A unit rate is a ratio that compares a quantity to exactly one unit of another quantity. For example, 60 km per 1 hour (60 km/h) or $3.50 per 1 pound.

How do I find the unit rate?

Divide the first quantity by the second quantity. For example, if 5 apples cost $10, the unit rate is $10 / 5 = $2 per apple.

Why are unit rates useful?

Unit rates make comparison easy. When two items have different package sizes or quantities, converting to a per-unit cost lets you see which is the better deal instantly.

Unit Rate — How to Find and Compare Unit Rates

Grade: 6-7 | Topic: Arithmetic

What You Will Learn

After this lesson you will know what a unit rate is, how to calculate one by dividing, and how to use unit rates to compare prices, speeds, and other real-world quantities. You will also be able to solve word problems that ask you to find the "better deal" or predict quantities using a known rate.

Theory

What is a rate?

A rate compares two quantities that have different units. Unlike a ratio (which compares same-type quantities), a rate involves two different measurements:

150 kilometers in 3 hours (distance and time)
$12 for 4 pounds (money and weight)
240 words in 4 minutes (words and time)

What is a unit rate?

A unit rate is a rate where the second quantity is exactly one unit. It answers the question: "How much per one?"

$\text{Unit rate} = \frac{\text{total quantity}}{\text{number of units}}$

Using the examples above:

$\frac{150 \text{ km}}{3 \text{ h}} = 50 \text{ km/h} \qquad \frac{\$12}{4 \text{ lb}} = \$3\text{/lb} \qquad \frac{240 \text{ words}}{4 \text{ min}} = 60 \text{ words/min}$

The word "per" (or the symbol "/") signals a unit rate: km per hour, dollars per pound, words per minute.

Using unit rates to compare

When you need to find the better deal between two products with different sizes or prices, convert each to its unit rate and compare:

Product	Total price	Size	Unit rate
Brand A	$4.80	6 oz	$\frac{4.80}{6} = \$ 0.80$ per oz
Brand B	$5.25	7 oz	$\frac{5.25}{7} = \$ 0.75$ per oz

Brand B has the lower unit price, so it is the better deal.

Using unit rates to predict

Once you know the unit rate, you can scale up to find any quantity:

$\text{Total} = \text{unit rate} \times \text{number of units}$

If a car travels 55 km/h, in 4 hours it covers:

$55 \times 4 = 220 \text{ km}$

Worked Examples

Example 1: Finding a unit price (easy)

Problem: A pack of 8 markers costs $6.40. What is the price per marker?

Step 1: Divide the total cost by the number of markers.

$\text{Unit price} = \frac{\$6.40}{8} = \$0.80$

Answer: Each marker costs $0.80.

Example 2: Finding a speed (easy)

Problem: A runner covers 12 km in 1.5 hours. What is the runner's speed in km/h?

Step 1: Divide the distance by the time.

$\text{Speed} = \frac{12 \text{ km}}{1.5 \text{ h}} = 8 \text{ km/h}$

Answer: The runner's speed is 8 km/h.

Example 3: Comparing unit prices (medium)

Problem: Store A sells 3 kg of rice for $5.10. Store B sells 5 kg of the same rice for $8.00. Which store offers the better deal?

Step 1: Find the unit price at Store A.

$\frac{\$5.10}{3 \text{ kg}} = \$1.70 \text{ per kg}$

Step 2: Find the unit price at Store B.

$\frac{\$8.00}{5 \text{ kg}} = \$1.60 \text{ per kg}$

Step 3: Compare.

$\$1.60 < \$1.70$

Answer: Store B is the better deal at $1.60 per kg.

Example 4: Using a unit rate to predict (medium)

Problem: A factory produces 360 toys in 8 hours. At the same rate, how many toys will it produce in 14 hours?

Step 1: Find the unit rate (toys per hour).

$\frac{360}{8} = 45 \text{ toys/hour}$

Step 2: Multiply by the target time.

$45 \times 14 = 630$

Answer: The factory will produce 630 toys in 14 hours.

Example 5: Unit rate with mixed units (challenging)

Problem: A car uses 38 liters of fuel to travel 456 km. A truck uses 65 liters to travel 520 km. Which vehicle is more fuel-efficient?

Step 1: Find the car's unit rate (km per liter).

$\frac{456 \text{ km}}{38 \text{ L}} = 12 \text{ km/L}$

Step 2: Find the truck's unit rate.

$\frac{520 \text{ km}}{65 \text{ L}} = 8 \text{ km/L}$

Step 3: Compare. The higher the km/L, the more efficient.

$12 \text{ km/L} > 8 \text{ km/L}$

Answer: The car is more fuel-efficient. It travels 12 km per liter compared to the truck's 8 km per liter.

Common Mistakes

Mistake 1: Dividing in the wrong order

❌ "8 markers cost $6.40, so the unit price is $\frac{8}{6.40} = 1.25$ markers per dollar."

✅ $\frac{\$ 6.40}8 = $0.80$ per marker.

Why this matters: The unit rate depends on which quantity you want "per one" of. For a unit price, divide the cost by the number of items — not the other way around. Always ask: "per one what?"

Mistake 2: Comparing rates with different units

❌ Comparing 60 km/h with 15 m/s directly and concluding 60 is faster.

✅ Convert to the same unit first: $15 \text{ m/s} = 15 \times 3.6 = 54 \text{ km/h}$ . Now compare: 60 km/h > 54 km/h.

Why this matters: Unit rates can only be compared when the units match. Always convert to the same unit before drawing conclusions.

Mistake 3: Rounding too early

❌ $\frac{\$ 5.10}3 \approx $1.67$ (rounded to 2 decimal places too soon)

✅ $\frac{\$ 5.10}3 = $1.70$ exactly.

Why this matters: Premature rounding, especially in comparison problems, can flip the result. Calculate the exact value first and round only at the final answer if needed.

Practice Problems

Try these on your own before checking the answers:

A 6-pack of juice costs $7.20. What is the price per bottle?
A cyclist rides 45 km in 2.5 hours. What is the cyclist's speed in km/h?
Brand X: 400 g for $3.20. Brand Y: 750 g for $5.25. Which is the better buy?
A printer can print 120 pages in 5 minutes. How many pages can it print in 12 minutes?
Water flows from a tap at 15 liters per minute. How long does it take to fill a 225-liter tank?

Click to see answers

$\frac{7.20}{6} = \$ 1.20$ per bottle.
$\frac{45}{2.5} = 18$ km/h.
Brand X: $\frac{3.20}{400} = \$ 0.008 $per gram. Brand Y:$ \frac5.25750 = $0.007$ per gram. Brand Y is cheaper per gram.
Unit rate: $\frac{120}{5} = 24$ pages/min. In 12 min: $24 \times 12 = 288$ pages.
$\frac{225}{15} = 15$ minutes.

Summary

A unit rate compares a quantity to exactly one unit of another quantity (e.g., $/item, km/h).
To find a unit rate, divide the total quantity by the number of units.
To compare two options, convert each to a unit rate with the same units, then see which is higher or lower depending on the context.
To predict totals, multiply the unit rate by the desired number of units.
Always check that you are dividing in the correct order — ask yourself "per one what?"

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What You Will Learn​

Theory​

What is a rate?​

What is a unit rate?​

Using unit rates to compare​

Using unit rates to predict​

Worked Examples​

Example 1: Finding a unit price (easy)​

Example 2: Finding a speed (easy)​

Example 3: Comparing unit prices (medium)​

Example 4: Using a unit rate to predict (medium)​

Example 5: Unit rate with mixed units (challenging)​

Common Mistakes​

Practice Problems​

Summary​

Related Topics​