WorkKeys Applied Math flashcards

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

Keyword: total

In word problems, 'total' or 'in all' usually signals addition: combine the given quantities to find the combined amount.

Keyword: difference

'Difference' or 'how many more' signals subtraction: subtract the smaller quantity from the larger to find the gap.

Checking division

Multiply the quotient by the divisor; adding any remainder should return the original dividend, confirming the answer.

Rounding to estimate

Round each number to a convenient place value, compute mentally, and use the estimate to eliminate implausible answer choices.

Remainder rounding rule

When items must all be accommodated, a nonzero remainder means the quotient rounds up, such as buses needed for a group.

Common denominator

A shared multiple of two denominators; fractions must be rewritten over it before they can be added or subtracted.

Dividing fractions

Multiply the first fraction by the reciprocal of the second: a/b divided by c/d equals a/b times d/c.

Decimal to percent

Multiply the decimal by 100 and append the percent sign; for example, 0.42 becomes 42%.

Percent of a number

Convert the percent to a decimal and multiply by the base; 20% of 45 equals 0.20 times 45, or 9.

Unit conversion direction

Converting to a smaller unit multiplies by the conversion factor; converting to a larger unit divides by it.

Unit rate

A ratio rewritten with a denominator of 1, found by dividing the quantity by the number of units, such as price per ounce.

Comparing fractions

Cross-multiply: for a/b and c/d, compare ad with bc; the larger product sits under the larger fraction.

Order of operations

Evaluate parentheses first, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

Solving a proportion

Set two ratios equal and cross-multiply to get an equation, then divide to isolate the unknown value.

Scale factor

The ratio relating a drawing or model to the real object; multiply a measured length by it to find actual size.

Weighted average

Sum each value multiplied by its weight, then divide by the total of the weights; unequal weights shift the result.

Percent change formula

Subtract the old value from the new, divide by the old value, and multiply by 100 to express the change as a percent.

Discount calculation

Multiply the original price by one minus the discount rate; a 30% discount means paying 70% of the price.

Sales tax computation

Multiply the taxable subtotal by the tax rate and add the result to the subtotal to obtain the final amount due.

Rectangle area and perimeter

Area equals length times width; perimeter equals twice the sum of length and width, measured in linear units.

Triangle area

Area equals one-half times the base times the perpendicular height, not the length of a slanted side.

Circle formulas

Circumference equals pi times diameter; area equals pi times the radius squared, where radius is half the diameter.

Distance formula

Distance equals rate multiplied by time; rearrange to rate equals distance divided by time when time is known.

Mean versus median

The mean is the sum divided by the count; the median is the middle of an ordered list and resists extreme outliers.

Range of data

The range is the maximum value minus the minimum value and shows how widely the data values are spread.

Reading a data table

Match the row and column labels to the requested category first, then apply the needed operation to those cells only.

Simple interest

Interest equals principal times annual rate times time in years; it is added to principal to find the total owed.

Compound growth formula

Final amount equals principal times one plus the rate raised to the number of periods, reflecting growth on prior interest.

Successive percent changes

Chain percent changes by multiplying their factors; a 20% rise then a 10% fall gives 1.20 times 0.90, or 8% net gain.

Reverse percent

Divide the final amount by the remaining percent factor; a price of 60 after a 25% discount came from 60 divided by 0.75.

Three-part ratio

For parts a:b:c with a known total, divide the total by a+b+c to get the multiplier, then scale each part.

Combined work rate

Add individual rates as reciprocals of their times; the reciprocal of the sum gives the time working together.