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TEAS math guide

Free TEAS math practice test with worked answers

Twenty original questions in the style of the ATI TEAS 7 math section, 12 on numbers and algebra and 8 on measurement and data. Try each one on paper first, then open the answer.

How to use this set

  1. Set a timer for 30 minutes. The real section gives you about 90 seconds a question; 20 questions at that pace is 30 minutes.
  2. Work every question on paper. Write the units next to each number.
  3. Only then open the answer. Read the worked steps even when you got it right, because the steps are what repeat on test day.
  4. Mark each miss as a careless slip, a wrong method, or a missing fact. Study the second and third kind first.

These questions are written by Lemma for practice. They follow the public shape of the TEAS 7 math section but are not ATI questions, and a score here does not predict your real score. For a calibrated number, take ATI's own practice assessment.

Numbers and algebra

Question 1

Write 7/8 as a decimal and as a percent.

  1. 0.78 and 78%
  2. 0.875 and 87.5%
  3. 0.875 and 8.75%
  4. 1.14 and 114%
Show the answer and the steps

Answer: 0.875 and 87.5%

  1. Divide the top by the bottom: 7 ÷ 8 = 0.875.
  2. Multiply by 100 to get a percent: 0.875 × 100 = 87.5%.

Watch for: Reading 7/8 as 0.78 by putting the digits side by side. A fraction is a division, not two digits.

Question 2

Which list is in order from least to greatest?

  1. 59%, 0.6, 5/8, 2/3
  2. 0.6, 59%, 5/8, 2/3
  3. 2/3, 5/8, 0.6, 59%
  4. 5/8, 59%, 0.6, 2/3
Show the answer and the steps

Answer: 59%, 0.6, 5/8, 2/3

  1. Put every number in decimal form: 59% = 0.59, 0.6 = 0.60, 5/8 = 0.625, 2/3 ≈ 0.667.
  2. Order the decimals: 0.59 < 0.60 < 0.625 < 0.667.

Watch for: Comparing a percent, a decimal and a fraction without converting them to one form first.

Question 3

Find 3 2/5 + 1 3/4.

  1. 4 5/9
  2. 4 11/20
  3. 5 3/20
  4. 5 1/4
Show the answer and the steps

Answer: 5 3/20

  1. Use a common denominator of 20: 3 8/20 + 1 15/20.
  2. Add the whole numbers: 3 + 1 = 4. Add the fractions: 8/20 + 15/20 = 23/20 = 1 3/20.
  3. Combine: 4 + 1 3/20 = 5 3/20.

Watch for: Adding the numerators and the denominators across (2 + 3 over 5 + 4). Denominators are not added.

Question 4

Find 2 1/2 × 1 3/5.

  1. 3 3/10
  2. 4
  3. 3 1/10
  4. 4 1/2
Show the answer and the steps

Answer: 4

  1. Turn both into improper fractions: 5/2 × 8/5.
  2. Cancel the 5s: 1/2 × 8/1 = 8/2 = 4.

Watch for: Multiplying the whole numbers and the fractions separately (2 × 1 and 1/2 × 3/5). Convert first.

Question 5

Solve for x: 5(x − 2) = 3x + 6.

  1. x = 2
  2. x = 4
  3. x = 8
  4. x = 16
Show the answer and the steps

Answer: x = 8

  1. Distribute: 5x − 10 = 3x + 6.
  2. Subtract 3x from both sides: 2x − 10 = 6.
  3. Add 10: 2x = 16. Divide by 2: x = 8.
  4. Check: 5(8 − 2) = 30 and 3(8) + 6 = 30.

Watch for: Writing 5x − 2 after distributing, which multiplies only the first term.

Question 6

A tutor charges a $15 sign-up fee plus $22 per hour. A student paid $103 in all. How many hours did the student book?

Type your answer with its unit.

Show the answer and the steps

Answer: 4 hours

  1. Write the equation: 15 + 22h = 103.
  2. Subtract 15: 22h = 88.
  3. Divide by 22: h = 4.

Watch for: Dividing 103 by 22 first. The fee is charged once, so take it out before dividing by the hourly rate.

Question 7

Solve: 4 − 2x ≥ 10.

  1. x ≥ −3
  2. x ≤ −3
  3. x ≤ 3
  4. x ≥ 7
Show the answer and the steps

Answer: x ≤ −3

  1. Subtract 4 from both sides: −2x ≥ 6.
  2. Divide both sides by −2 and flip the inequality sign: x ≤ −3.
  3. Check x = −4: 4 − 2(−4) = 12, and 12 ≥ 10 is true.

Watch for: Not flipping the sign when dividing by a negative number.

Question 8

A pair of clogs is on sale for 20% off. The sale price is $68. What was the original price?

  1. $81.60
  2. $85
  3. $88
  4. $90
Show the answer and the steps

Answer: $85

  1. A 20% discount means you pay 80% of the original: 0.80 × original = 68.
  2. Divide: original = 68 ÷ 0.80 = 85.

Watch for: Adding 20% of $68 back on. The 20% was taken off the original price, not off the sale price.

Question 9

A unit had 40 admissions in September and 46 in October. By what percent did admissions increase?

  1. 6%
  2. 13%
  3. 15%
  4. 18%
Show the answer and the steps

Answer: 15%

  1. Change = 46 − 40 = 6.
  2. Percent change = change ÷ starting amount = 6 ÷ 40 = 0.15 = 15%.

Watch for: Dividing by the new amount (6 ÷ 46 ≈ 13%). Percent change always uses the starting amount.

Question 10

A cleaning mix uses 2 parts concentrate to 7 parts water. How many mL of concentrate go with 63 mL of water?

Type your answer with its unit.

Show the answer and the steps

Answer: 18 mL

  1. Set up the ratio as a proportion: 2/7 = c/63.
  2. Cross-multiply: 7c = 126.
  3. Divide: c = 18.

Watch for: Treating 2 : 7 as 2 out of 7 total, then taking 2/7 of 63. The 7 parts are water only, not the total.

Question 11

A medication is ordered at 15 mg per kg per day, divided into 3 equal doses. The patient weighs 72 kg. How many mg is one dose?

Type your answer with its unit.

Show the answer and the steps

Answer: 360 mg

  1. Daily total: 15 mg/kg × 72 kg = 1,080 mg per day.
  2. Split into 3 equal doses: 1,080 ÷ 3 = 360 mg.

Watch for: Stopping at the daily total. The question asks for one dose.

Question 12

A bag of 1,000 mL of fluid is set to run in over 8 hours. At what rate, in mL per hour, should it run?

Type your answer with its unit.

Show the answer and the steps

Answer: 125 mL per hour

  1. Rate = amount ÷ time = 1,000 mL ÷ 8 h.
  2. 1,000 ÷ 8 = 125 mL per hour.

Watch for: Dividing hours by mL. Put the amount on top and the time underneath, and the units tell you the answer is mL per hour.

Measurement and data

Question 13

A patient weighs 154 lb. Using 1 kg = 2.2 lb, what is the weight in kg?

  1. 33.6 kg
  2. 70 kg
  3. 154 kg
  4. 338.8 kg
Show the answer and the steps

Answer: 70 kg

  1. Pounds to kilograms means fewer units, so divide: 154 ÷ 2.2.
  2. 154 ÷ 2.2 = 70 kg.

Watch for: Multiplying by 2.2 (338.8). A kilogram is bigger than a pound, so the kg number must be smaller.

Question 14

A prescription is 2,450 mg. How many grams is that?

  1. 0.245 g
  2. 2.45 g
  3. 24.5 g
  4. 245 g
Show the answer and the steps

Answer: 2.45 g

  1. 1 g = 1,000 mg, so divide mg by 1,000.
  2. 2,450 ÷ 1,000 = 2.45 g.

Watch for: Moving the decimal the wrong way or the wrong number of places. Check that the answer makes sense: a gram is much bigger than a milligram, so there are fewer of them.

Question 15

Six clinic visits last 7, 9, 10, 12, 12 and 15 minutes. What is the median length?

  1. 10 minutes
  2. 10.8 minutes
  3. 11 minutes
  4. 12 minutes
Show the answer and the steps

Answer: 11 minutes

  1. The list is already in order and has an even number of values, so the median is the mean of the two middle values.
  2. The middle two are 10 and 12: (10 + 12) ÷ 2 = 11.

Watch for: Picking the mean (10.8) or the mode (12) instead of the middle of the ordered list.

Question 16

A triangular bandage has a base of 14 cm and a height of 9 cm. What is its area?

  1. 23 cm²
  2. 63 cm²
  3. 126 cm²
  4. 252 cm²
Show the answer and the steps

Answer: 63 cm²

  1. Area of a triangle = ½ × base × height.
  2. ½ × 14 × 9 = 63 cm².

Watch for: Forgetting the ½, which gives the area of the rectangle around the triangle (126 cm²).

Question 17

A round tray has a radius of 7 cm. Using π ≈ 3.14, what is its circumference?

  1. 21.98 cm
  2. 43.96 cm
  3. 153.86 cm
  4. 307.72 cm
Show the answer and the steps

Answer: 43.96 cm

  1. Circumference = 2 × π × r.
  2. 2 × 3.14 × 7 = 43.96 cm.

Watch for: Using the area formula (π × r²), which gives 153.86 cm² and is a different quantity.

Question 18

A tank measures 40 cm by 25 cm by 30 cm. Given 1 cm³ = 1 mL, how many liters does it hold?

  1. 3 L
  2. 30 L
  3. 300 L
  4. 3,000 L
Show the answer and the steps

Answer: 30 L

  1. Volume = length × width × height = 40 × 25 × 30 = 30,000 cm³.
  2. 30,000 cm³ = 30,000 mL.
  3. 1 L = 1,000 mL, so 30,000 ÷ 1,000 = 30 L.

Watch for: Stopping at 30,000 and calling it liters. The units were cm³ and mL until the last step.

Question 19

A table lists weekday clinic visits: Mon 12, Tue 18, Wed 15, Thu 21, Fri 9. What percent of the week's visits happened on Thursday?

  1. 21%
  2. 25%
  3. 28%
  4. 30%
Show the answer and the steps

Answer: 28%

  1. Total visits: 12 + 18 + 15 + 21 + 9 = 75.
  2. Thursday's share: 21 ÷ 75 = 0.28 = 28%.

Watch for: Reading 21 as 21%. A count is not a percent until you divide by the total.

Question 20

A line passes through (2, 5) and (6, 13). What is its slope?

  1. −2
  2. 1/2
  3. 2
  4. 4
Show the answer and the steps

Answer: 2

  1. Slope = change in y ÷ change in x = (13 − 5) ÷ (6 − 2).
  2. 8 ÷ 4 = 2.

Watch for: Putting x on top (4 ÷ 8 = 1/2). Slope is rise over run: y over x.

After you finish

Count your misses by area. If most are in numbers and algebra, work the fraction, percent and equation topics. If most are in measurement and data, work unit conversion and charts first. Then retry only the questions you missed, two days later, with fresh numbers.

Fresh numbers are the part a static worksheet cannot give you. On Lemma every topic generates new problems, and each step you type is checked by a computer algebra system, so a repeat attempt tests the method, not your memory of the answer.

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Questions

Are these the real TEAS questions?

No. Every question was written for Lemma, following the public shape of the TEAS 7 math section. Nothing is copied from ATI or from paid question banks.

How many questions are on the real TEAS math section?

38 questions in 57 minutes, with 34 scored. This set has 20 so that you can finish it in a single sitting.

Will a high score on this set mean I will pass the TEAS?

Not by itself. It tells you which topics to study. For a calibrated estimate, take an official ATI practice assessment closer to your test date.

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Sources

Facts checked 2026-10-14. Independent practice, not affiliated with ATI or McGraw Hill.