WorkKeys Applied Math cheat sheet

Level 3 problems use whole numbers and one or two operations; the operation is stated or implied directly by the wording.

Keywords: 'total' and 'in all' signal addition; 'left' and 'difference' signal subtraction; 'each' and 'per' signal multiplication or division.

Addition/subtraction order check: for a - b, the larger number must come first unless a negative result is acceptable.

Division is the inverse of multiplication: if a x b = c, then c / b = a, which verifies a quotient.

Rounding to estimate: round each number to the nearest ten or hundred, compute, then compare the estimate to the answer choices.

Average of a list = sum of the values divided by the count of values.

A remainder in division means the quotient rounds up when every item must be placed (e.g., number of buses needed).

Money amounts add and subtract like decimals: line up the decimal point and keep two places.

To add or subtract fractions, rewrite over a common denominator, then combine numerators and simplify.

To multiply fractions, multiply numerators and multiply denominators; to divide, multiply by the reciprocal of the divisor.

Decimal to percent: multiply by 100 (0.35 = 35%). Percent to decimal: divide by 100.

Percent of a number = rate x base; e.g., 15% of 80 = 0.15 x 80 = 12.

Unit conversion within a system uses a ratio equal to 1: 1 ft = 12 in, 1 yd = 3 ft, 1 lb = 16 oz, 1 hr = 60 min.

To convert a larger unit to a smaller unit, multiply; to convert a smaller unit to a larger unit, divide.

A unit rate is a ratio with denominator 1; find it by dividing the quantity by the number of units (cost per item, miles per hour).

Compare fractions by cross-multiplying: a/b vs c/d, compare ad to bc.

Multi-step order: perform operations inside parentheses first, then multiply/divide left to right, then add/subtract left to right.

Proportion setup: part/whole = part/whole, or a/b = c/d; solve by cross-multiplying ad = bc.

Scale drawings and maps use a ratio such as 1 in = 25 mi; multiply the drawing length by the scale factor.

Weighted average = sum of (value x weight) divided by sum of weights; it differs from a simple average when weights differ.

Percent increase or decrease = (new - old) / old x 100; a positive result is an increase, negative a decrease.

Discount: sale price = original x (1 - discount rate). Markup: price = cost x (1 + markup rate).

Total cost with tax = subtotal x (1 + tax rate); compute tax on the subtotal, not on the discounted price unless stated.

A rate compares unlike units (miles per gallon); a ratio compares like or unlike quantities and can be scaled.

Rectangle area = length x width; perimeter = 2(length + width). Triangle area = 1/2 x base x height.

Circle: circumference = pi x diameter; area = pi x radius squared, with radius = diameter / 2.

Volume of a rectangular solid = length x width x height; volume of a cylinder = pi x radius squared x height.

Distance = rate x time; rearrange to rate = distance / time and time = distance / rate.

Mean = sum / count; median = middle value of an ordered list (average the two middle values if the count is even); mode = most frequent value.

Range = maximum - minimum; a large range indicates widely spread data.

Read tables and charts by matching row and column labels first, then applying the needed operation to the correct cells only.

Pythagorean relationship for right triangles: a squared + b squared = c squared, where c is the hypotenuse.

Compound growth: final amount = principal x (1 + rate)^periods; simple interest = principal x rate x time.

Successive percent changes multiply: a 20% increase then a 10% decrease gives 1.20 x 0.90 = 1.08, an 8% net increase.

Break a multi-constraint problem into sub-goals; solve the binding constraint (the one that limits the outcome) first.

When comparing options, convert each to a common basis such as cost per unit or total cost over the same time period.

Reverse percent: if a price after a 25% discount is $60, original = 60 / 0.75 = $80.

Ratios of three or more parts use a common multiplier: parts 2:3:5 with total 100 means multiplier = 100 / (2+3+5) = 10.

Check reasonableness by estimating with rounded numbers; an answer far from the estimate signals an error.

Rate problems with combined work: combined rate = sum of individual rates (1/a + 1/b = 1/t).