ACT WorkKeys Applied Math Formula Guide: Percent, Ratios, Conversions, Area, Volume, and Rates
The formulas are simple. The trick is recognizing when a workplace question is asking for percent, unit price, ratio, area, volume, or rate.
The formula problem on ACT WorkKeys Applied Math
Most people do not miss these questions because they forgot a fancy formula. They miss them because they recognize the formula too late. A floor-tile problem is really an area problem. A glove-price problem is really a unit-price problem. A machine-output problem is really a rate problem.
That is why this guide works like a workplace translation card instead of a school math handout. It shows what the question sounds like, what formula to use, how to work it, and which trap answer to avoid.
ACT allows calculators on WorkKeys Applied Math, but the calculator only speeds up arithmetic. It does not choose the math for you.
Formula quick card
Percent
Part = Percent × Whole
Sounds like: discount, tax, marked down, completed
Unit Price
Total Cost ÷ Units
Sounds like: better deal, cost per item, best value
Rate
Amount ÷ Time
Sounds like: per hour, per minute, at the same rate
Area
Length × Width
Sounds like: cover, floor, paint, tile, square feet
Volume
L × W × H
Sounds like: container, storage, cubic feet, capacity
Average
Total ÷ Number of Values
Sounds like: average output, mean, typical amount
Quick formula card for ACT WorkKeys Applied Math
| Workplace task | Formula or setup | Watch out for |
|---|---|---|
| Find a percent of a number | Part = Percent × Whole | Convert percent to decimal |
| Find final price after discount | Original price − Discount | Do not stop at the discount |
| Compare prices | Unit price = Total cost ÷ Units | Lowest total price may not be best |
| Scale a recipe or mixture | Set up equal ratios | Match the correct units |
| Find rate | Rate = Amount ÷ Time | Check minutes vs hours |
| Find total from rate | Total = Rate × Time | Use the same time unit |
| Find rectangular area | Area = Length × Width | Final unit is square units |
| Find perimeter | Perimeter = 2L + 2W | Do not confuse with area |
| Find rectangular volume | Volume = L × W × H | Needs three dimensions |
| Find average | Average = Total ÷ Number of values | Add all values first |
| Convert feet to inches | Feet × 12 = Inches | Convert before dividing |
| Buy enough packages | Needed amount ÷ Package size | Round up when partial package is needed |
Percent Formula: Discounts, Increases, Tax, and Parts of a Whole
What the question sounds like
- A supplier gives a 15% discount...
- Sales tax is 6%...
- Production increased by 12%...
- The item is marked down...
Trap answer
$48 is the discount, not the final price.
Worked example
A replacement pump costs $320. The supplier gives a 15% discount.
15% = 0.15, so $320 × 0.15 = $48 discount.
Subtract the discount: $320 − $48 = $272 final price.
Answer: $272
Mini-drill
A tool costs $85 and is marked down 20%.
20% = 0.20, so $85 × 0.20 = $17 and $85 − $17 = $68.
Answer: $68
Percent Increase Formula
What the question sounds like
- The price increased by...
- Production rose by...
- The crew needs 10% extra material...
Trap answer
25 feet is only the extra amount, not the full order.
Worked example
A job requires 250 feet of cable and the supervisor orders 10% extra.
250 × 0.10 = 25 extra feet.
250 + 25 = 275 feet total.
Answer: 275 feet
Unit Price Formula
What the question sounds like
- Which supplier is cheaper?
- Which package is the better value?
- What is the cost per item?
Trap answer
The lower total price is not always the better buy.
Worked example
Pack A costs $18 for 12 batteries, so $18 ÷ 12 = $1.50 each.
Pack B costs $28 for 20 batteries, so $28 ÷ 20 = $1.40 each.
Pack B has the lower unit price.
Answer: Pack B
Mini-drill
A box of 50 masks costs $17.50.
$17.50 ÷ 50 = $0.35 per mask.
Answer: $0.35 per mask
Ratio and Proportion
What the question sounds like
- For every...
- A mixture uses...
- At the same ratio...
- How much is needed for...
Trap answer
Multiplying 15 × 4 ignores that 4 ounces goes with every 3 gallons, not every gallon.
Worked example
A cleaning mixture uses 4 ounces of concentrate for every 3 gallons of water.
For 15 gallons: 15 ÷ 3 = 5 groups.
4 ounces × 5 = 20 ounces.
Answer: 20 ounces
Mini-drill
A recipe uses 6 cups of mix for every 9 gallons of water.
For 27 gallons: 27 ÷ 9 = 3, then 6 × 3 = 18.
Answer: 18 cups
Rate Formula
What the question sounds like
- per hour
- each minute
- at the same rate
- produces
- packs
- earns per hour
Trap answer
Do not treat the total amount as if it happened in one hour.
Worked example
A machine produces 420 parts in 7 hours.
420 ÷ 7 = 60 parts per hour.
At the same rate for 10 hours: 60 × 10 = 600 parts.
Answer: 600 parts
Average Formula
What the question sounds like
- Average number...
- Mean...
- Average production...
- Average time...
Trap answer
Do not divide before you total all the values.
Worked example
A team completes 38, 42, 47, and 33 orders over four days.
Add first: 38 + 42 + 47 + 33 = 160.
160 ÷ 4 = 40.
Answer: 40 orders per day
Measurement conversions
| Conversion | Use this |
|---|---|
| 1 foot | 12 inches |
| 1 yard | 3 feet |
| 1 hour | 60 minutes |
| 1 pound | 16 ounces |
| 1 gallon | 4 quarts |
| 1 quart | 2 pints |
| 1 pint | 2 cups |
Worked example
A worker has a 15-foot roll of trim. Each piece must be 20 inches long.
Convert first: 15 × 12 = 180 inches.
Then divide: 180 ÷ 20 = 9 full pieces.
Answer: 9 pieces
Mini-drill
A shift lasts 7 hours and 30 minutes. Thirty minutes is 0.5 hour, so the shift length is 7.5 hours.
Area Formula
What the question sounds like
- Cover the floor
- Paint the wall
- Tile the room
- How many square feet?
Trap answer
6 boxes cover only 240 square feet, so they are not enough.
Worked example
A room is 22 feet by 11 feet, and flooring covers 40 square feet per box.
22 × 11 = 242 square feet.
242 ÷ 40 = 6.05 boxes, so round up to 7 boxes.
Answer: 7 boxes
Perimeter Formula
What the question sounds like
- Around the edge
- Border
- Fence
- Trim
- Edging
Trap answer
Area covers the floor. Perimeter goes around the edge.
Worked example
A room is 14 feet by 9 feet and trim goes around the base of all four walls.
2 × 14 = 28 and 2 × 9 = 18.
28 + 18 = 46 feet.
Answer: 46 feet
Volume Formula
What the question sounds like
- How much space?
- Capacity
- Container
- Storage bin
- Cubic feet
Trap answer
Multiplying only length × width gives area, not volume.
Worked example
A storage container is 6 feet long, 5 feet wide, and 4 feet high.
6 × 5 × 4 = 120 cubic feet.
Answer: 120 cubic feet
Rounding rules
Round up when buying whole items
- Boxes
- Cases
- Rolls
- Containers
- Packages
- People for coverage
- Trucks or trips
Worked example
A job needs 52 feet of wire and wire is sold in 10-foot rolls.
52 ÷ 10 = 5.2 rolls.
You need 6 rolls because 5 rolls provide only 50 feet.
Do not round too early in multi-step problems unless the workplace situation forces it.
The formula disguise table
Many WorkKeys Applied Math questions hide the formula inside workplace wording. This is the part worth memorizing before a practice set.
| If the question says... | Think... |
|---|---|
| Which is the better buy? | Unit price |
| Marked down | Percent discount |
| Increased by | Percent increase |
| For every | Ratio |
| At the same rate | Rate |
| How many more are needed? | Subtract first |
| Covers the floor | Area |
| Around the edge | Perimeter |
| How much space inside? | Volume |
| Comes in boxes of... | Divide, then maybe round up |
| Including delivery, tax, or fee | Add after calculating |
| Already has... | Subtract before buying more |
Five-minute mini drill
Drill 1
A $75 jacket is discounted 20%. What is the final price?
$75 × 0.20 = $15, then $75 − $15 = $60
Answer: $60
Drill 2
A box of 30 filters costs $21. What is the cost per filter?
$21 ÷ 30 = $0.70
Answer: $0.70 per filter
Drill 3
A crew installs 135 feet of cable in 3 hours. At the same rate, how many feet in 8 hours?
135 ÷ 3 = 45 per hour, then 45 × 8 = 360
Answer: 360 feet
Drill 4
A room is 16 feet by 12 feet. Carpet covers 48 square feet per roll. How many rolls are needed?
16 × 12 = 192, then 192 ÷ 48 = 4
Answer: 4 rolls
Drill 5
A drawing uses a scale of 1 inch = 5 feet. A wall is 4 inches on the drawing. What is the actual length?
4 × 5 = 20
Answer: 20 feet
What to memorize vs. what to recognize
Memorize these
- Percent as decimal
- Unit price formula
- Rate formula
- Area formula
- Perimeter formula
- Volume formula
- Common conversions
- Round-up rule for supplies
Recognize these
- Better deal means unit price
- For every means ratio
- Same rate means rate
- Covers usually means area
- Around usually means perimeter
- Container usually means volume
- Already has usually means subtract first
- Including usually means add at the end
How to practice before test day
Do not practice formulas by copying them over and over. Practice them in job language. For each formula, write a money version, a measurement version, and a quantity version.
Division, for example, can mean $48 for 12 items, 96 inches split into 16-inch pieces, or 240 bottles packed into cases of 24. Same operation. Different workplace setup.
After every problem, ask whether you answered the exact question, used the right unit, stopped one step too early, or rounded the right way for the workplace situation.
Turn formula mistakes into a score plan
Missed a percent, ratio, area, or rate question? SimpuTech's ACT WorkKeys Applied Math AI coach can explain the setup and help you decide what to practice next.