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TEAS math fractions: rules, worked examples and practice

Fractions on the TEAS math section come in five jobs: simplify, add and subtract, multiply and divide, compare and order, and convert between fractions, decimals and percents. They sit inside numbers and algebra, the larger of the two math content areas, and they also show up inside word problems on doses, recipes, time and fluids. If you know six rules and can do each one fast without the calculator, most fraction questions take under a minute.

This page has each rule with a worked example, a conversion table to learn, 16 practice questions with answers and reasons, the mistakes that cost points, and a 10-day plan. Test facts come from ATI, which writes the TEAS; the examples and questions are ours.

Where fractions are on the TEAS math section

The TEAS 7 math section has 38 questions in 57 minutes. 34 are scored: 18 in numbers and algebra and 16 in measurement and data. The other 4 are unscored trial questions you can't tell apart from the rest, so treat every question as if it counts.

ATI doesn't say how many questions use fractions. In practice they are inside a large share of numbers and algebra items, because a percent, a ratio and a proportion are all fractions written another way. That is why fractions are worth more study time than their single line in the outline suggests.

A basic calculator is built into the exam, and you can't bring your own. It works in decimals. When the answer choices are fractions or mixed numbers, it is usually faster to stay in fractions on your scratch paper than to convert every choice.

Fraction words you need

How to simplify a fraction

Rule: divide the top and bottom by the same number until nothing but 1 divides both.

Example 1. Simplify 18/24. Both are even: 9/12. Both divide by 3: 3/4. Done, because 3 and 4 share no factor. Dividing by the GCF (6) at once gets you there in one step.

If you can't see the GCF, divide by small primes in turn: 2, then 3, then 5. Check the last digit: an even number divides by 2, a number ending in 0 or 5 divides by 5, and a number whose digits add up to a multiple of 3 divides by 3 (for 48: 4 + 8 = 12, so 48 divides by 3).

Why it matters on the test: answer choices are written several ways. If you get 6/8 and the choices show 3/4, you are right. If both 6/8 and 3/4 are listed, the question wants lowest terms: pick 3/4.

Mixed numbers and improper fractions

Mixed to improper: multiply the whole number by the bottom, add the top, keep the bottom.

Example 2. 3 2/5 = (3 × 5 + 2)/5 = 17/5.

Improper to mixed: divide the top by the bottom. The answer is the whole number, the remainder goes on top.

Example 3. 29/6: 6 goes into 29 four times (24), remainder 5. So 29/6 = 4 5/6.

Turn every mixed number into an improper fraction before you multiply or divide. Adding and subtracting can stay in mixed numbers, as long as you handle the borrowing below.

How to add and subtract fractions

Rule: the bottoms must match. Find the LCD, rewrite each fraction over it, then add or subtract the tops. The bottom stays the same.

Finding the LCD fast: list the multiples of the bigger denominator until the smaller one divides in. For 4 and 6: 6, 12. 4 goes into 12, so the LCD is 12. For 8 and 12: 12, 24. 8 goes into 24, so it's 24. Multiplying the two bottoms always works too (it gives a common denominator, maybe not the least), and you simplify at the end.

Example 4. 2/3 + 3/4. LCD 12. 2/3 = 8/12 and 3/4 = 9/12. 8/12 + 9/12 = 17/12 = 1 5/12.

Example 5, with borrowing. 5 1/4 − 2 2/3. LCD 12: 5 3/12 − 2 8/12. You can't take 8 twelfths from 3 twelfths, so borrow 1 from the 5: 1 = 12/12, and 5 3/12 becomes 4 15/12. Now 4 15/12 − 2 8/12 = 2 7/12.

Check with decimals if you have time: 5.25 − 2.67 ≈ 2.58, and 7/12 ≈ 0.58. The answers agree.

The common wrong answer on this kind of question comes from subtracting the smaller top from the bigger one (8 − 3 = 5) and writing 3 5/12. Test writers know that mistake and put it among the choices.

How to multiply fractions

Rule: top times top, bottom times bottom. No common denominator needed.

Cross-cancel first to keep the numbers small: any top and any bottom that share a factor can be divided by it before you multiply.

Example 6. 3/8 × 4/9. The 4 and the 8 share 4: they become 1 and 2. The 3 and the 9 share 3: they become 1 and 3. Now 1/2 × 1/3 = 1/6. Without cancelling you get 12/72, which also simplifies to 1/6, more slowly.

Example 7, mixed numbers. 2 1/2 × 1 1/3 = 5/2 × 4/3 = 20/6 = 10/3 = 3 1/3. Multiplying the whole numbers and the fractions separately (2 × 1 and 1/2 × 1/3) gives 2 1/6, which is wrong: always convert first.

A whole number times a fraction: put the whole number over 1. 6 × 2/3 = 6/1 × 2/3 = 12/3 = 4.

How to divide fractions

Rule: keep the first fraction, change ÷ to ×, flip the second fraction. Then multiply.

Example 8. 3/4 ÷ 3/8 = 3/4 × 8/3 = 24/12 = 2. Sense check: there are two 3/8s in 3/4, since 3/8 + 3/8 = 6/8 = 3/4.

Example 9. 4 1/2 ÷ 1 1/2 = 9/2 ÷ 3/2 = 9/2 × 2/3 = 18/6 = 3. Three pieces of 1 1/2 make 4 1/2.

Flip only the second fraction, the one you divide by. Flipping the first gives the reciprocal of the right answer, and that reciprocal is often one of the choices.

Negative fractions and the order of operations

The TEAS outline says arithmetic with rational numbers, and rational numbers include negatives. The sign rules are the same as for whole numbers: same signs multiply or divide to a positive, different signs to a negative.

Example 10. −2/3 ÷ 4/9 = −2/3 × 9/4 = −18/12 = −3/2, or −1 1/2.

The order of operations applies too: parentheses, exponents, multiplication and division left to right, then addition and subtraction left to right.

Example 11. 1/2 + 1/3 × 3/4. Multiply first: 1/3 × 3/4 = 1/4. Then 1/2 + 1/4 = 3/4. Adding first gives 5/6 × 3/4 = 5/8, a wrong answer that is easy to land on.

How to compare and order fractions

Three ways, from fastest to most general:

1. Same bottoms: the bigger top is bigger. 5/9 > 4/9.
2. Two fractions, different bottoms: cross-multiply. For 5/8 and 7/11, multiply each top by the other bottom: 5 × 11 = 55 and 7 × 8 = 56. The bigger product sits on the side of the bigger fraction, so 7/11 is bigger.
3. Many numbers in mixed forms: turn them all into decimals. This is where the calculator helps.

Example 12. Put in order from least to greatest: 2/3, 0.65, 5/8, 60%. As decimals: 0.667, 0.65, 0.625, 0.60. Order: 60%, 5/8, 0.65, 2/3.

Benchmarks save time. Compare each fraction to 1/2: 3/7 is less than 1/2 (3.5 would be half of 7), 5/9 is more. If one is below 1/2 and the other above, you are done without any math.

Converting fractions, decimals and percents

ATI's outline names this skill directly. The moves:

• Fraction to decimal: divide the top by the bottom. 3/8 = 3 ÷ 8 = 0.375.
• Decimal to fraction: write the digits over 10, 100 or 1,000 by the number of decimal places, then simplify. 0.45 = 45/100 = 9/20.
• Decimal to percent: move the point two places right. 0.375 = 37.5%.
• Percent to decimal: move the point two places left. 0.4% = 0.004, and 125% = 1.25.
• Fraction to percent: to a decimal first, then move the point. 7/20 = 0.35 = 35%. Or scale the bottom to 100: 7/20 = 35/100.
• Percent to fraction: put it over 100 and simplify. 125% = 125/100 = 5/4 = 1 1/4.

The conversion table to learn

Know these on sight; they come up again and again in answer choices.

Learn the eighths as a chain: each eighth is 12.5%, so 3/8 is three of them (37.5%) and 5/8 is five (62.5%).

TEAS math fraction word problems

Most fraction questions on the test come as a short story. Three patterns cover most of them.

A fraction of a number

"Of" means multiply. Example 13. 3/5 of the 240 applicants passed the first round. How many passed? 240 × 3/5 = 720/5 = 144. Faster: 240 ÷ 5 = 48, and 48 × 3 = 144.

What is left after parts are used

Example 14. A nurse spends 1/3 of a 12-hour shift charting and 1/4 giving medications. How many hours are left for everything else? Used: 1/3 + 1/4 = 4/12 + 3/12 = 7/12. Left: 1 − 7/12 = 5/12. Hours: 12 × 5/12 = 5 hours.

Add the used fractions first, then take them from 1. Taking 1/3 of the shift and then 1/4 of what is left is a different question; read whether the second fraction is of the whole or of the rest.

Scaling a rate up or down

Example 15. A recipe uses 3/4 cup of milk for 2 servings. How much for 5 servings? Per serving: 3/4 ÷ 2 = 3/8 cup. For 5: 3/8 × 5 = 15/8 = 1 7/8 cups. Or set a proportion: (3/4)/2 = x/5, so x = 5 × 3/4 ÷ 2 = 15/8.

Example 16, a fraction in an equation. 2/5 of a number is 8. What is the number? (2/5)x = 8. Multiply both sides by the reciprocal, 5/2: x = 8 × 5/2 = 20.

More story problems, sorted by type with a setup for each, are in our TEAS math word problems guide.

TEAS math fractions practice: 16 questions

Give yourself 20 minutes, a little faster than the real section's 90 seconds a question, since these are single skills. Use scratch paper; use a calculator only on questions 6 and 16, as you might on test day.

1. Simplify 36/48. A) 6/8 B) 3/4 C) 9/12 D) 2/3
2. 1/6 + 3/8 = A) 4/14 B) 13/24 C) 1/2 D) 11/24
3. 6 1/3 − 3 3/4 = A) 3 5/12 B) 2 7/12 C) 3 7/12 D) 2 5/12
4. 5/6 × 3/10 = A) 1/4 B) 8/16 C) 15/16 D) 1/2
5. 2 2/3 ÷ 4/9 = A) 32/27 B) 6 C) 1 5/27 D) 3
6. Which is greatest? A) 4/7 B) 0.56 C) 55% D) 9/16
7. 7/8 written as a percent is: A) 78% B) 87.5% C) 8.75% D) 0.875%
8. 0.36 written as a fraction in lowest terms is: A) 36/100 B) 18/50 C) 9/25 D) 3/6
9. 2/5 of the 85 patients on a unit are over 65. How many are over 65? A) 17 B) 34 C) 42 D) 51
10. An IV bag holds 1,000 mL, and 3/8 of it has run in. How many mL are left? A) 375 B) 600 C) 625 D) 800
11. A student studies 1 1/4 hours Monday, 2 2/3 hours Tuesday and 3/4 hour Wednesday. Total? A) 3 2/3 B) 4 1/2 C) 4 2/3 D) 5 1/12
12. Solve for x: (3/4)x = 27. A) 20 1/4 B) 36 C) 27 3/4 D) 81
13. 3/4 − 1/2 ÷ 2 = A) 1/8 B) 1/4 C) 1/2 D) 1
14. A recipe uses 2/3 cup of oats for 4 muffins. How much for 10 muffins? A) 1 1/3 cups B) 1 2/3 cups C) 2 cups D) 2 2/3 cups
15. Which fraction is between 1/3 and 1/2? A) 2/7 B) 3/10 C) 5/12 D) 4/7
16. What is 120% of 45? A) 5.4 B) 37.5 C) 50 D) 54

Answers and reasons

1. B. The GCF of 36 and 48 is 12: 36 ÷ 12 = 3, 48 ÷ 12 = 4. A and C have the same value but aren't in lowest terms.
2. B. LCD 24: 4/24 + 9/24 = 13/24. A adds tops and bottoms, which is never right.
3. B. LCD 12: 6 4/12 − 3 9/12. Borrow: 5 16/12 − 3 9/12 = 2 7/12. A is the answer you get by taking 4 from 9 instead of borrowing.
4. A. Cross-cancel: 5 and 10 become 1 and 2; 3 and 6 become 1 and 2. 1/2 × 1/2 = 1/4.
5. B. 8/3 × 9/4 = 72/12 = 6. A multiplies without flipping.
6. A. 4/7 ≈ 0.571, 9/16 = 0.5625, 0.56, 0.55. 4/7 is the largest.
7. B. 7 ÷ 8 = 0.875; move the point two places: 87.5%.
8. C. 36/100, divide both by 4: 9/25. A and B are the same value, not in lowest terms.
9. B. 85 ÷ 5 = 17; 17 × 2 = 34.
10. C. Left: 1 − 3/8 = 5/8. 1,000 × 5/8 = 625 mL. A is the amount that ran in, not what is left.
11. C. LCD 12: 15/12 + 32/12 + 9/12 = 56/12 = 4 8/12 = 4 2/3.
12. B. Multiply both sides by 4/3: 27 × 4/3 = 36. Check: 3/4 of 36 is 27.
13. C. Divide first: 1/2 ÷ 2 = 1/4. Then 3/4 − 1/4 = 1/2. A subtracts first.
14. B. Per muffin: 2/3 ÷ 4 = 1/6 cup. For 10: 10/6 = 1 2/3 cups.
15. C. 1/3 ≈ 0.333 and 1/2 = 0.5. 5/12 ≈ 0.417 is between them; 2/7 ≈ 0.286 and 3/10 = 0.3 are below, 4/7 ≈ 0.571 is above.
16. D. 120% = 1.2; 45 × 1.2 = 54. A percent over 100 gives more than the number you started with.

Missed three or more? Find which rule each miss broke (borrowing, flipping the wrong fraction, order of operations, the used-versus-left trap) and redo the matching worked example above before trying again. For a timed set that mixes fractions with the rest of the section, use our TEAS math practice test, or check where all four sections stand with the free TEAS practice test, which scores you against your program's minimum.

Mistakes with fractions on the TEAS

• Adding tops and bottoms. 1/2 + 1/3 is not 2/5. Common bottoms first, always.
• Skipping the borrow. In mixed-number subtraction, a smaller top on the first number means you borrow 1 as a full fraction (12/12, 8/8).
• Multiplying mixed numbers in pieces. Convert to improper fractions before you multiply or divide.
• Flipping the wrong fraction. Only the divisor (the second one) flips.
• Answering the wrong part. "How much is left" and "how much was used" are both among the choices. Underline what the question asks.
• Reaching for the calculator on every step. 1/3 becomes 0.3333333 and rounding drifts. Stay in fractions when the choices are fractions.
• Forgetting the order of operations. Multiplication and division come before addition and subtraction, with fractions too.
• Not checking size. If you divide by a fraction under 1, the answer gets bigger. If you multiply by one, it gets smaller. A result that goes the wrong way is a setup error.

A 10-day TEAS fractions plan

About 30 minutes a day. If fractions are your only weak spot, this fits inside a wider plan such as how to pass TEAS math.

The formulas and unit conversions that sit next to fractions in the same questions are on one sheet in our TEAS math formulas and conversions guide.

TEAS math fractions FAQ

Are fractions on the TEAS math section?

Yes. ATI's numbers and algebra content area, 18 of the 34 scored math questions, includes converting among fractions, decimals and percents and doing arithmetic with rational numbers. Fractions also appear in measurement and data questions and in word problems.

Can the TEAS calculator do fractions?

The built-in calculator is a basic one that works in decimals. You can turn a fraction into a decimal by dividing, but when the answer choices are fractions, working on paper is often faster and avoids rounding errors.

Do I need to simplify my answers?

There is nothing to write in on a multiple-choice question, so you simplify to match a choice. If your answer isn't listed, simplify it or convert it to a decimal or mixed number; the same value can be written several ways.

Are there negative fractions on the TEAS?

They can appear, since the outline covers rational numbers, which include negatives. The sign rules are the same as for whole numbers.

How fast should I be on a fraction question?

The section allows about 90 seconds a question. A single-step fraction question should take well under a minute, which leaves time for the longer word problems.

What is the fastest way to learn fractions for the TEAS?

Learn the six rules on this page, the conversion table, and the three word-problem patterns, then practise by hand daily for a week or two. Untimed accuracy first, then speed.

Sources

• ATI, ATI TEAS exam details (math questions, minutes, content areas and scored counts, calculator). Read for our format guide, October 2026.
• ATI, What type of questions are on the ATI TEAS Version 7?

More on TEAS math: how to pass TEAS math, the TEAS math formula sheet, TEAS math word problems, or all TEAS guides. If you aren't sure whether math is the section holding your score back, the free TEAS practice test shows your gap in each section against your program's minimum.