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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.

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.

Answer: 6 miles per hour

Practice problems

1. Which ratio is equivalent to 5:8?

Choices: 10:16 · 8:5 · 15:16 · 5:13

Show solution
  1. Warm-up: First identify exactly what the question is asking: Which ratio is equivalent to 5:8?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. Multiply both parts of 5:8 by 2.
  4. 5 x 2 = 10 and 8 x 2 = 16.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: 10:16

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

Show solution
  1. Warm-up: First identify exactly what the question is asking: A recipe uses 12 cups of flour for 4 batches. How many cups per batch?
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Divide cups by batches.
  4. 12 divided by 4 equals 3.
  5. Check the result by substituting or estimating: the response should match 3 and make sense in the original problem.

Answer: 3

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

Show solution
  1. Warm-up: First identify exactly what the question is asking: A car travels 150 miles in 5 hours. How many miles per hour?
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Divide 150 by 5.
  4. The unit rate is 30 miles per hour.
  5. Check the result by substituting or estimating: the response should match 30 and make sense in the original problem.

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. Core Practice: First identify exactly what the question is asking: Which ratio is equivalent to 12:18 in simplest form?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. Divide both 12 and 18 by 6.
  4. 12:18 becomes 2:3.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: 2:3

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

Show solution
  1. Core Practice: First identify exactly what the question is asking: A pack of 6 notebooks costs 18 dollars. What is the cost per notebook?
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Divide cost by notebooks.
  4. 18 divided by 6 is 3 dollars each.
  5. Check the result by substituting or estimating: the response should match 3 and make sense in the original problem.

Answer: 3

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