Understand the Concept of a Unit Rate

Lesson 1 of 1: Unit Rates

In this lesson:

• Define a unit rate and explain "per one"
• Compute a unit rate from any ratio
• Use unit rates to compare and scale

Learning Objectives for Today's Lesson

By the end of this lesson, you should be able to:

1. Define a unit rate as associated with a ratio () and explain "per one"
2. Use rate language — "per," "for each," "each," "every" — to describe a unit rate
3. Compute a unit rate from a given ratio by dividing
4. Interpret unit rates that are fractions less than 1
5. Apply unit rates to compare prices and scale quantities

Connect to Ratios: A New Question Arises

New question: How much flour for every 1 cup of sugar?

What Is a Unit Rate?

A unit rate is from ratio — how much of quantity 1 per 1 of quantity 2. Find it by dividing .

• Ratio → cup flour per cup of sugar
• Ratio → dollars per hamburger

Worked Example: Flour and Sugar

Ratio: 3 cups flour to 4 cups sugar →

Unit rate: cup of flour per cup of sugar

Worked Example: Hamburgers and Dollars

Ratio: (dollars to hamburgers)

Unit rate: per hamburger

Contrast — same situation, two forms:

• "$75 for 15 hamburgers" → ratio language (both quantities given)
• "$5 per hamburger" → rate language (amount per 1 unit) ✓

Rate Language Signals a Unit Rate

Always label: "$5 per hamburger" not just "5"

Quick Check: Identify the Language Type

Is each statement ratio language or rate language?

1. "For every 3 cups of flour, there are 4 cups of sugar"
2. "3/4 cup of flour per cup of sugar"
3. "For every $75 spent, you get 15 hamburgers"
4. "$5 per hamburger"

Three-Step Method for Any Unit Rate

Step 1: Identify the ratio — name both quantities in order

Step 2: Divide: compute

Step 3: State: "[result] [first unit] per [second unit]"

Scenario A: Speed in Miles Per Hour

A car travels 150 miles in 3 hours.

Result is a whole number.

Scenario B: Price Per Granola Bar

8 granola bars cost $6.

Result is a decimal.

Scenario C: Flour per Cup of Sugar

Scenario D: Direction Determines the Unit Rate

Same recipe, different question:

Q1: Flour per cup of sugar? → ratio → cup flour per cup sugar

Q2: Sugar per cup of flour? → ratio → cups sugar per cup flour

Rule: The quantity after "per" is always the denominator.

Your Turn: Find Two Unit Rates

Find the unit rate. Include the "per [unit]" label.

1. $60 for 12 items → unit rate = ___

2. 5 miles in 2 hours → unit rate = ___

Express problem 2 as a fraction or decimal.

Your Turn: Unit Rate Answers

1. $60 for 12 items:

2. 5 miles in 2 hours:

Did you include the "per [unit]" label in both answers?

Applying Unit Rates: Comparing Prices

Store A: 5 oranges for $2.00 → $2.00 ÷ 5 = $0.40 per orange

Store B: 3 oranges for $1.30 → $1.30 ÷ 3 ≈ $0.43 per orange

Store A is the better deal — lower cost per orange.

Scaling with a Unit Rate

Unit rate = cup flour per cup of sugar → multiply to find any amount

Your Turn: Compare and Scale

Problem 1: Brand X: 6 pens for $4.20. Brand Y: 4 pens for $3.00.
Which is the better deal? Find the unit rate for each.

Problem 2: Speed = 50 miles per hour.
How far in 3 hours? How far in hour?

Pause and solve both.

Key Ideas: Unit Rates Summary

✓ Unit rate from ratio — means " [first unit] per 1 [second unit]"

✓ Compute by dividing — result may be whole, decimal, or fraction

✓ Rate language: per · for each · each · every — always label "per [unit]"

Quantity after "per" = denominator — direction determines which unit rate

Unit rates can be less than 1 — cup per cup is completely valid

Simplifying to = ratio; dividing = unit rate

Next Lesson: Ratio and Rate Reasoning

In 6.RP.A.3 you will:

• Solve rate problems using unit rates in real-world contexts
• Build tables of equivalent ratios with the unit rate as multiplier
• Apply unit rate reasoning to percent problems

The unit rate is the engine behind all of 6.RP.A.3.