A fast car with light trails and a glowing speedometer, illustrating speed as a rate.
Unit 1 · Ratios, Rates & Percents · 6.RP

Lesson 1.2 — Rates & Unit Rates

A rate compares two different kinds of units. A unit rate tells you the amount "per 1."

🎙️ Narration script

Welcome back! Last time we met ratios. Today we're zooming in on a special kind of ratio called a rate.

So what makes a rate special? A rate compares two different kinds of units. Think miles and hours. Or dollars and pounds. Those aren't the same type of thing, and that's exactly the point.

Now, the most useful version of a rate is the unit rate. A unit rate tells you the amount "per one." And that little word, "per," just means "for each one." So "fifty miles per hour" means fifty miles for each one hour. Easy.

Let's work an example. A car travels one hundred fifty miles in three hours. How fast is that, per hour? We divide. One hundred fifty divided by three is fifty. So the car is going fifty miles per hour. We made the second number into a one, and that's our unit rate.

Here's a real-life one you'll actually use. Imagine two bags of chips. A twelve ounce bag costs three dollars, and a sixteen ounce bag costs three dollars and twenty cents. Which is the better buy? Find the price per ounce. The first works out to twenty-five cents per ounce. The second is only twenty cents per ounce. So the bigger bag is the better deal, because its unit price is lower.

To find any unit rate, just divide the first quantity by the second, then label it with the units.

Quick recap. A rate compares different units. A unit rate is the amount per one, and you find it by dividing. And comparing unit rates is how you spot the faster speed or the better buy. Great job!

1 Core idea

A rate is a special ratio that compares two different units — like miles and hours, or dollars and pounds. A unit rate rewrites it as an amount per 1 (50 miles per 1 hour). The unit rate is the most useful form because it lets you compare and predict.

🧩 Think of it like… the little shelf tag at the grocery store that shows the "price per ounce." It shrinks every package — a tiny bag and a giant bag — down to the cost of just one ounce, so you can compare them fairly on the same scale. A unit rate does exactly that: it squeezes any rate down to "per 1."
Where it breaks: the per-ounce tag only tells the whole story when the price grows steadily. If buying in bulk triggers a surprise "third bag half off," the cost per ounce changes partway and a single unit rate no longer describes the whole purchase.

2 Key terms

Rate
A ratio comparing two different units (miles per hour, $ per pound).
Unit rate
A rate with a denominator of 1 (the amount "per 1").
"Per"
Means "for each 1" — "per hour" = "for each 1 hour."
Better buy
The option with the lower unit price (cost per 1 unit).

3 Real-life examples

  • Speed: 150 miles in 3 hours → 150 ÷ 3 = 50 miles per hour.
  • Price: $6 for 4 pounds of apples → 6 ÷ 4 = $1.50 per pound.
  • Heart rate: 120 beats in 2 minutes → 60 beats per minute.
  • Better buy: 12 oz for $3.00 ($0.25/oz) vs 16 oz for $3.20 ($0.20/oz) → the 16 oz is the better buy.
🤔 Pause & think: Runner A covers 100 m in 20 s. Runner B covers 150 m in 25 s. Who is faster — and why can't you decide just by looking at who ran the longer distance?
Reveal the thinking
A's unit rate is 100 ÷ 20 = 5 m/s; B's is 150 ÷ 25 = 6 m/s, so B is faster. Distance alone is misleading because B also took more time — speed is a rate, comparing the two different units (meters and seconds). Only "per 1 second" puts both runners on the same fair scale.

4 Common doubts

What's the difference between a rate and a ratio?

A rate compares different units (miles & hours). A plain ratio usually compares the same kind of thing (apples & oranges).

What does "per" actually mean?

"For each 1." "60 miles per hour" = 60 miles for each 1 hour.

How do I find the unit rate?

Divide the first quantity by the second (so the second becomes 1).

How do I pick the better deal?

Compare unit prices — the lower cost per unit wins.

5 Step-by-step

  1. Write the rate as a fraction with units (150 miles / 3 hours).
  2. Divide the top by the bottom to make the denominator 1 (150 ÷ 3 = 50).
  3. Label with the units: 50 miles per hour.
  4. Use it to predict (5 hours → 5 × 50 = 250 miles) or to compare two options.

📊 See it

hours miles 00 150 2100 3150 +50 mi+50 mi+50 mi

Double number line — each hour adds 50 miles. The unit rate is the step size.

✅ Check yourself
  1. A car travels 180 miles in 3 hours. What is its unit rate (speed)?
    answer 180 ÷ 3 = 60 miles per hour.
  2. Which is the better buy: 8 pens for $4.00, or 5 pens for $2.75?
    answer $4.00 ÷ 8 = $0.50/pen vs $2.75 ÷ 5 = $0.55/pen → the 8-pack is cheaper per pen.
⚡ Quick recap. A rate compares different units; a unit rate is "per 1" (divide to make the second quantity 1); compare unit rates to find the faster speed or the better buy.

Grounded in CA CCSS-M, Grade 6 · 6.RP.2 (Ratios & Proportional Relationships), California Department of Education. Hero image generated with Gemini Nano Banana Pro.