TEAS numbers and algebra: every skill, with worked examples and practice
Numbers and algebra is 18 of the 34 scored questions on TEAS math, a little over half the section. It tests fractions, decimals and percents, operations with positive and negative numbers, ordering numbers, solving one-variable equations and inequalities, ratios, rates and proportions, percent problems, estimation, and turning words into math.
Below is each skill with its rule and worked examples, 15 practice questions with answers, a 10-day plan and the mistakes that cost points. It is middle-school and early high-school math; the exam gives you an on-screen calculator, so the questions test setup more than arithmetic.
How many numbers and algebra questions are on the TEAS?
| Math content area | Scored questions | What it covers |
|---|---|---|
| Numbers and algebra | 18 | Fractions, decimals, percents; ordering numbers; operations; equations and inequalities; ratios, rates, proportions; percent problems; estimation; word problems |
| Measurement and data | 16 | Charts and graphs, mean, median and mode, geometry, unit conversions |
| Total | 34 scored + 4 unscored = 38 | 57 minutes, about 90 seconds a question |
The skills in numbers and algebra also run through measurement and data: a unit conversion is a proportion, and a graph question often ends in a percent. That is why this area is the place to start when math is your weak section. For the plan across the whole section, read how to pass TEAS math.
The skills ATI lists in numbers and algebra
| Skill | What a question asks | Section below |
|---|---|---|
| Convert fractions, decimals and percents | Write 3/8 as a percent | Converting |
| Operations with rational numbers | Work out −6 + 4 × (−3) | Operations |
| Compare and order rational numbers | Put 0.45, 3/7, 44% in order | Ordering |
| Solve equations with one variable | Solve 2(x + 4) = 5x − 1 | Equations |
| Solve inequalities | Solve −2x + 5 > 13 | Inequalities |
| Translate words into expressions and equations | "Five less than twice a number" | Translating |
| Real-world percent problems | Original price before a discount | Percents |
| Ratios, rates and proportions | Split staff 3:5; miles per hour | Ratios |
| Estimation and rounding | About how much is 49.7 × 6.1? | Estimation |
Converting fractions, decimals and percents
- Fraction → decimal: divide the top by the bottom. 3/8 = 3 ÷ 8 = 0.375.
- Decimal → percent: multiply by 100 (move the point two places right). 0.375 = 37.5%.
- Percent → decimal: divide by 100 (two places left). 0.6% = 0.006. This one trips people: 0.6% is not 0.6.
- Percent → fraction: put it over 100 and simplify. 45% = 45/100 = 9/20.
- Decimal → fraction: read the place value. 0.125 is 125 thousandths = 125/1000 = 1/8.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3, 2/3 | 0.333…, 0.666… | 33.3%, 66.7% |
| 1/4, 3/4 | 0.25, 0.75 | 25%, 75% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1666… | 16.7% |
| 1/8, 3/8, 5/8, 7/8 | 0.125, 0.375, 0.625, 0.875 | 12.5%, 37.5%, 62.5%, 87.5% |
| 1/10 | 0.1 | 10% |
Knowing this table by sight saves calculator time on a dozen questions. Fractions in depth (simplifying, mixed numbers, the four operations) are in TEAS math fractions.
Order of operations and negative numbers
Work in this order: parentheses, exponents, multiplication and division (left to right), addition and subtraction (left to right). PEMDAS is the usual memory aid; the trap is that M and D are one step, and A and S are one step, each done left to right.
Worked example 1. 8 − 2 × (3 + 1)² ÷ 4. Parentheses: 3 + 1 = 4. Exponent: 4² = 16. Multiply and divide left to right: 2 × 16 = 32, then 32 ÷ 4 = 8. Subtract: 8 − 8 = 0.
Worked example 2. 12 ÷ 3 × 2. Left to right: 12 ÷ 3 = 4, then 4 × 2 = 8 (not 12 ÷ 6 = 2).
| Rule for negatives | Example |
|---|---|
| Same signs multiply or divide to a positive | −3 × −4 = 12; −20 ÷ −5 = 4 |
| Different signs multiply or divide to a negative | −12 ÷ 3 = −4; 6 × −2 = −12 |
| Subtracting a negative is adding | 5 − (−2) = 7 |
| Adding numbers with different signs: subtract, keep the sign of the larger | −9 + 4 = −5 |
| A negative squared is positive, unless the minus sits outside | (−3)² = 9, but −3² = −9 |
Type negative numbers into the calculator with parentheses, (−3)², so it squares what you mean.
Comparing and ordering numbers
Turn everything into decimals, line up the decimal points, then compare place by place.
Worked example 3. Order from least to greatest: 0.45, 3/7, 44%, 0.405. As decimals: 0.45, 0.4286, 0.44, 0.405. In order: 0.405, 3/7, 44%, 0.45.
Worked example 4. Which is greatest: −0.3, −1/4, −0.35? As decimals: −0.3, −0.25, −0.35. With negatives, the one closest to zero is greatest: −1/4.
Two checks: a longer decimal is not a bigger number (0.405 is less than 0.45), and on a number line, everything left of zero gets smaller as its digits grow.
Solving one-variable equations
Whatever you do to one side, do to the other. Undo in reverse order: first clear parentheses and gather like terms, then undo adding or subtracting, then undo multiplying or dividing.
Worked example 5. 3x − 7 = 11. Add 7: 3x = 18. Divide by 3: x = 6. Check: 3 × 6 − 7 = 11.
Worked example 6. 2(x + 4) = 5x − 1. Distribute: 2x + 8 = 5x − 1. Subtract 2x: 8 = 3x − 1. Add 1: 9 = 3x. x = 3. Check: 2(7) = 14 and 5(3) − 1 = 14.
Worked example 7. x/4 + 2 = 5. Subtract 2: x/4 = 3. Multiply by 4: x = 12.
On multiple choice, plugging each answer back in is a fair method when the algebra stalls: it takes about 15 seconds per option with the calculator.
Inequalities
Solve them like equations, with one extra rule: when you multiply or divide both sides by a negative number, flip the sign.
Worked example 8. −2x + 5 > 13. Subtract 5: −2x > 8. Divide by −2 and flip: x < −4. Check with x = −5: −2(−5) + 5 = 15, and 15 > 13.
Worked example 9. A clinic can spend at most $500 on supplies. It has spent $140 and boxes cost $24 each. How many boxes can it buy? 140 + 24b ≤ 500, so 24b ≤ 360 and b ≤ 15: 15 boxes.
Read the words: "at least" is ≥, "at most" and "no more than" are ≤, "more than" is >, "fewer than" is <. On a number line, an open circle means the endpoint is not included (< or >); a closed circle means it is (≤ or ≥).
Translating words into math
| Words | Math | Example |
|---|---|---|
| sum, more than, increased by, total | + | "6 more than n" = n + 6 |
| difference, less than, decreased by | − | "5 less than x" = x − 5 (order flips) |
| product, times, of, twice | × | "twice a number" = 2n; "30% of y" = 0.3y |
| quotient, per, divided by, ratio of | ÷ | "miles per hour" = miles ÷ hours |
| is, equals, gives, results in | = | "... is 17" = ... = 17 |
Worked example 10. "Twice a number decreased by 3 is 17." 2n − 3 = 17, so 2n = 20 and n = 10.
Worked example 11. "A phone plan costs $25 a month plus $0.10 per text. Write the cost of t texts." C = 25 + 0.10t.
The common miss is "less than": "5 less than x" starts with x. Twenty more examples by type are in TEAS math word problems.
Percent problems
One equation solves almost all of them: part = percent × whole. Find which two you know.
Worked example 12. What is 15% of 240? 0.15 × 240 = 36.
Worked example 13. 30 is what percent of 120? 30 = p × 120, so p = 0.25 = 25%.
Worked example 14. A price rises from $80 to $92. Percent change = (new − old) ÷ old = 12 ÷ 80 = 0.15 = 15% increase. Always divide by the old value.
Worked example 15. After a 20% discount, a textbook costs $56. What was the original price? You paid 80% of it: 0.8 × P = 56, so P = $70. Adding 20% to $56 ($67.20) is the trap answer.
Ratios, rates and proportions
- Ratio: a comparison, 3:5 or 3/5. Total parts = 3 + 5 = 8.
- Rate: a ratio with units, such as 60 miles per hour or $0.30 per ounce. A unit rate is per one.
- Proportion: two equal ratios. Solve by cross-multiplying.
Worked example 16. The ratio of nurses to aides on a floor is 3:5, and there are 40 staff. 40 ÷ 8 parts = 5 per part, so 15 nurses and 25 aides.
Worked example 17. Which is the better buy: 12 oz for $3.60 or 16 oz for $4.48? $3.60 ÷ 12 = $0.30 an ounce; $4.48 ÷ 16 = $0.28 an ounce. The 16 oz pack.
Worked example 18. A recipe uses 3 cups of rice for 4 servings. How much for 10 servings? 3/4 = x/10, so 4x = 30 and x = 7.5 cups.
Worked example 19. On a map, 1 inch is 25 miles. How far apart are towns 3.2 inches apart? 3.2 × 25 = 80 miles.
Keep units in the same place on both sides of a proportion (cups over servings = cups over servings). Unit conversions work the same way; the conversion chart is in TEAS math formulas and conversions.
Estimation and rounding
To round, look one place to the right of the place you want: 5 or more rounds up, 4 or less stays.
- 3.14159 to the nearest hundredth: the next digit is 1, so 3.14.
- 6.4851 to the nearest tenth: the next digit is 8, so 6.5.
- 2,467 to the nearest hundred: the next digit is 6, so 2,500.
Worked example 20. About how much is 49.7 × 6.1? Round each: 50 × 6 = 300. When the question says "estimate" or "about", the answer choices are usually far enough apart that the rounded answer is the right one; the exact product (303.17) may not even be listed.
Estimating also checks your calculator work: if you expected about 300 and the screen says 3,031.7, a decimal slipped.
To see how many of these skills you already have, take our free TEAS practice test: 15 questions across the four sections, math included, scored against your program's minimum.
15 TEAS numbers and algebra practice questions
Our own questions in the style of the skills above. Give yourself 90 seconds each and use a calculator only where the exam would.
- Write 5/8 as a percent.
Answer: 62.5%. 5 ÷ 8 = 0.625. - Write 0.035 as a percent.
Answer: 3.5%. - Order from least to greatest: 2/3, 0.6, 65%, 0.66.
Answer: 0.6, 65%, 0.66, 2/3. 2/3 = 0.667. - Work out −6 + 4 × (−3).
Answer: −18. Multiply first: 4 × (−3) = −12. - Work out 18 − 3² × 2 + 4.
Answer: 4. 9 × 2 = 18; 18 − 18 + 4 = 4. - Solve 4x + 9 = 37.
Answer: x = 7. - Solve 3(x − 2) = x + 10.
Answer: x = 8. 3x − 6 = x + 10, so 2x = 16. - Solve −3x + 4 ≤ 19.
Answer: x ≥ −5. Dividing by −3 flips the sign. - What is 35% of 260?
Answer: 91. - A price goes from $45 to $54. What is the percent increase?
Answer: 20%. 9 ÷ 45 = 0.2. - After a 25% discount, scrubs cost $36. What was the original price?
Answer: $48. 36 ÷ 0.75. - The ratio of students who passed to those who didn't is 7:2. There are 63 students. How many passed?
Answer: 49. 63 ÷ 9 = 7 per part; 7 × 7. - Four cans cost $5.20. What do 10 cans cost?
Answer: $13.00. $1.30 a can. - "Seven less than three times a number is 20." Find the number.
Answer: 9. 3n − 7 = 20. - Estimate 198 × 4.9.
Answer: about 1,000. 200 × 5.
For 24 more questions across both math content areas, take the TEAS math practice test.
A 10-day plan for TEAS numbers and algebra
About 30 minutes a day: 15 minutes on the skill, 15 minutes of problems without looking at the worked examples.
| Day | Study | Done when you can |
|---|---|---|
| 1 | Converting fractions, decimals, percents | Fill in the equivalents table from memory |
| 2 | Order of operations and negatives | Get 10 mixed expressions right, including (−3)² vs −3² |
| 3 | Comparing and ordering | Order any 4 mixed numbers in under a minute |
| 4 | One-variable equations | Solve equations with parentheses on both sides |
| 5 | Inequalities | Say when the sign flips and graph the answer |
| 6 | Translating words | Write the equation for 10 sentences, "less than" included |
| 7 | Percent problems | Solve part, whole, percent change and discount problems |
| 8 | Ratios, rates, proportions | Split a total by a ratio; find the better unit price |
| 9 | Estimation and rounding | Estimate 10 products within the right answer choice |
| 10 | The 15 questions above, timed, then a mixed math set | 13 of 15 in under 23 minutes; redo every miss |
Mistakes that cost points in numbers and algebra
- Writing "5 less than x" as 5 − x. It is x − 5.
- Forgetting to flip the inequality after dividing by a negative.
- Dividing by the new value for a percent change. Always divide by the old one.
- Adding the discount back to find an original price. Divide by what share you paid.
- Reading 0.6% as 0.6. It is 0.006.
- Multiplying before dividing when division comes first, left to right.
- Calling the longer decimal bigger. 0.405 < 0.45.
TEAS numbers and algebra FAQ
How many numbers and algebra questions are on the TEAS 7?
18 scored questions, out of 34 scored math questions. The other 16 are measurement and data, and 4 more math questions are unscored.
Is there algebra on the TEAS?
Yes, at the level of pre-algebra and early algebra: one-variable equations and inequalities and turning words into equations. ATI's math outline lists equations and inequalities with one variable, so spend your hours there rather than on quadratics or systems of equations.
Do you get a calculator for TEAS math?
Yes. A calculator is built into the exam screen; you can't bring your own. See TEAS exam day tips.
What is the hardest part of numbers and algebra?
For most people it is word problems: percents, ratios and translating sentences, where the setup, not the arithmetic, decides the answer.
How long does it take to study numbers and algebra?
If you remember the basics, the 10-day plan above at 30 minutes a day covers it. If fractions and negatives feel new, double the early days before moving on.
Sources
- ATI, ATI TEAS exam details: math questions, minutes and content areas. Read for our format guide, October 2026.
- ATI, ATI TEAS Version 7 content outline: the numbers and algebra objectives, including percent problems and estimation and rounding.
- OpenStax, Prealgebra 2e and Elementary Algebra 2e, Rice University: order of operations, signed numbers, equations, inequalities, ratios and percents.
More math guides: how to pass TEAS math, TEAS math word problems, TEAS math fractions, TEAS math formulas, the TEAS math practice test, or all guides. To see your math score against your program's minimum, take the free practice test: 15 questions, scored, with the reason for every answer.