Unit Rate Word Problems Review

📝 Practice Worksheets

Unit Rate Assessments Unit Rate Stories Price Per Ounce Unit Rate Problems

🛠️ Related Tools

Unit Rate Explorer Equivalent Rate Explorer

🔑 Key Concepts

A unit rate compares a quantity to exactly 1 unit.
Equivalent rates keep the same relationship while scaling quantities up or down.
Price problems often require multiplying a unit cost or comparing prices per item.
Fractional unit rates may require multiplying or dividing fractions.
When comparing rates, make sure both answers use the same unit before deciding which is greater.

✏️ Worked Examples

Example 1: Unit Cost

Problem: The unit cost for a pound of ground beef is 💲3.98. At that rate, how much would it cost for 2.5 pounds?

The unit cost is already given:

$ 💲3.98 \text{ per pound} $

Multiply by 2.5 pounds:

$ 3.98 \times 2.5 $

Think of $2.5$ as $2+\frac{1}{2}$:

$ 3.98 \times 2 = 7.96 $

$ 3.98 \times 0.5 = 1.99 $

$ 7.96 + 1.99 = 9.95 $

Answer: 💲9.95

Example 2: Least Expensive Brand

Problem: Which brand of juice boxes is the least expensive per box?

Find each unit price by dividing total cost by number of boxes.

Brand A:

$ 2.80 \div 8 = 0.35 $

Brand B:

$ 3.84 \div 12 = 0.32 $

Brand C:

$ 4.62 \div 14 = 0.33 $

Brand D:

$ 5.44 \div 16 = 0.34 $

The least cost per box is $ 💲0.32 $.

Answer: Brand B

Example 3: Miles Per Gallon

Problem: Brandon's car traveled 288 miles on 12 gallons of gas. How far did his car travel per gallon?

“Per gallon” means miles for 1 gallon.

Divide miles by gallons:

$ 288 \div 12 $

$ 12 \times 20 = 240 $

$ 288 - 240 = 48 $

$ 12 \times 4 = 48 $

$ 20 + 4 = 24 $

Answer: 24 miles per gallon

Example 4: Cost Per Square Foot

Problem: A home costs 💲125 per square foot. How much does the house cost if it has 2,880 square feet?

The unit rate is:

$ \$125 \text{ per square foot} $

Multiply by 2,880 square feet:

$ 125 \times 2880 $

Break 125 into $100+25$:

$ 2880 \times 100 = 288000 $

$ 2880 \times 25 = 72000 $

$ 288000 + 72000 = 360000 $

Answer: 💲360,000

Example 5: Fractional Speed

Problem: Jadon was driving at a rate of $ \frac{3}{4} $ of a mile per minute. At that rate, how far will Jadon have driven in 8 minutes?

The rate is:

$ \frac{3}{4} \text{ mile per minute} $

Multiply by 8 minutes:

$ \frac{3}{4} \times 8 $

$ \frac{3}{4} \times \frac{8}{1} = \frac{24}{4} $

$ \frac{24}{4} = 6 $

Answer: 6 miles

Example 6: Difference in Unit Cost

Problem: Three cans of brand A corn cost 💲1.77. Four cans of brand B corn cost 💲2.24. What is the difference in cost per can?

Brand A:

$ 1.77 \div 3 = 0.59 $

Brand B:

$ 2.24 \div 4 = 0.56 $

Find the difference:

$ 0.59 - 0.56 = 0.03 $

Answer: Brand A costs 💲0.03 more per can.

Example 7: Miles Per Minute

Problem: Aaliyah drove 14 miles in 16 minutes. What was Aaliyah's rate of speed per minute?

“Per minute” means miles for 1 minute.

Divide miles by minutes:

$ 14 \div 16 = \frac{14}{16} $

Simplify:

$ \frac{14}{16} = \frac{7}{8} $

As a decimal:

$ \frac{7}{8} = 0.875 $

Answer: $ \frac{7}{8} $, or 0.875, mile per minute

Example 8: Savings with a Pass

Problem: A monthly zoo pass costs 💲30. One-day admission costs 💲7.50. If a person goes to the zoo 5 times in a month, how much money is saved by buying the monthly pass?

Find the cost without the pass:

$ 7.50 \times 5 = 37.50 $

The monthly pass costs:

$ 💲30 $

Find the savings:

$ 37.50 - 30 = 7.50 $

Answer: 💲7.50 is saved by buying the monthly pass.

🧠 Math Vocabulary

Rate: a comparison of two quantities with different units.
Unit Rate: a rate that compares a quantity to exactly 1 unit.
Equivalent Rate: a rate that describes the same relationship using different values.
Fractional Rate: a rate that includes a fraction, such as $ \frac{3}{4} $ mile per minute.
Ratio Table: a table used to organize equivalent ratios or rates.
Proportion: an equation showing that two ratios or rates are equal.
Unit Cost: the cost for 1 item, 1 pound, 1 ounce, or another single unit.
Per: a word meaning “for each one.”

💡 Main Idea

Unit rate problems can appear in many forms, including prices, speed, gas mileage, fractional rates, and savings comparisons. The key is to identify what “per 1 unit” means and then divide, multiply, or compare equivalent rates as needed.

📚 What You Should Already Know

Students should know how to divide decimals, multiply decimals, simplify fractions, multiply fractions, compare rates, and interpret words such as “per,” “each,” and “at that rate.”

🚀 What Comes Next

After reviewing unit rate word problems, students can extend these ideas to proportional relationships, constant of proportionality, percent problems, scale drawings, slope, and linear relationships.

🧩 Embed This Video in Your LMS

Teachers can embed this YouTube video directly into Canvas, Google Classroom, Schoology, or another learning platform. Click below to show the embed code.