Ratios, rates and proportions

To solve a TEAS proportion, put like units in the same row, keep each situation in its own column, then cross-multiply: if a/b = x/d, then x = a × d ÷ b. This free lab has you build that units table from a word problem before you calculate, then shows the cross-multiplication and checks your answer.

What you do in this lab

  • Place the quantities from a word problem into a two-row units table, with keyboard-friendly menus, and get feedback on the setup.
  • Solve recipe, map scale, rate, unit price and ratio-to-total problems.
  • See the cross-multiplication written out, plus a warning when a part-to-part ratio is used as part-to-whole.

TEAS details

  • Objectives: M.1.5 Multistep applications; M.1.8 Proportions; 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 13, Recognize ratios, rates and proportion; Chapter 15, Translate a situation into a model

How do you set up a proportion from a word problem?

Make a small table. Each row is one unit, such as cups of flour or loaves, and each column is one situation: the one you know and the one you are asked about. Put x in the empty cell.

Read the table as two equal fractions and cross-multiply. For 3 cups per 2 loaves and x cups for 5 loaves: 3/2 = x/5, so 2x = 15 and x = 7.5 cups.

What is a unit rate?

A unit rate is the amount for one unit: dollars per bottle, liters per minute or miles per inch. Divide the total by the number of units. A pack of 6 bottles for $3.12 costs $3.12 ÷ 6 = $0.52 per bottle. Comparing unit rates is the quickest way to find the better buy.

How do you use a ratio to find part of a total?

A ratio such as 5:7 compares two groups with each other (part to part). To use it with a total, add the parts: 5 + 7 = 12. The first group is 5/12 of the total, so with 48 people it has 5/12 × 48 = 20.

Multiplying 48 by 5/7 is the common mistake: 5/7 compares the two groups, not one group with the whole.

When is a proportion the wrong tool?

A proportion only works when the ratio stays the same. If more workers finish a job in less time, the relationship is inverse, not proportional, so a straight proportion gives the wrong answer. Check that doubling one quantity really doubles the other before you cross-multiply.

How do ratio 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). Ratios, rates and proportions are part of Numbers and Algebra, and they also appear inside measurement and conversion questions.

How do you solve a proportion?

Write two equal ratios with like units in the same position, then cross-multiply and divide. For 3/2 = x/5, multiply 3 × 5 = 15 and divide by 2 to get x = 7.5.

What is the difference between a ratio and a rate?

A ratio compares two quantities, often of the same kind, such as 5 nurses to 7 assistants. A rate compares quantities with different units, such as 12 liters per 3 minutes. A unit rate is a rate for one unit, such as 4 liters per minute.

How do I split a total using a ratio?

Add the ratio parts to get the total number of parts, then take each group’s share of the total. With a 2:3 ratio and 40 items, there are 5 parts, so the groups are 2/5 × 40 = 16 and 3/5 × 40 = 24.

How do I compare two prices?

Find each unit price by dividing the cost by the number of units, then compare. The lower unit price is the better buy.

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.

Last updated .