TEAS 7 math practice guide: worked examples and a formula sheet

What to practice for TEAS 7 math

ATI groups TEAS 7 math into number and algebra, plus measurement and data. Use the official outline to check your coverage. This page teaches selected skills; it is not a complete course, full exam simulation, or a claim that these exact examples will appear on your test.

Try covering each solution and writing your setup first. After checking it, record whether a miss came from the relationship, arithmetic, units, or the wording of the request. Those four problems call for different repairs. A remembered answer is less useful than a method you can explain with new numbers.

• See ATI's math objectives on page 6 of the outline

Fractions and percentages: keep the same whole

Worked example: 7 of 20 workshop seats are occupied. The occupied fraction is 7/20. Divide 7 by 20 to get 0.35, then multiply by 100 to express it as 35%. Because 7 is less than half of 20, an answer below 50% is reasonable.

The common mistake is dividing the whole by the part. Here, 20 ÷ 7 answers a different question. Label the fraction as occupied seats divided by all seats before calculating. If the question instead asks for empty seats, first find 20 − 7 = 13; 13/20 = 65% are empty.

Changed-fact check: if 9 of the same 20 seats are occupied, the result is 9/20 = 0.45 = 45%. The denominator stays 20 because the total has not changed. State which part the question asks about before reusing a calculation.

Percent discounts: distinguish the reduction from the final price

Worked example: a fictional workshop ticket costs $64 before a 25% discount, with no tax or fees in this example. The reduction is 0.25 × $64 = $16. The amount paid is $64 − $16 = $48. Alternatively, keep 75% of the original price: 0.75 × $64 = $48.

If you answer $16 when asked for the final price, the multiplication was correct but the task was unfinished. Underline the requested quantity: discount amount or amount remaining. A 25% discount is not a $25 discount.

Ratios: count all the parts before dividing

Worked example: a display has red and blue markers in a 3:5 ratio, with 64 markers altogether. There are 3 + 5 = 8 equal ratio parts. Each part is 64 ÷ 8 = 8 markers, so red = 3 × 8 = 24 and blue = 5 × 8 = 40. Check both the total, 24 + 40 = 64, and the simplified ratio, 24:40 = 3:5.

The red fraction of the total is 3/8, not 3/5. The ratio 3:5 compares red with blue; it does not compare red with all markers. Draw eight small boxes and label three red if the wording is confusing.

One-variable equations: undo operations and check the result

Worked example: solve 5x + 9 = 44. Subtract 9 from both sides to get 5x = 35. Divide both sides by 5, giving x = 7. Substitute into the original equation: 5 × 7 + 9 = 44, so the result satisfies it.

A tempting shortcut is to divide 44 by 5 immediately and forget the added 9. Write one balanced operation per line. For a word problem, define x with its unit before building the equation; solving an equation correctly is not enough if it represents the wrong quantity.

Metric conversion: cancel units before counting containers

Worked example: you have 2.35 L of water and want to fill 250 mL containers. NIST's milli- prefix means one-thousandth, so 1 L = 1,000 mL. Convert first: 2.35 L × 1,000 mL/L = 2,350 mL. Then 2,350 mL ÷ 250 mL per container = 9.4 container-volumes.

If asked how many containers can be filled completely, the answer is 9, with 100 mL left over: 2,350 − (9 × 250) = 100. If asked for the equivalent number of container-volumes, 9.4 is appropriate. Do not round up to 10 full containers when the water is insufficient.

Write conversion factors so the old unit cancels. Switching from liters to smaller milliliters should increase the numerical value. An answer of 0.00235 mL is a warning that the conversion went in the wrong direction.

• Check NIST's metric prefix reference

Geometry and data: decide which measurement is requested

Worked geometry example: a rectangular mat is 8.5 m long and 4 m wide. Its area is 8.5 × 4 = 34 m². Its perimeter is 2 × (8.5 + 4) = 25 m. Covering the surface calls for area; measuring the border calls for perimeter. The square unit helps you spot which result is which.

Worked data example: five recorded task times are 5, 7, 7, 9 and 27 minutes. In this ordered list, the median is the middle value, 7 minutes. The mean is (5 + 7 + 7 + 9 + 27) ÷ 5 = 11 minutes. The large value 27 pulls the mean upward; it does not change the middle position.

Before reading a graph, check both axis labels, the units and the scale intervals. A plotted value of 4 on an axis labeled ‘hundreds of items’ means 400 items. Do not assume an axis begins at zero or count grid lines without reading their values.

A compact TEAS math formula sheet

Use this short reference to recall a relationship, then close it and practice choosing when that relationship applies. It is a study aid, not an authorized test-day aid or a complete list of everything the TEAS can assess.

1. Percent = part ÷ whole × 100. A percent of a quantity = decimal rate × that quantity.
2. Percent change = (new value − original value) ÷ original value × 100, when the original value is nonzero.
3. Rate = amount ÷ time. Keep the time units consistent with the question.
4. Rectangle: area = length × width; perimeter = 2 × (length + width). Triangle: area = base × perpendicular height ÷ 2.
5. Circle: circumference = 2πr; area = πr². The radius r is half the diameter.
6. Mean = sum of values ÷ number of values. Median = middle of the ordered list, or the mean of the two middle values for an even-sized list.
7. Metric reminders: 1 L = 1,000 mL; 1 g = 1,000 mg; 1 m = 100 cm. Check whether a question asks for length, area or volume before converting.

Turn a missed calculation into a useful next session

Choose one error type and make the repair visible. For a setup error, write why the relationship fits. For an arithmetic error, calculate in smaller steps. For a unit error, include units in every factor. For a reading error, name the requested quantity before working.

Then try different values without the solution visible and explain the result aloud or on paper. Keep a note of any correct guesses. When a short check is available, use it to select a starting topic—not to infer a TEAS score, admission decision, or probability of passing. Reading, science, and English preparation still matter outside this math guide.

• Use the blank mistake-review worksheet
• Explore TEAS math guides and quick sheets