Free ATI TEAS 7 Mathematics guide
October 2026 - Percent & Decimals Study Guide for nursing students in
A percentage is a fraction of 100, so 45% is 0.45. To find a percentage of a number, multiply. To find what percentage one number is of another, divide the part by the whole and multiply by 100. Percentage increase and decrease always use the original value as the denominator — never the new one.
The three percentage questions
Every percentage problem on the exam is one of these three, and each has a fixed setup.
- What is 30% of 250? Multiply:
0.30 × 250 = 75. - 75 is what percent of 250? Part over whole, times 100:
75 ÷ 250 = 0.3, so 30%. - 30% of what number is 75? Part over rate:
75 ÷ 0.30 = 250.
Converting in both directions
Percent to decimal: move the point two places left, so 7% is 0.07 and 145% is 1.45. Decimal to percent: two places right, so 0.008 is 0.8%.
The direction is easy to get wrong under pressure. Sanity-check against 50% = 0.5: if your conversion of 5% gives something bigger than that, you moved the point the wrong way.
Percentage change
Worked example
A ward recorded 45 falls last year and 36 this year. What is the percentage decrease?
- Find the absolute change:
45 - 36 = 9. - Divide by the original value, not the new one:
9 ÷ 45 = 0.2. - Multiply by 100: 20%.
A 20% decrease. Dividing by 36 instead would give 25%, which is the distractor this question type always offers.
Percentages do not add across different totals. A 10% rise followed by a 10% fall does not return you to where you started: 100 rises to 110, then falls by 11 to 99. Apply each change to the value in front of you at the time.
Multipliers, which are faster than two steps
For increases and decreases, one multiplication does the whole job.
| Change | Multiplier | Example |
|---|---|---|
| Increase by 15% | × 1.15 | 200 × 1.15 = 230 |
| Decrease by 15% | × 0.85 | 200 × 0.85 = 170 |
| Increase by 8% then 5% | × 1.08 × 1.05 | 200 × 1.08 × 1.05 = 226.80 |
| Reverse a 20% increase | ÷ 1.20 | 240 ÷ 1.20 = 200 |
Terms to know
- Percent
- Out of one hundred. 45% is
45/100or0.45. - Percentage change
- The change divided by the original value, times 100.
- Multiplier
- A single decimal that applies a percentage change in one step.
- Reverse percentage
- Working back to the original value after a change has been applied.
- Percentage point
- The arithmetic difference between two percentages. A rise from 20% to 25% is five percentage points, but a 25% increase.
What the TEAS asks most
The same core ideas appear in different wording. If you can answer these without stopping to think, you have what this section requires.
What is X% of this number?
Convert to a decimal and multiply.
What percentage increase or decrease is this?
Change divided by the original value, times 100. The original is always the denominator.
After a discount of X%, what is the price?
Multiply by (100 − X)% as a decimal. Apply discount before tax unless told otherwise.
The price after a 20% rise is £X. What was it before?
Divide by 1.20. Subtracting 20% from the new price gives the wrong answer.
Key points
- Percent to decimal, move two places left; decimal to percent, two places right.
- Percentage of a number: multiply. What percent one is of another: divide part by whole.
- Percentage change always divides by the original value.
- Use multipliers: ×1.15 to add 15%, ×0.85 to remove it.
- To reverse a percentage change, divide by the multiplier rather than subtracting.
Review quiz
4 questions on this topic, each with the reasoning worked through. Pick an answer to see how it went, or open the explanation straight away.
-
Question 1 of 4
A textbook costs £48. It is reduced by 25%. What is the sale price?
Show the answer and explanation
Correct answer: C. £36
48 × 0.75 = 36. £12 is the discount itself rather than the price paid — the most common slip on discount questions — and £38.40 applies a 20% reduction instead of 25%. -
Question 2 of 4
A clinic's weekly attendance rose from 80 to 92. What was the percentage increase?
Show the answer and explanation
Correct answer: C. 15%
The change is 12, and
12 ÷ 80 = 0.15, so 15%. Choice A quotes the raw change as if it were a percentage, 13% comes from dividing by the new figure of 92, and 87% is80 ÷ 92— the ratio of the two values rather than the change between them. -
Question 3 of 4
After a 20% increase, a supplier's charge is £150. What was the charge before the increase?
Show the answer and explanation
Correct answer: B. £125
Dividing by the multiplier gives
150 ÷ 1.20 = 125, and a check confirms it:125 × 1.20 = 150. £120 comes from taking 20% off £150, which is the trap in every reverse-percentage question, and £180 adds a further 20% instead of removing it. -
Question 4 of 4
A value of 250 increases by 10%, then decreases by 10%. What is the final value?
Show the answer and explanation
Correct answer: B. 247.50
250 × 1.10 = 275, then275 × 0.90 = 247.50. Returning to 250 assumes the two changes cancel, but the decrease is taken from the larger figure, so a sequence of equal percentage moves in opposite directions always lands slightly below the start.
Put this TEAS topic into practice
Build a set on percent and decimals and use the rationale on every question to reinforce what you just reviewed.
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