Percent change and the base

Every TEAS percent problem has a base: the whole, or the original amount before a change. Find the base first, then use part = percent × base. Percent change divides the change by the original amount. This free lab makes you mark the base before you calculate, then shows a bar model and each step.

What you do in this lab

  • Choose the base in a word problem before calculating, and see why it is the base.
  • Work eight kinds of percent problems: part, percent, whole, increase, discount, percent change up or down, and the original amount before a change.
  • See a bar model with the base drawn as 100%, and specific feedback on common mistakes such as dividing by the new amount.

TEAS details

  • Objectives: M.1.5 Multistep applications; M.1.6 Percent applications; M.1.9 Ratios/rates/change
  • ATI item formats practised: Fill in the blank, Multiple choice
  • Practice mode gives hints and step-by-step feedback; exam style asks for the answer first and gives one all-or-nothing result, as the TEAS scores every item right or wrong.
  • In the book: Chapter 14, Find the base in percent problems

What is the base in a percent problem?

The base is the amount that counts as 100%: the whole group, or the original amount before a change. Words like “of the”, “original”, “before” and “from” usually point to it.

Once you know the base, every percent problem is the same equation: part = percent × base. If the part is unknown, multiply. If the percent is unknown, divide the part by the base. If the base is unknown, divide the part by the percent.

  • The part: part = percent × base: 15% of 240 = 0.15 × 240 = 36
  • The percent: percent = part ÷ base × 100: 18 of 24 = 18 ÷ 24 = 0.75 = 75%
  • The base: base = part ÷ percent: 36 is 45% of what? 36 ÷ 0.45 = 80

How do you calculate percent increase or decrease?

Percent change = (new − original) ÷ original × 100. The original amount is the base. Going from 80 to 100 is a 20 ÷ 80 = 25% increase, but going from 100 back to 80 is a 20 ÷ 100 = 20% decrease, because the base changed.

For a new amount after a change, multiply by 1 plus or minus the rate: a 15% raise multiplies by 1.15, and a 15% discount multiplies by 0.85. Two changes multiply: +10% then −10% gives 1.10 × 0.90 = 0.99, a 1% net decrease, not zero.

How do you find the original price after a discount?

Divide, do not add back. After a 20% discount the sale price is 80% of the original, so original = sale price ÷ 0.80. A $64 sale price came from $64 ÷ 0.80 = $80.

Adding 20% of $64 back gives $76.80, which is wrong because it uses the sale price as the base.

What is the difference between percent and percentage points?

A rise from 15% to 20% is 5 percentage points, but it is a one-third (about 33.3%) increase relative to 15%. Read which one a question asks for.

How do percent questions show up on the TEAS 7?

The TEAS 7 Math section has 38 questions in 57 minutes, and 34 of them are scored. ATI groups the scored math questions into Numbers and Algebra (18) and Measurement and Data (16). Percent problems belong to Numbers and Algebra, and ATI’s help page lists percentages, including finding percentages of numbers and percentage increase or decrease, among the math to know.

Questions are usually short stories about prices, groups or amounts that changed. Many are multiple choice, where the wrong options are often the answers you get from the wrong base.

What is the formula for percent change?

Percent change = (new − original) ÷ original × 100. A positive result is an increase and a negative result is a decrease. Always divide by the original amount, not the new one.

How do I find what percent one number is of another?

Divide the part by the whole (the base) and multiply by 100. 18 out of 24 is 18 ÷ 24 = 0.75, which is 75%.

How do I find the whole when I know the part and the percent?

Divide the part by the percent written as a decimal. If 36 is 45% of a number, the number is 36 ÷ 0.45 = 80.

Why is a 25% increase not undone by a 25% decrease?

The base changes. 80 up 25% is 100, but 100 down 25% is 75, because the second 25% is taken of 100, not of 80.

Can I use a calculator on the TEAS math section?

Yes. ATI says a basic on-screen calculator is built into the exam and is available on every question in every section. It adds, subtracts, multiplies and divides, and has percent, square root, decimal point, backspace and memory keys. It is not a scientific or graphing calculator, and personal, phone and watch calculators are not allowed.

Keep going

Sources

Facts checked 2026-10-25. Practice items and data in this lab are original and invented; they are not real TEAS questions.

Independence

TEASPATH is independent of ATI. ATI TEAS® and TEAS® are registered trademarks of Assessment Technologies Institute, L.L.C., which is not affiliated with and does not endorse TEASPATH. Practice results are not official scores or admission predictions.

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