TEAS Math: Ratios, Proportions, and Percentages — The Complete Problem-Solving Guide

If there is one topic cluster that dominates the TEAS Math section, it is ratios, proportions, and percentages. These three interconnected concepts show up in straightforward computation questions, multi-step word problems, data interpretation items, and even dosage-style nursing scenarios. Mastering them is not optional — it is the single fastest way to raise your Math score.

This guide walks you through the underlying concepts, teaches you reliable solving methods, and gives you worked examples modeled on actual TEAS question styles. Whether you are comfortable with math or rebuilding your skills from scratch, you will finish this article with a clear system for tackling every ratio, proportion, and percentage problem the test can throw at you.

Why These Topics Matter So Much on the TEAS

The TEAS Math section contains 38 questions covering Numbers and Algebra, Measurement and Data, and Applied Mathematics. Ratios, proportions, and percentages cut across all three domains. You will see them in unit conversion problems, dosage calculations, statistical comparisons, discount and tax scenarios, and data table interpretation. Conservatively, 12-16 of the 38 questions involve one or more of these skills. Getting them right consistently can be the difference between a passing and a competitive score.

Part 1: Ratios

What Is a Ratio?

A ratio compares two quantities and tells you how much of one thing exists relative to another. You can write it three ways: 3:5, 3 to 5, or 3/5. All three mean the same thing — for every 3 of the first quantity, there are 5 of the second.

Ratios can compare part-to-part (nurses to patients) or part-to-whole (nurses to total staff). Reading the problem carefully to determine which comparison is being made is critical for choosing the right numbers.

Simplifying Ratios

Simplify a ratio the same way you simplify a fraction — divide both sides by their greatest common factor (GCF). For example, 12:18 simplifies to 2:3 because the GCF of 12 and 18 is 6. On the TEAS, answer choices are almost always in simplified form, so always reduce before selecting your answer.

Ratio Problem Types on the TEAS

• Finding a ratio from given quantities: 'There are 15 boys and 20 girls. What is the ratio of boys to girls?' → 15:20 → 3:4
• Using a ratio to find a missing value: 'The ratio of nurses to patients is 1:4. If there are 7 nurses, how many patients are there?' → 7 × 4 = 28
• Dividing a total using a ratio: 'A solution is mixed in a 2:3 ratio. If you need 500 mL total, how much of each part?' → Total parts = 5, each part = 100 mL, so 200 mL and 300 mL
• Three-part ratios: 'Red, blue, and green beads are in a 2:3:5 ratio. If there are 60 beads total, how many are blue?' → Total parts = 10, each part = 6, blue = 18

Part 2: Proportions

What Is a Proportion?

A proportion states that two ratios are equal: a/b = c/d. Proportions let you find an unknown value when you know three of the four numbers. This is the single most useful technique on the TEAS Math section because it applies to unit conversions, scaling, dosage, map distances, recipe adjustments, and more.

Cross-Multiplication: The Go-To Method

To solve a/b = c/d, cross-multiply: a × d = b × c. Then isolate the unknown variable. This method works every time and avoids the errors students make when trying to 'reason through' the answer.

Example: A patient needs medication at a rate of 250 mg per 5 mL. How many mL are needed for a 400 mg dose? Set up the proportion: 250/5 = 400/x. Cross-multiply: 250x = 2000. Divide: x = 8 mL.

Common Proportion Scenarios on the TEAS

• Unit conversions: 'If 1 inch = 2.54 cm, how many centimeters are in 7.5 inches?' → 1/2.54 = 7.5/x → x = 19.05 cm
• Dosage calculations: 'A vial contains 100 mg in 2 mL. How many mL for 350 mg?' → 100/2 = 350/x → x = 7 mL
• Scale and map problems: 'On a map, 1 cm = 50 miles. Two cities are 3.5 cm apart. What is the actual distance?' → 3.5 × 50 = 175 miles
• Recipe scaling: 'A recipe uses 3 cups of flour for 24 cookies. How much flour for 60 cookies?' → 3/24 = x/60 → x = 7.5 cups
• Rate problems: 'A nurse checks 12 patients in 3 hours. At this rate, how many patients in an 8-hour shift?' → 12/3 = x/8 → x = 32 patients

Proportion Pitfalls to Avoid

• Mismatched units: Make sure both ratios compare the same things in the same order
• Forgetting to simplify: Always reduce your final answer and check if it makes logical sense
• Rounding too early: Carry at least two decimal places through your calculation before rounding at the end
• Picking the wrong numbers from word problems: Underline the quantities and their labels before setting up the proportion

Part 3: Percentages

What Is a Percentage?

A percentage is a ratio out of 100. The word 'percent' literally means 'per hundred.' Understanding this definition unlocks every percentage problem: 45% means 45 out of 100, or 0.45 as a decimal, or 9/20 as a fraction. The TEAS expects you to move fluently between all three forms.

Converting Between Forms

• Percent to decimal: Divide by 100 (move the decimal point two places left). 72% = 0.72
• Decimal to percent: Multiply by 100 (move the decimal point two places right). 0.085 = 8.5%
• Percent to fraction: Put the percent over 100 and simplify. 60% = 60/100 = 3/5
• Fraction to percent: Divide the numerator by the denominator, then multiply by 100. 7/8 = 0.875 = 87.5%

The Three Core Percentage Formulas

Every percentage problem boils down to the relationship: Part = Percent × Whole. Rearranging this one formula gives you all three question types:

• Finding the part: 'What is 30% of 250?' → 0.30 × 250 = 75
• Finding the percent: 'What percent of 80 is 20?' → (20 ÷ 80) × 100 = 25%
• Finding the whole: '15 is 60% of what number?' → 15 ÷ 0.60 = 25

Percent Increase and Decrease

Percent change problems appear frequently on the TEAS. The formula is: Percent Change = ((New Value − Original Value) ÷ Original Value) × 100. A positive result means an increase; a negative result means a decrease.

Example: A patient's heart rate went from 80 bpm to 92 bpm. What is the percent increase? → ((92 − 80) ÷ 80) × 100 = (12 ÷ 80) × 100 = 15% increase.

Watch out for problems that ask for the new value after a percent change. Use: New Value = Original × (1 + rate) for increases and Original × (1 − rate) for decreases. A $120 item marked 25% off costs $120 × 0.75 = $90.

Tax, Tip, and Discount Problems

These are real-world percentage applications the TEAS loves. For tax or tip, multiply the base amount by the percentage and add it to the original. For discounts, multiply by the percentage and subtract. When problems combine multiple steps (discount then tax), apply them in order — do not add the percentages together.

Example: A $200 item is 15% off, then 8% sales tax is applied. Discount: $200 × 0.85 = $170. Tax: $170 × 1.08 = $183.60. Note that applying both percentages to the original ($200 × 0.93) would give $186 — which is wrong and is a common distractor.

Part 4: Putting It All Together — Multi-Step Problems

The hardest TEAS Math questions combine ratios, proportions, and percentages in a single problem. For example: 'In a class of 40 students, the ratio of nursing majors to biology majors is 3:2. If 75% of nursing majors passed the TEAS on their first attempt, how many nursing majors passed?' Step 1: Find nursing majors: total parts = 5, nursing = (3/5) × 40 = 24. Step 2: Find 75% of 24: 0.75 × 24 = 18 nursing majors passed.

The key to multi-step problems is working one step at a time. Write out each intermediate answer before moving to the next calculation. This prevents the careless errors that cost points under time pressure.

Quick-Solve Strategies for Test Day

• Estimate first: Before calculating, estimate the ballpark answer. If 30% of 250 should be around 75, and your calculation gives 750, you know you moved a decimal wrong
• Use friendly numbers: To find 15% of something, find 10% (move the decimal) then add half of that for the extra 5%
• Check answer choices: If three answers are close together and one is far off, the outlier is probably from a common error — eliminating it narrows your odds
• Set up every proportion on paper: Even if the problem looks simple, writing it down prevents the unit-mismatch errors that plague mental math
• Convert percentages to fractions when they are cleaner: 33.3% is easier as 1/3, and 12.5% is easier as 1/8

Practice Problems

Test yourself with these TEAS-style problems. Work each one fully before checking the answer.

• Problem 1: A hospital has 45 nurses and 15 doctors. What is the simplified ratio of doctors to total staff? → Answer: 15:(45+15) = 15:60 = 1:4
• Problem 2: A medication comes in a 125 mg/5 mL concentration. How many mL are needed for a 300 mg dose? → 125/5 = 300/x → x = 12 mL
• Problem 3: A student scored 68 out of 80 questions correctly. What percentage did they score? → (68/80) × 100 = 85%
• Problem 4: A town's population grew from 12,000 to 14,400. What was the percent increase? → ((14400 − 12000)/12000) × 100 = 20%
• Problem 5: In a 2:3:5 solution mixture totaling 400 mL, how many mL of the second ingredient are needed? → Total parts = 10, second ingredient = (3/10) × 400 = 120 mL

Final Tips for Ratio, Proportion, and Percentage Questions

• Always read the question twice — once for the scenario, once for what it actually asks you to find
• Label every number with its unit before plugging it into a formula
• Simplify ratios immediately to match answer choice format
• For percentage problems, identify which number is the 'whole' before calculating
• If your answer does not match any choice, check for common errors: wrong order in ratio, decimal misplacement, or dividing when you should multiply

Ratios, proportions, and percentages are the backbone of TEAS Math — and they are among the most learnable skills on the entire exam. Unlike abstract algebra or geometry proofs, these problems follow predictable patterns that reward consistent practice. Drill the methods in this guide until cross-multiplication and percent formulas feel automatic, and you will walk into test day with the confidence that nearly half the Math section is already in the bag.