ATI TEAS Math Word Problems: How to Set Up Ratios, Percents, and Conversions

Word problems test setup before calculation

ATI's Version 7 Mathematics outline asks you to solve real-world problems with one- or multi-step operations, percentages, proportions, ratios and rates of change, and expressions, equations, and inequalities, plus estimation and conversions within and between the standard and metric systems. "Word problem" is not a separate ATI category with its own item count. It is the way many of those objectives are presented.

That matters because a memorized formula list cannot tell you which quantity is the whole, whether two ratios correspond, or which direction a conversion goes. Translation builds the model; arithmetic comes after the model is right. ATI's own public outline includes a sample percent problem in which the unknown is the whole, not the part, which is exactly the kind of setup choice this guide practices.

Mathematics has 38 questions, 34 of them scored, in 57 minutes, about 1.5 minutes per question. Version 7 is still ATI's current exam as of October 2026, with no successor announced, so this outline applies to 2027 test dates too. When the relationship is clear but the notation is rusty, use the ATI TEAS Math formulas and conversions guide.

Use the six-step setup loop

Work through six decisions:

1. Goal: State exactly what the problem asks you to find.
2. Quantities: List the known numbers and what each represents.
3. Units: Attach a unit to every quantity and to the unknown.
4. Relationship: Choose a ratio, proportion, percent equation, rate, conversion, or equation.
5. Estimate: Predict a reasonable range or direction for the answer.
6. Solve and check: Calculate, then check units, size, and meaning.

The first three steps turn language into a clean inventory. Step four is the model choice. The last two catch setups that produce correct arithmetic for the wrong question.

Write the unknown with a label, such as x minutes or x liters. A bare x is easy to solve correctly and interpret wrongly. To build the habit on fresh scenarios, work Math scenarios with worked steps in full ATI TEAS prep → and write the labeled unknown before you calculate.

Translate ratios by keeping the order

A ratio compares quantities in a stated order. If a pattern uses 4 green tiles for every 7 gold tiles, write:

4 green / 7 gold

Flipping both the wording and the fraction is fine. Flipping only one is not. Labels prevent that mistake.

Worked ratio example

A mosaic uses green and gold tiles in a 4:7 ratio. A larger version uses 35 gold tiles. How many green tiles keep the pattern?

Goal: green tiles.

Quantities: 4 green for 7 gold; 35 gold in the larger version.

Relationship: 4 green / 7 gold = x green / 35 gold

Because 35 is five times 7, x is five times 4: x = 20 green tiles.

Check: 20:35 reduces to 4:7, and both counts grew by the same factor.

Don't add the ratio parts unless the question asks about the total. The ratio 4:7 is not the fraction 4/7 of all tiles. Green tiles are 4/(4 + 7), or 4/11, of the whole pattern.

Use proportions only for equal relationships

A proportion says two ratios are equal. Before you cross-multiply, check that both ratios describe the same relationship with matching units in matching positions.

Worked rate example

A label printer makes 18 labels in 3 minutes at a constant rate. How many minutes does it need for 90 labels?

Goal: time in minutes.

Relationship: 18 labels / 3 minutes = 90 labels / x minutes

Cross-multiply: 18x = 270, so x = 15 minutes.

Estimate: 90 labels is five times 18, so the time should be five times 3 minutes. Fifteen fits.

A unit rate works too: 18 ÷ 3 = 6 labels per minute, and 90 ÷ 6 = 15 minutes. Use whichever representation is easiest to check.

A proportion needs a stable relationship. If the printer speeds up as it warms, a constant-rate proportion no longer models the situation.

Find the whole in percent problems

Percent means "per hundred," but percent problems ask different things:

• Find a part when the percent and whole are known.
• Find the percent when the part and whole are known.
• Find the whole when the part and percent are known.
• Find an increase or decrease relative to the original amount.

"Of" often signals multiplication, but keywords are not enough. Name the whole and the quantity the question wants.

Worked percent-of-a-whole example

A reading list has 240 pages, and a student has finished 35% of it. How many pages are finished?

part = percent × whole = 0.35 × 240 = 84 pages

Estimate: 35% is a little more than one third, and one third of 240 is 80, so 84 is reasonable.

If the question asked for pages remaining, you would need one more step: 240 − 84 = 156 pages. The first result is correct arithmetic but the wrong answer to that question.

Worked find-the-whole example

A clinic has seen 45 patients so far today, which is 60% of the patients scheduled. How many are scheduled?

part = percent × whole, so 45 = 0.60 × whole, and whole = 45 ÷ 0.60 = 75 patients.

Check: 60% of 75 is 45. The whole must be larger than the part, so an answer below 45 would be a setup error.

Worked percent-change example

A storage bin held 50 folders and now holds 62. What is the percent increase?

The change is 62 − 50 = 12. Percent change uses the original amount as the base: 12 ÷ 50 × 100% = 24%.

Dividing by 62 would use the new amount and answer a different comparison. If you keep picking the wrong base, revisit percent problems you set up backward with Fix It in full ATI TEAS prep → and label the whole before calculating.

Convert units so the unwanted unit cancels

A conversion factor is a ratio equal to one. Orient it so the unit you want to remove appears once on top and once on the bottom. The metric prefixes do the rest: kilo means 1,000 and milli means one-thousandth.

Worked single conversion

A walking route is 2.4 kilometers long. How long is it in meters?

2.4 km × (1,000 m / 1 km) = 2,400 m

Kilometers cancel and meters remain. The number should get bigger, because a meter is smaller than a kilometer.

Worked conversion with a count

A container holds 1.5 liters of water. How many 250-milliliter cups can it fill completely?

Put both in the same unit first: 1.5 L × (1,000 mL / 1 L) = 1,500 mL.

Then divide: 1,500 mL ÷ 250 mL per cup = 6 cups.

The units reduce to cups. Multiplying by 250 instead would give an impossible volume, not a count.

For conversions between standard and metric units, use the relationship the problem gives you. Don't swap in an approximate factor from memory when the question states an exact one. To keep the common metric relationships automatic, review conversion facts with Math flashcards in full ATI TEAS prep →.

Multi-step problems need a labeled middle step

A multi-step problem often chains models. Write each intermediate result with its label so it can feed the next step.

Worked mixed example

A trail crew has marked 40% of a 3.6-kilometer route. How many meters are still unmarked?

Goal: unmarked distance in meters.

Step 1: If 40% is marked, 100% − 40% = 60% remains.

Step 2: 0.60 × 3.6 km = 2.16 km

Step 3: 2.16 km × (1,000 m / 1 km) = 2,160 m

Check: More than half the route remains, so the answer should exceed 1,800 m, half of 3.6 km. It does.

Finding the marked distance first, subtracting, then converting gives the same 2,160 m. Equivalent methods agree when labels and operations are consistent.

Choose equations from relationships, not keywords

"A fixed fee of 6 dollars plus 4 dollars per hour totals 30 dollars" translates to:

6 + 4h = 30

The fixed amount appears once and the rate multiplies the hours. Then 4h = 24, so h = 6 hours. Check by substituting: 6 + 4(6) = 30.

Words such as "more," "total," or "each" help, but the operation depends on the sentence. Ask what is fixed, what repeats, and what total or limit connects them.

For inequalities, the boundary word decides the symbol. "At most 30" includes 30 and uses ≤. "More than 30" excludes 30 and uses >.

Estimate before you use the calculator

The exam has a basic on-screen calculator on every question: the four operations, percent, square root, and memory keys. It is not a scientific or graphing calculator, and personal calculators are not allowed. You may also have one blank sheet of scratch paper or a small whiteboard. None of that chooses the model for you.

An estimate catches:

• a decimal entered as a whole-number percent.
• a conversion done in the wrong direction.
• a ratio set up backward.
• a result larger than a stated total.
• an answer in the wrong unit.

Round only enough to get a range. For 19.8 × 4.1, the estimate 20 × 4 = 80 says the exact answer (81.18) should be near 80.

Some TEAS questions are fill in the blank: you type the number with no options. ATI asks you to follow the formatting instructions exactly, such as whether to use a leading zero, so read them before you type.

Check the answer three ways

Before you select or type an answer, ask:

1. Unit: Is the answer in the unit the question asks for?
2. Size: Does it fit your estimate and any stated limits?
3. Meaning: Did I answer the goal, not a middle step?

If choices are given, don't force your work toward the nearest one. Recheck the translation first, because a wrong option may match a predictable middle value or a reversed setup. Every TEAS question is scored right or wrong with no penalty for guessing, so enter your best answer even when you are unsure.

The free ATI TEAS practice questions include original Math scenarios for testing the loop, and the ATI TEAS time management guide covers how setup time fits the 57-minute clock.

Practice setup without a formula sheet

Take four original scenarios: one ratio or rate, one proportion, one percent, and one conversion. For each, write only the goal, labeled quantities, units, relationship, and estimate. Solve all four only after every setup is written.

Separating setup from arithmetic shows whether a miss came from the model or the calculation. ATI publishes no word-problem count and promises no particular scenario themes, so practice relationships that transfer. Then run a mixed Math set and check each setup in full ATI TEAS prep →, comparing every result with its original goal.