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Ratios and Unit Rates

A free Pre-Algebra lesson from the “Number Foundations” unit, with a worked example and practice problems including step-by-step solutions.

A ratio compares two quantities. Equivalent ratios are made by multiplying or dividing both parts by the same nonzero number. A unit rate compares a quantity to one unit, like miles per hour or dollars per item. In Number Foundations, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.

What you'll learn

Why it matters: Miles per gallon, dollars per ounce, and players per team are all unit rates. Comparing two grocery deals is exactly comparing two unit prices.

Worked example

Problem. A runner travels 18 miles in 3 hours. What is the unit rate?

  1. A unit rate compares distance to 1 hour.
  2. Divide 18 miles by 3 hours.
  3. 18 divided by 3 equals 6, so the rate is 6 miles per hour.
  4. Connect the calculation back to Ratios and Unit Rates so the method, not just the arithmetic, is clear.

Answer: 6 miles per hour

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.

Practice problems

1. Which ratio is equivalent to 5:8?

Choices: 10:16 · 8:5 · 15:16 · 5:13

Show solution
  1. Multiply both parts of 5:8 by 2.
  2. 5 x 2 = 10 and 8 x 2 = 16.

Answer: 10:16

2. A recipe uses 12 cups of flour for 4 batches. How many cups per batch?

Show solution
  1. Divide cups by batches.
  2. 12 divided by 4 equals 3.

Answer: 3

3. A car travels 150 miles in 5 hours. How many miles per hour?

Show solution
  1. Divide 150 by 5.
  2. The unit rate is 30 miles per hour.

Answer: 30

4. Which ratio is equivalent to 12:18 in simplest form?

Choices: 2:3 · 3:2 · 6:9 · 1:6

Show solution
  1. Divide both 12 and 18 by 6.
  2. 12:18 becomes 2:3.

Answer: 2:3

5. A pack of 6 notebooks costs 18 dollars. What is the cost per notebook?

Show solution
  1. Divide cost by notebooks.
  2. 18 divided by 6 is 3 dollars each.

Answer: 3

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