Mastering TEAS Math Word Problems
The Math section of the ATI TEAS 7 consists of 38 questions to be completed within 57 minutes. Questions fall into two main sub-areas: Numbers & Algebra and Measurement & Data. While basic computational problems test straightforward arithmetic, word problems test your ability to interpret real-world situations, extract numerical information, and apply mathematical operations correctly.
Many students find word problems challenging under timed conditions because extra context can obscure the core calculation. By using a systematic approach, you can break down nursing-style word problems into clear, manageable steps.
A 5-Step Method for TEAS Math Word Problems
Applying a repeatable framework helps eliminate confusion and prevents unnecessary calculation errors during the exam.
Step 1: Identify the Target
Start by reading the last sentence of the question prompt first. This reveals exactly what quantity you need to find. Are you solving for a total fluid intake, a dosage volume, a missing price, or an unknown variable? Clearly defining the target variable and its required units prevents you from solving for the wrong value.
Step 2: Extract the Relevant Data
Read the entire prompt from the beginning and write down the essential numbers, ratios, or rates on your scratch paper. Discard narrative details that do not affect the math, such as patient names, room numbers, or non-numerical clinical background. Focus strictly on given values and their relationship to one another.
Step 3: Choose the Operation or Model
Determine how the given quantities connect mathematically. Translate common key phrases into mathematical operations:
- Addition: total, combined, sum, overall, increased by.
- Subtraction: difference, remaining, how much more, decreased by.
- Multiplication: of (when following fractions or percents), per, product, times.
- Division: per, out of, ratio of, split equally, average.
- Proportion: equal rates comparing two amounts (such as milligrams per milliliter).
Step 4: Set Up and Solve the Equation
Write out the algebraic equation or proportion clearly before doing calculations. Keep your work organized to avoid simple computational slips. Isolate the variable step by step, using inverse operations to solve for the target value.
Step 5: Check Units and Reasonableness
Before finalizing your answer, perform two quick sanity checks:
- Does the numerical value make sense given the problem context?
- Does your answer match the requested units of measurement?
For instance, if a problem asks for the volume of a routine oral medication dose, an answer of 500 milliliters is likely incorrect because it is unrealistically large for a single dose.
Essential Math Skills in Word Problems
Word problems in the TEAS 7 Math section combine narrative text with foundational mathematical concepts. Understanding how to set up calculations across key topic areas ensures you can handle various problem scenarios.
Ratios and Proportions
A proportion states that two ratios are equal. In medical settings, proportions are frequently used to calculate dosages, convert units, or determine scale. The standard proportion equation is:
$$\frac{a}{b} = \frac{c}{d}$$
To solve for an unknown variable $x$ in a proportion, cross-multiply the terms:
$$a \cdot d = b \cdot c$$
Then divide to isolate $x$.
Percentages and Percent Change
Percent problems require converting percentages to decimals or fractions. The word "of" indicates multiplication, while "is" indicates an equals sign.
To find a percentage of a number: $$\text{Part} = \text{Percent (as a decimal)} \times \text{Whole}$$
To calculate percent change (increase or decrease): $$\text{Percent Change} = \frac{|\text{New Value} - \text{Original Value}|}{\text{Original Value}} \times 100%$$
Single-Variable Linear Equations
Linear equations represent situations where a constant rate is combined with a fixed amount. The general form is:
$$ax + b = c$$
Where $a$ represents the variable rate, $b$ is the fixed starting value, and $c$ is the total amount. Solving requires isolating $x$ using inverse mathematical operations.
Worked Examples
Below are three step-by-step worked examples demonstrating how to apply the 5-step method to nursing-style math scenarios.
Example 1: Solving a Dosage Proportion
Question: A medication order calls for 400 milligrams of an antibiotic. The hospital pharmacy supplies the liquid antibiotic at a concentration of 250 milligrams per 5 milliliters. How many milliliters of liquid antibiotic should be prepared?
- Step 1: Identify the Target. We need to find the volume of liquid in milliliters (mL) corresponding to a 400 mg dose.
- Step 2: Extract Relevant Data.
- Concentration ratio: 250 mg per 5 mL
- Target dose: 400 mg
- Unknown volume: $x$ mL
- Step 3: Choose the Operation. Set up a direct proportion comparing milligrams to milliliters. $$\frac{\text{mg}}{\text{mL}} = \frac{\text{mg}}{\text{mL}}$$
- Step 4: Set Up and Solve. $$\frac{250}{5} = \frac{400}{x}$$ Cross-multiply: $$250 \cdot x = 5 \cdot 400$$ $$250x = 2,000$$ Divide by 250: $$x = \frac{2,000}{250} = 8$$
- Step 5: Check Reasonableness. Since 400 mg is greater than 250 mg, the volume must be greater than 5 mL. An answer of 8 mL is reasonable and correctly stated in milliliters.
Example 2: Solving a Single-Variable Linear Equation
Question: A home health care service charges a fixed intake assessment fee of $45 plus $30 per hour for in-home care visits. If a client receives a total bill of $225 for one visit, how many hours of in-home care were provided?
- Step 1: Identify the Target. Find the number of hours of care provided, represented by $h$.
- Step 2: Extract Relevant Data.
- Fixed assessment fee = $45
- Hourly rate = $30 per hour
- Total bill = $225
- Step 3: Choose the Operation. Model the situation using a single-variable linear equation. $$\text{Total Bill} = \text{Fixed Fee} + (\text{Hourly Rate} \times h)$$
- Step 4: Set Up and Solve. $$225 = 45 + 30h$$ Subtract 45 from both sides: $$225 - 45 = 30h$$ $$180 = 30h$$ Divide by 30: $$h = \frac{180}{30} = 6$$
- Step 5: Check Reasonableness. 6 hours at $30 per hour equals $180. Adding the $45 fixed fee gives $225. The answer of 6 hours is correct.
Example 3: Percentages and Remaining Balance
Question: A clinic has a total monthly budget of $4,500 for routine medical supplies. During the first two weeks of the month, the clinic spends 68% of its supply budget. How much money remains in the budget for the rest of the month?
- Step 1: Identify the Target. Find the remaining dollar amount in the budget (not the amount spent).
- Step 2: Extract Relevant Data.
- Total budget = $4,500
- Percent spent = 68%
- Percent remaining = $100% - 68% = 32%$
- Step 3: Choose the Operation. Multiply the total budget by the remaining percentage expressed as a decimal (0.32).
- Step 4: Set Up and Solve. $$\text{Remaining Budget} = 4,500 \times 0.32 = 1,440$$ Alternatively, calculate the spent amount first: $$4,500 \times 0.68 = 3,060$$ Then subtract from the total: $$4,500 - 3,060 = 1,440$$
- Step 5: Check Reasonableness. 32% is roughly one-third of the budget. One-third of $4,500 is $1,500. A remaining amount of $1,440 is logical.
Strategies for Exam Day
To maximize your score on word problems during test day, keep these practical tips in mind:
- Watch Out for Multi-Step Questions: Some word problems require performing an initial calculation before solving for the final answer. Ensure you complete all required steps.
- Keep Track of Units: If a problem provides rates in minutes but asks for total hours, convert units before completing your calculations.
- Avoid Calculation Traps: Read carefully to distinguish between words like "increased to" versus "increased by," or "amount spent" versus "amount remaining."
Practice with EntranceReady
Building speed and accuracy on math word problems requires practical experience with timed practice questions. A great way to begin your preparation is by taking a free 20-question diagnostic test to assess your initial skill level and focus your study time.
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