A repeatable method before using the calculator
- Name the unknown and its unit. Write “sale price in dollars,” not just “x.” This prevents reporting a discount when the question asks what you pay.
- Label the known values. Keep numbers attached to their units and meanings. Identify a fixed amount, a rate, a total or a percentage base.
- Represent the relationship. Use a small equation, ratio or sketch. Do not search for one keyword that supposedly always means “multiply.”
- Estimate, then calculate. Decide whether the result should be larger or smaller than the starting amount. Keep intermediate precision unless instructed otherwise.
- Check the original situation. Substitute back, inspect the units and apply any rounding or whole-item constraint.
ATI’s math outline includes real-world numerical operations, percentages, proportions, rates, equations, measurement and data. The lesson below focuses on interpreting word problems within that scope. It is not a complete math mock exam.
Source: ATI TEAS Version 7 content outline, Mathematics objectives.
Choose a relationship, not a keyword
- A total split into shares: use ratio parts, and identify whether the comparison is part-to-part or part-to-whole.
- A percentage change: identify the original base, then distinguish the change from the final amount.
- An amount per unit: use a rate with units; convert incompatible units first.
- A starting fee plus repeated charges: use a fixed amount plus rate × quantity.
- A physical measurement: decide whether the task asks for length, area or volume before choosing a formula.
Words such as “more,” “each” and “of” help describe a relationship but do not replace it. “How many more?” can ask for a difference, while “20% more than” needs a percentage base. Reading the whole sentence is part of solving the problem.
Eight worked examples, including the wrong turn
These are original, ungraded CARE teaching examples. The complete solutions are intentionally visible; no private question-bank items or graded answer keys are used here. For feedback after submitting an answer, continue to the free TEAS Math sample.
1. Ratio: distinguish a part from the whole
A study group has 35 learners. The ratio of morning-session learners to evening-session learners is 3:4. Find the number in the evening session.
3 + 4 = 7 equal parts; 35 ÷ 7 = 5 learners per part
Work and check: Evening has 4 parts, so 4 × 5 = 20 learners. Morning has 15. Checking both quantities gives 15 + 20 = 35 and 15:20 simplifies to 3:4.
Wrong turn: Using 4/3 of 35 treats the morning group as the whole. The whole has 7 ratio parts, not 3.
Use this elsewhere: When a ratio splits a total, add the ratio parts before allocating the total.
2. Percentage discount: keep track of what remains
A workbook costs $64 before a 15% discount. There is no tax or shipping charge. Find the sale price.
Discount = 0.15 × $64 = $9.60
Work and check: Subtract the discount: $64 − $9.60 = $54.40. A second setup is 0.85 × $64 = $54.40, because 85% of the original price remains.
Wrong turn: $9.60 is the amount saved, not the amount paid. Before choosing an answer, reread which quantity is requested.
Use this elsewhere: Label each intermediate value. A correct calculation can answer the wrong question.
3. Reverse percentage: find the original amount
After a 20% reduction, a course fee is $72. Find its original price.
0.80 × original price = $72
Work and check: Divide by 0.80: $72 ÷ 0.80 = $90. Check forward: 20% of $90 is $18, and $90 − $18 = $72.
Wrong turn: Adding 20% of $72 gives $86.40, which uses the reduced amount as the percentage base. The reduction was based on the original price.
Use this elsewhere: In a reverse-percentage problem, write an equation for the remaining fraction of the original.
4. Unit rate: align the units before multiplying
A printer produces 84 pages in 6 minutes at a constant rate. Find how many pages it produces in 15 minutes.
84 pages ÷ 6 minutes = 14 pages per minute
Work and check: Multiply 14 pages/minute × 15 minutes = 210 pages. The minutes cancel, leaving pages. Since 15 minutes is more than twice 6 minutes, more than twice 84 pages is reasonable.
Wrong turn: Dividing 15 by 14 reverses the relationship. Check the units instead of choosing multiplication or division by habit.
Use this elsewhere: A constant-rate assumption matters. Do not apply a constant rate if the prompt describes a changing one.
5. Fixed cost plus a repeated cost
A club pays $18 to reserve a room plus $7 for each participant’s materials. Its total budget is $95. Find the greatest whole number of participants it can cover.
18 + 7n ≤ 95
Work and check: Subtract $18 to leave $77 for materials, then divide by $7: n ≤ 11. Eleven participants cost $95; twelve cost $102 and exceed the budget.
Wrong turn: Dividing 95 by 7 spends the room charge again. Separate the fixed part from the per-person part before solving.
Use this elsewhere: For “at most” or a budget limit, check the next whole number as well as your proposed result.
6. Measurement: carry the unit through the setup
An event has 2.4 liters of water. Each cup holds 150 milliliters. With no spillage, find how many full cups can be filled.
2.4 liters × 1,000 milliliters/liter = 2,400 milliliters
Work and check: 2,400 milliliters ÷ 150 milliliters/cup = 16 cups. Multiplying back, 16 × 150 = 2,400 milliliters.
Wrong turn: Dividing 2.4 by 150 mixes liters and milliliters. Convert first or include the conversion factor in a single labeled expression.
Use this elsewhere: This is ordinary volume arithmetic, not medication dosing. Always use the conversion supplied by a problem when one is given.
7. Geometry: buying a border is not covering an area
A rectangular poster is 1.2 meters wide and 0.8 meters tall. Find the length of trim needed to surround its edges once, ignoring joins and waste.
Perimeter = 2 × (1.2 + 0.8) meters
Work and check: The total is 4 meters. The calculation 1.2 × 0.8 = 0.96 gives square meters of area, which answers a different question.
Wrong turn: Using area because two dimensions are given. Read what is being purchased: edge trim requires length; surface covering requires area.
Use this elsewhere: The requested unit is a clue to the relationship: meters and square meters cannot be substituted.
8. Rounding: the situation determines the final step
A group needs to transport 53 people. Each van has 8 passenger seats. Find the minimum number of vans, assuming every seat can be used.
53 ÷ 8 = 6.625 vans
Work and check: Six vans have only 48 seats, so the group needs 7 vans. This is rounding up to satisfy capacity, not rounding to a specified decimal place.
Wrong turn: Rounding down leaves five people without seats. A decimal answer is also unusable when only whole vans can be hired.
Use this elsewhere: If the prompt instead asks for a numerical value to the nearest tenth, follow that instruction. Do not apply capacity rounding to every decimal.
An error log should identify the step that failed
Simply writing the correct answer does not tell you what to change. After reviewing a worked example or a submitted practice answer, classify the error:
- Interpretation: you calculated a different quantity than the one requested. Rewrite the unknown with its unit.
- Setup: you used the wrong base, inverted a rate or omitted a fixed cost. Explain the relationship in words before rewriting the equation.
- Execution: your equation was correct but arithmetic or conversion was not. Show one operation per line and check by reversing it.
- Final constraint: you rounded too soon or ignored a whole-item requirement. Return to the wording rather than applying a memorized rounding habit.
Keep a short record: “mistake → corrected setup → check.” For example, “used discounted price as the base → 0.80x = 72 → 90 − 18 = 72.” That preserves the reasoning you need on a new problem.
Use the method on a different problem
Before opening practice, choose one example and explain why its wrong turn fails. Then use the free Math sample. Write your setup before submitting, and compare the reasoning after feedback—not only whether your answer was marked correct.
A short sample cannot establish mastery of every math objective or predict an ATI score. For practice across the full exam, explore CARE TEAS preparation. If you are planning another official attempt, first check the score and retake policy checklist.
Continue your TEAS preparation
- Anatomy and physiology — Learn body systems and explain how their structures support their functions.
- Scores and retakes — Read a score report and verify the program rules that govern the next attempt.
- Try the free TEAS sample or explore CARE TEAS preparation.
CARE is independent of ATI. These lessons and worked examples are original CARE-created educational material, not official ATI questions or a prediction of your exam score.