NLN NEX Math flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Order of operations

Evaluate in this sequence: grouping symbols first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.

Dividing by a fraction

Multiply by the reciprocal: a ÷ (b/c) = a × (c/b). For example, 3/4 ÷ 2/5 becomes 3/4 × 5/2, which equals 15/8.

Percent to decimal conversion

Divide the percent by 100 and drop the percent sign, so 45% becomes 0.45 and 7.5% becomes 0.075. To reverse, multiply the decimal by 100.

Cross-multiplication

A proportion a/b = c/d is true exactly when ad = bc. Multiply each numerator by the opposite denominator to solve for an unknown value.

Percent change formula

Percent change equals (new value − original value) divided by the original value, times 100. A positive result is an increase; a negative result is a decrease.

Least common denominator

The smallest number that both denominators divide evenly into. Rewrite each fraction with this denominator before adding or subtracting so the pieces are the same size.

Rounding a decimal

Find the place value being rounded to, then check the single digit to its right. A digit of 5 or greater rounds up; a digit of 4 or less keeps the digit as is.

Comparing two fractions

Cross-multiply by multiplying each numerator by the opposite denominator. The fraction whose product is larger is the greater of the two fractions.

Distributive property

a(b + c) = ab + ac. Multiply the factor outside the parentheses by every term inside, then combine like terms, as in 3(x + 4) = 3x + 12.

Like terms

Terms with exactly the same variable part, including exponents. Only like terms can be combined: 5x + 3x = 8x, but 5x + 3x² stays as written.

Slope formula

For two points, m = (y₂ − y₁)/(x₂ − x₁), the vertical change per unit of horizontal change. A horizontal line has slope 0; a vertical line has undefined slope.

Inequality sign reversal

Multiplying or dividing both sides of an inequality by a negative number reverses the symbol's direction. Adding or subtracting a negative number does not reverse it.

Solving a two-step equation

Undo operations in reverse order: add or subtract first to isolate the variable term, then multiply or divide. Every operation must be applied to both sides.

"Less than" word order

In word problems, "5 less than x" means x − 5, and "5 is less than x" means 5 < x. The phrase order differs from the subtraction order.

Distance formula d = rt

Distance equals rate multiplied by time. Rearranged, rate = distance ÷ time and time = distance ÷ rate; units must be consistent before computing.

Checking an equation solution

Substitute the proposed value into the original equation and simplify each side separately. If both sides end up equal, the value is a solution.

Perimeter of a rectangle

Perimeter equals twice the length plus twice the width: P = 2l + 2w. Perimeter is a length, so it is reported in linear units such as inches or meters.

Area of a triangle

Area = one-half times base times height, A = ½bh. The height must be perpendicular to the chosen base and need not be one of the sides.

Circumference of a circle

C = 2πr, or equivalently C = πd, because the diameter is twice the radius. Using π ≈ 3.14 gives a decimal answer in linear units.

Volume of a rectangular prism

Volume = length × width × height, V = lwh. Volume is measured in cubic units, so a box measuring 2 by 3 by 4 has volume 24 cubic units.

Triangle angle sum

The three interior angles of any triangle add to 180°. In a right triangle one angle measures 90°, so the remaining two angles add to 90°.

Converting units by canceling

Multiply by a fraction equal to 1 relating the units, placing the unwanted unit opposite where it appears so it cancels. For example, 3 feet × (12 inches/1 foot) = 36 inches.

Common metric and time conversions

1 kilometer = 1,000 meters, 1 meter = 100 centimeters, 1 kilogram = 1,000 grams, 1 liter = 1,000 milliliters, and 1 hour = 60 minutes.

Scaling effect on area and volume

If every length is multiplied by a factor k, area is multiplied by k² and volume by k³. Doubling the sides of a square makes its area four times larger.

Mean (average)

The mean is the sum of all values divided by the number of values. It is pulled toward unusually large or unusually small values in the data set.

Median of a data set

Order the values from least to greatest and take the middle one. If the number of values is even, average the two middle values.

Mode and range

The mode is the value appearing most often; a data set may have no mode or several. The range is the greatest value minus the least value.

Weighted average

Multiply each value by its weight, add those products, then divide by the total weight. Use it when some values count more than others, such as course grades.

Average speed for a trip

Total distance divided by total time. Averaging the two speeds is incorrect unless the times are equal, because more time is spent at the slower speed.

Finding a missing value from mean

The total of all values equals the mean multiplied by the count of values. Subtract the known values from that total to obtain the missing one.

Reading a graph's scale

Check the numbers and interval spacing on each axis before comparing bar heights or line positions; truncated or uneven scales can make small differences look large.

Percent of a total from a table

Divide the part by the total of the matching row or column, then multiply by 100. Confirm that the total used answers the question actually asked.