of a flat shape, found by adding all side lengths. For a rectangle, use 2 times length plus 2 times width. It is measured in linear units, not square units.

The amount of surface a flat shape covers, measured in square units. Rectangle: length times width. Triangle: one-half base times height. Circle: pi times the radius squared.

The distance around a circle, equal to pi times the diameter, or 2 times pi times the radius. Using 3.14 for pi is usually expected when answer choices are far apart.

The space a three-dimensional object occupies, measured in cubic units. For a rectangular box, multiply length by width by height. A cylinder uses pi times radius squared times height.

A word that means nearly the same thing as another word, such as brief and short. Synonym questions ask you to pick the answer closest in meaning to the given word, ignoring words that only sound alike.

A word with the opposite meaning of another word, such as scarce and plentiful. Antonym questions ask for the choice most nearly opposite to the given word, so eliminate answers that mean the same thing.

A hint inside a sentence or nearby sentence that reveals an unfamiliar word's meaning, such as a restatement, contrast, or example. Using these clues beats guessing from how the word sounds.

A word part attached to the front of a root that changes its meaning, such as un- meaning not, pre- meaning before, or re- meaning again. Recognizing prefixes helps you decode unfamiliar vocabulary quickly.

A word part attached to the end of a root that changes meaning or part of speech, such as -less meaning without, -able meaning capable of, or -tion turning a verb into a noun.

The base part of a word that carries its core meaning, before prefixes or suffixes are added. For example, port meaning carry appears in transport, import, and portable.

The central point a passage is making about its topic, often stated in the first or last sentence. Supporting details explain, illustrate, or prove it. Distinguish it from a single interesting detail.

A fact, example, or reason in a passage that backs up the main idea. Detail questions often ask what the passage states, so the correct answer must be directly stated, not merely plausible.

A conclusion drawn from evidence in the passage but not stated outright. A valid inference must be supported by the text; avoid answers that rely on outside knowledge or go beyond what is written.

The author's attitude toward the subject, revealed by word choice, such as critical, humorous, or neutral. Tone questions ask how the writer feels, not what the passage is about.

Mass per unit volume of a substance, calculated as mass divided by volume. Objects denser than water sink; less dense objects float. Density does not change when a sample is cut in half.

The amount of matter in an object, measured in grams or kilograms. Unlike weight, mass stays the same regardless of gravity, so an object has the same mass on the Moon as on Earth.

The force gravity exerts on an object's mass, measured in newtons or pounds. It equals mass times gravitational acceleration, so it decreases where gravity is weaker, such as on the Moon.

A push or pull that can change an object's speed or direction, measured in newtons. In the formula force equals mass times acceleration, greater mass or acceleration requires greater force.

The tendency of an object to resist changes in motion. An object at rest stays at rest and a moving object keeps moving in a straight line unless an outside force acts on it.

Speed in a stated direction, such as 40 miles per hour north. Because direction matters, an object moving in a circle at constant speed still changes velocity and is therefore accelerating.

The rate at which velocity changes over time, including speeding up, slowing down, or changing direction. Measured in meters per second squared, it equals change in velocity divided by elapsed time.

The factor by which a machine multiplies an applied force, equal to output force divided by input force. A lever with a long effort arm gains advantage; no machine creates energy, only trades force for distance.

The fixed pivot point on which a lever turns. Its position determines the lever's mechanical advantage: moving the fulcrum closer to the load lets a smaller effort force lift a heavier load.

A rigid bar that pivots on a fulcrum to move a load. Classes differ by the arrangement of fulcrum, effort, and load: a crowbar is first class, a wheelbarrow second class, a fishing rod third class.

A wheel with a grooved rim and a rope that changes the direction of an applied force or multiplies it. A single fixed pulley changes direction only; movable pulleys can halve the effort needed.

The comparison of teeth on a driving gear to teeth on a driven gear. A small gear turning a large gear increases torque while reducing speed; the reverse increases speed while reducing torque.

A twisting force that tends to rotate an object, equal to force multiplied by the distance from the pivot. A longer wrench produces more torque with the same push, making a stubborn bolt easier to turn.

Force applied over an area, calculated as force divided by area. The same force on a smaller area produces greater pressure, which is why a sharp knife cuts more easily than a dull one.

Electrical potential difference between two points, measured in volts. It is the electrical pressure that pushes current through a circuit; a higher voltage drives more current through the same resistance.

The flow of electric charge through a conductor, measured in amperes. In a series circuit it is the same at every point; in a parallel circuit it splits among the branches.

The opposition to current flow in a material, measured in ohms. Longer, thinner, or hotter wires have more resistance. Resistors are added deliberately to limit current in a circuit.

The relationship among voltage, current, and resistance: voltage equals current times resistance (V = I x R). Rearranged, current equals voltage divided by resistance, and resistance equals voltage divided by current.

A circuit with a single path for current, so every component carries the same current. Total resistance is the sum of the individual resistances, and one broken component stops current everywhere.

A circuit with multiple branches, so current splits and each branch receives the full source voltage. Total resistance is less than the smallest branch resistance, and one failed branch leaves the others working.

The rate at which a circuit uses or delivers energy, measured in watts. Power equals voltage times current (P = V x I), so a device drawing 2 amps at 12 volts uses 24 watts.