Unit rates

What is a unit rate?

A unit rate tells you how much of one quantity there is per single unit of another.

• 60 km per 1 hour
• $1.25 per 1 muffin
• 12 pages per 1 minute

To find a unit rate, divide the first quantity by the second.

Finding unit rates

Unit price and comparison shopping

A unit price is a unit rate for cost. It shows the better buy.

Example: Which is the better buy?

The 750 g package is cheaper per gram. Store shelf labels often show the unit price (per 100 g or per kg) to help you compare.

(The better buy isn’t always the right buy: if food will spoil before you eat it, a bigger package wastes money.)

Using unit rates to scale

Once you have a unit rate, multiply to find any amount.

Example: A car uses 7 L of gas every 100 km. How much for 350 km?

• Unit rate: 7 ÷ 100 = 0.07 L/km
• 0.07 × 350 = 24.5 L

Example: Earning $16.50/h, how much for 7.5 hours?

16.50 × 7.5 = $123.75

Flipping a rate

Rates can be read both ways:

• 4 apples per $1 → $0.25 per apple
• 75 km/h → 1/75 h per km (0.8 minutes per km)

Choose the version that answers the question.

Worked examples

Example 1: 8 L of juice for $10. Find the unit price.

10 ÷ 8 = $1.25/L.

Example 2: Runner A: 400 m in 80 s. Runner B: 300 m in 57 s. Who is faster?

A: 5 m/s. B: 300 ÷ 57 ≈ 5.26 m/s. B is faster.

Example 3: 6 pack of yogurt for $4.50 or 8 pack for $5.60?

$0.75 vs $0.70 each → 8 pack.

Common mistakes

• Dividing the wrong way, giving grams per dollar instead of dollars per gram.
• Comparing unit prices with different units (per g vs per kg).
• Rounding too much so close prices look equal.

Try it yourself

1. $7.50 for 5 L. Unit price?
2. 225 km in 2.5 h. Speed?
3. Which is the better buy: 12 eggs for $4.20 or 18 eggs for $5.94?
4. At $3.60/kg, how much do 2.5 kg cost?

Answers: 1) $1.50/L 2) 90 km/h 3) 18 eggs ($0.33 vs $0.35 each) 4) $9.00

Quick recap

• A unit rate has 1 as the second quantity; find it by dividing.
• Unit price helps find the better buy.
• Multiply a unit rate to scale up.