Free WorkKeys Applied Math Exam Flashcards

Workplace calculations with multiple operations must follow Parentheses, then Exponents, then Multiplication and Division (left to right), then Addition and Subtraction (left to right). Skipping this order changes the answer: 2 + 3 x 4 is 14, not 20, because multiplication precedes addition.

Multiply numerators together and denominators together: (a x c)/(b x d). You do NOT need a common denominator for multiplication; the common-denominator rule applies only to addition and subtraction of fractions.

When a problem asks how many containers, batches, or shifts are needed, round UP, because a partial container still must be purchased or scheduled. When it asks how many whole units fit, round DOWN, because the remainder cannot be used.

Line up the decimal points vertically before adding or subtracting, and pad shorter numbers with trailing zeros. Misaligning by one place shifts the answer by a factor of 10, the most common arithmetic error in workplace bookkeeping.

Multiply the whole number by the denominator and add the numerator: 3 1/4 = (3 x 4 + 1)/4 = 13/4. Convert mixed numbers before multiplying or dividing; leaving them mixed forces error-prone two-step arithmetic.

Divide the numerator by the denominator: 3/8 = 3 / 8 = 0.375. This conversion is required whenever a workplace answer must be in decimal form, such as money, measurements, or calculator output.

Multiply the hourly rate by the number of hours worked: pay = rate x hours. Verify decimal placement: a $14.50 rate over 40 hours is $580.00, not $58.00 or $5,800.

Under FLSA-style rules, hours worked beyond 40 in a week are paid at 1.5 x the regular rate. Compute regular pay for the first 40 hours and overtime pay for the remainder, then add; never apply 1.5x to all hours.

Divide minutes by 60: 20 min = 20/60 = 1/3 hour (about 0.333), and 45 min = 0.75 hour. Use this conversion whenever a labor charge or wage problem gives time in hours and minutes, because hourly rates multiply only by hours.

Convert both times to 24-hour format (add 12 to PM hours except 12 itself) and subtract: 7:45 AM to 4:15 PM becomes 07:45 to 16:15, or 8 hours 30 minutes. Mixing AM/PM subtraction directly is the most common time-clock error.

Calculate gross elapsed time first, then subtract only the unpaid break minutes to get paid work hours. A 30-minute unpaid lunch means 8h30m elapsed becomes 8h paid; forgetting to subtract overstates pay, and subtracting twice understates it.

Start at the purchase price and count up to the cash tendered using the fewest denominations: price $13.65, tendered $20.00 means add $0.35 to reach $14.00, then $1 and $5 bills to reach $20. Counting up avoids subtraction errors and gives the customer the correct bills and coins.

Gross pay is total earnings before deductions; net (take-home) pay is what remains after taxes, insurance, retirement, and other withholdings. Workplace math problems specify which one to calculate; computing gross when net is asked, or vice versa, is a frequent miss.

Annual is approximately weekly x 52, and monthly is approximately annual / 12. Use 52 weeks (not 4.33 weeks) for weekly-to-annual conversions, because the extra fraction of weeks per month accumulates across the year.

Percent change = (amount of change / original amount) x 100. The ORIGINAL (starting) value is always the denominator; using the new value as the denominator is the most common percent-change error.

Both use (change / original) x 100; the sign of the change tells the direction. A price rising from $24 to $30 is a 25% increase; falling from $30 to $24 is a 20% decrease, because the same $6 difference gives a different percentage when the base differs.

Discount amount = discount percent x original price; sale price = original minus discount. Always compute the discount amount first and subtract; multiplying by (1 - percent) in one step risks dropping a place value when working by hand.

Markup is added to COST: selling price = cost x (1 + markup percent). Margin is taken from SELLING PRICE: profit = price x margin percent. A 50% markup on a $10 cost yields $15, which is only a 33% margin on the $15 selling price, so the two terms are not interchangeable.

Two discounts applied in sequence multiply, not add: 20% off then 10% off yields a final price of 0.80 x 0.90 = 0.72 of original (28% off), not 30% off. Add the percentages only if both discounts are taken off the same original base.

Commission = commission rate x sales amount. A 5% commission on $18,000 in sales is $900; total compensation adds this to any base salary. Distinguish the commission rate (percent per dollar of sales) from the commission amount (the dollar result).

Sales tax applies to the discounted (sale) price, not the original price, and is added AFTER the discount is subtracted. Computing tax on the original price overcharges the customer and is a frequent register-error cause.

X percent of a whole multiplies the percent by the whole (15% of 200 = 30). Part is what percent of whole divides part by whole (30/200 = 15%). The two operations are inverses; recognizing which one the prompt asks for sets up the correct calculation.

Multiply feet by 12 to get inches; divide inches by 12 to get feet. For mixed measurements like 5 ft 8 in, convert the feet portion to inches and add, or convert everything to one unit before any further arithmetic.

Multiply pounds by 16 for ounces; divide ounces by 16 for pounds. Mixed weights like 3 lb 8 oz must be converted to a single unit (56 oz) before applying a per-ounce rate; keeping mixed units through a multiplication produces a wrong answer.

Whenever a problem gives measurements in two related units (feet and inches, pounds and ounces, hours and minutes), convert both to the smaller unit before adding, subtracting, multiplying, or dividing. Operating on mixed units directly is the leading source of measurement errors on the test.

Kilo- means 1,000, centi- means 1/100, and milli- means 1/1,000 of the base unit. Moving between prefixes shifts the decimal three places per step: 2.5 kg = 2,500 g = 2,500,000 mg. The decimal-shift pattern makes metric conversion faster than US-unit conversion.

1 kilogram is about 2.2046 pounds, and 1 pound is about 0.4536 kilograms. To convert 5 kg to pounds, multiply by 2.2046 (about 11.02 lb). Use the precise factor in shipping and medical contexts, because rounding to 2.2 introduces compounding error.

C = (F - 32) x 5/9 and F = (C x 9/5) + 32. Subtract 32 first when going from Fahrenheit to Celsius; multiplying before subtracting gives a wrong result. Water freezes at 0C / 32F and boils at 100C / 212F.

Divide total price by quantity to get price per single unit (per ounce, per pound, per item) and compare across package sizes. The lowest total price is not always the lowest unit price; bulk packages sometimes cost more per unit than smaller ones.

Speed = distance / time, distance = speed x time, and time = distance / speed. Identify which two values are given and which is unknown; the formula rearranges to isolate whichever variable the problem asks for.

For a/b = c/d, multiply diagonally: a x d = b x c, then solve for the unknown. Cross-multiplication converts a proportion into a single algebraic equation and is the fastest way to solve rate and ratio problems on the test.

A map scale like 1 inch = 10 miles means 1 map unit represents 10 real units; multiply map distance by the scale factor for real distance. Keep the units straight: a 3.5-inch map distance at 1 in = 10 mi is 35 miles, not 3.5 miles.

A unit rate expresses one quantity per 1 unit of another, such as $0.45 per ounce, 50 miles per hour, or 12 widgets per minute. Divide the numerator by the denominator so the denominator equals 1; comparing unit rates is the standard way to choose between options.

A 3:1 mixing ratio means 3 parts of one component to 1 part of another (4 total parts). To make 20 gallons of a 3:1 mix, split it as 15 gallons of the first and 5 of the second; multiply the total by (part / total parts) for each component.

For two workers with individual rates 1/a and 1/b (jobs per unit time), the combined rate is 1/a + 1/b = 1/combined; take the reciprocal to find the combined time. A worker who finishes in 4 hours and another in 6 hours together finish in 1/(1/4 + 1/6) = 2.4 hours.

When total work is fixed, workers and time are inversely proportional: workers1 x time1 = workers2 x time2. Doubling the crew halves the time; cutting the crew by a third triples the time. Distinguish inverse proportion from direct proportion; using the wrong one flips the answer.

Mean = sum of values / count of values. The sum and the count must use the same units, and every value must be included; skipping one value or counting it twice changes the mean. A workplace mean might be the average daily output, average wage, or average defect count.

Multiply the mean by the count to get the required total sum, then subtract the sum of the known values. If 4 days must average 50 units and three days produced 45, 52, and 48, the fourth day needs 200 - 145 = 55 units.

Multiply each value by its weight, sum those products, and divide by the total weight. A weighted average differs from a simple average when groups have different sizes; 80% on a 200-question section and 90% on a 50-question section averages to 82%, not 85%.

The median is the middle value when data is sorted; the mean is the arithmetic average. A single extreme value can shift the mean dramatically while leaving the median nearly unchanged, which is why income data and home prices are usually reported as medians.

Area = length x width, with both dimensions in the same unit. The result is in square units (sq ft, sq m). Adding the dimensions (length + width) gives the half-perimeter, not the area; this is a common confusion on basic geometry problems.

Area = 1/2 x base x height, where height is perpendicular to the base (not the slant side). For a 10-foot base and 6-foot height, area = 30 sq ft. Using a slant length as the height inflates the area.

Area = pi x r^2, where r is the radius (half the diameter). Squaring the diameter by mistake gives 4x the correct area; always convert diameter to radius first. Use the calculator's pi key, not 3.14, for precision.

Volume = length x width x height, all in the same unit. The result is cubic units (cubic feet, cubic meters). To find how many smaller boxes fit inside, divide the prism's volume by the smaller box's volume.

Volume = pi x r^2 x h, where r is the radius of the circular base and h is the height. Calculate r^2 first (radius squared), multiply by height, then by pi. Confusing diameter with radius quadruples the volume.

When an unplanted (or unwalked) border of width W runs along ALL edges of a rectangle, subtract 2W from BOTH the length and the width before multiplying. A 5-meter border on a 120 x 85 m field leaves a 110 x 75 m planted section; subtracting W only once or from only one dimension is the most common area error.

Concentration x Volume before dilution equals Concentration x Volume after. To dilute 200 mL of a 12% solution to 8%, solve 12 x 200 = 8 x V2, giving V2 = 300 mL (add 100 mL of solvent). Set up the equation before plugging in numbers to avoid sign and unit errors.

When the same product is sold at different per-unit prices across quantity tiers, compute the total cost (including unused units) for the amount needed at each tier. The lowest per-unit price may still cost more overall if the tier forces buying more than you need.

Total work = workers x time x per-worker rate. To find the time for a different crew size, keep total work fixed and rearrange: time2 = (workers1 x time1 x rate) / (workers2 x rate). Recognize this as a proportion, not an addition problem.

Profit margin = (revenue - cost) / revenue, expressed as a percent. Margin is computed on the SELLING price, while markup is computed on the COST; a 25% margin on $100 revenue means $25 profit and $75 cost. Confusing the two bases is a common error in retail problems.