Comparing Prices - Unit Rates

🔑 Key Concepts

  • A unit rate compares two quantities where the second quantity is 1 unit.
  • You can find a unit rate by dividing the total amount by the number of units.
  • Unit rates help compare prices and determine the best buy.
  • Some unit rates are decimals, and some are fractions.
  • Fractional unit rates are still valid unit rates because they describe an amount for exactly one unit.

✏️ Examples of Unit Rates

Example 1 — Price Per Ounce

A 90-ounce bag of rice costs 2.79 dollars.

To find the unit price, divide:

\[ 2.79 \div 90 = 0.031 \]

The unit rate is 0.031 dollars per ounce.

Example 2 — Cost Per Pound

A 6-pound pack of ground beef costs 13.44 dollars.

Divide to find the cost for 1 pound:

\[ 13.44 \div 6 = 2.24 \]

The unit rate is 2.24 dollars per pound.

Example 3 — Miles Per Hour

A car travels 180 miles in 3 hours.

Divide the distance by the time:

\[ 180 \div 3 = 60 \]

The unit rate is 60 miles per hour.

Example 4 — Fractional Cups Per Serving

A recipe uses \( \frac{3}{4} \) cup of sugar for 2 batches.

Divide to find the amount for 1 batch:

\[ \frac{3}{4} \div 2 = \frac{3}{8} \]

The unit rate is \( \frac{3}{8} \) cup per batch.

Example 5 — Fractional Miles Per Hour

A hiker walks \( \frac{5}{2} \) miles in 1 hour.

Since the time is already 1 hour, the unit rate is:

\[ \frac{5}{2} \text{ miles per hour} \]

This is also \( 2.5 \) miles per hour.

Example 6 — Dollars Per Item as a Fraction

Three notebooks cost 4.50 dollars.

Divide to find the cost of 1 notebook:

\[ 4.50 \div 3 = 1.50 \]

The unit rate is 1.50 dollars per notebook.

As a fraction, this is \( \frac{3}{2} \) dollars per notebook.

🧠 Math Vocabulary

  • Rate: A comparison of two quantities with different units.
  • Unit Rate: A rate where one of the quantities is 1.
  • Unit Price: The cost for one item or one unit of measure.
  • Best Buy: The choice with the lower unit price when comparing similar products.
  • Fractional Unit Rate: A unit rate written as a fraction.

💡 Main Idea

Unit rates help describe how much of one quantity happens for every 1 unit of another quantity. In this lesson, students find unit prices by dividing cost by the number of ounces, pounds, or items. This makes it easier to compare choices and determine the best value. Students also see that unit rates are not always whole numbers. Sometimes they are decimals, and sometimes they can be written as fractions.

📚 What You Should Already Know

Before this lesson, students should know how to divide whole numbers and decimals and understand that a rate compares two quantities with different units. It also helps to be comfortable reading word problems and deciding which quantity should be divided by the other.

🚀 What Comes Next

After learning to find unit rates, students can apply this skill to proportional relationships, constant of proportionality, tables, graphs, and real-world comparison problems. Fractional unit rates also lead naturally into more advanced ratio reasoning.

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