# The Definition of Unit RateSupport Page

Welcome to the Definition of Unit Rate support page.

We also have links to our unit rates worksheets.

## The Definition of Unit Rate Support Page

### The Definition of Unit Rate

• A rate compares two quantities with different units. It can be written as a fraction or a ratio.
• A Unit rate is the rate of one quantity compared to 1 unit of another quantity.
• Usually two different measures are compared, e.g. miles in an hour, number of words in a minute, number of objects in a pack, etc.
• Unit rates can also be thought of as a ratio with a denominator (or consequent) of 1. The unit rate is the value of the numerator.
• Unit rates are useful because they can be used to compare different sets of rates and decide which is the best/most efficient/fastest/slowest etc.

Here is a quick table showing unit rates with their related fractions and ratios.

 Unit Rate As a Fraction As a Ratio 5 miles in a minute 5 miles / 1 minute 5 miles : 1 minute 8 pens in a packet 8 pens / 1 packet 8 pens : 1 packet 15 pages in a day 15 pages / 1 day 15 pages : 1 day 30 questions in an hour 30 questions / 1 hour 30 questions : 1 hour 3 plants in 1 yard 3 plants / 1 yard 3 plants : 1 yard

### How to Determine Unit Rate?

Here is the process for finding the unit rate:

• Take the rate and divide the numerator by the denominator to find the unit rate.

You have now found the unit rate of your number.

Example: I read 12 books in 5 months = A rate of 12 books / 5 months = A unit rate of 2.4 books per month

### What is the difference between unit rate and unit price (or unit cost)?

Unit Price is the amount of money it costs for just one item, one litre, one kilogram, one pound, etc.

Unit Price is very similar to unit rate.

To find the unit price of an item, simply divide the amount of money by the number of items (or the number of litres, kilograms, etc.).

You have now found the unit price of your item.

Example: I buy 8 cartons of juice for \$12 = A rate of \$12 / 8 cartons = a unit price of \$1.50 per carton

### Examples of Finding Unit Rates and Unit Prices

These examples will help you understand how to find unit rates (and unit prices).

Example 1) Captain drives 250 miles in 4 hours. Find his unit rate in miles per hour.

• The rate is 250 miles / 4 hours.
• Divide the numerator by the denominator.
• To find the unit rate we need to divide 250 by 4.
• 250 ÷ 4 = 62.5
• The unit rate is 62.5 miles in an hour (it can also be written 62.5 miles per hour, 62.5 mph or 62.5 miles/hour).

Example 2) Tyger reads 100 pages of his book in 4 hours. What is the unit rate?

• The rate is 100 pages / 4 hours.
• Divide the numerator by the denominator.
• To find the unit rate, we need to divide 100 by 4.
• 100 ÷ 4 = 25
• The unit rate is 25 pagees in an hour (or 25 pages per hour).

Example 3) Sally spends 385 minutes doing her homework in a week. What is her unit rate in minutes per day?

• The rate is 385 minutes / 7 days.
• To find the unit rate we need to divide 385 by 7.
• 385 ÷ 7 = 55
• The unit rate is 55 minutes per day. She spends an average of 55 minutes per day doing homework.

Example 4) Frazer bakes 20 trays of cookies for a party. There are a total of 240 cookies. What is the unit rate of cookies per tray?

• The rate is 240 cookies / 20 trays.
• To find the unit rate we need to divide 240 by 20.
• 240 ÷ 20 = 12
• The unit rate is 12 cookies per tray.

Example 4) Quadra runs 5 miles in 32 minutes. What her unit rate in minutes per mile?

• The rate is 32 minutes / 5 miles.
• To find the unit rate we need to divide 32 by 5.
• 32 ÷ 5 = 6.4
• Her unit rate is 6.4 minutes per mile (or 6 minutes 24 seconds to run a mile)

Example 5) Captain buys 8 packs of fries for \$14. What is the unit price?

• The rate is \$14 / 8 packs.
• To find the unit price we need to divide 14 by 8.
• 14 ÷ 8 = 1.75
• The unit price is \$1.75 per pack of fries.

Example 6) It costs \$3100 to produce 40 remote control trucks. What is the unit cost?

• The rate is \$3100 / 40 trucks.
• To find the unit cost we need to divide 3100 by 40.
• 3100 ÷ 40 = 77.5
• The unit cost is \$77.50 per truck.

Example 7) I buy 3 packs of pens, with 4 pens in each pack for \$22. What is the unit price per pen?

• There are 3 x 4 = 12 pens in the 3 packs.
• The rate is \$22 / 12 pens.
• To find the unit price we need to divide 22 by 12.
• 22 ÷ 12 = 1.8333
• The unit price is \$1.83 per pen (to the nearest cent).

### Comparing Unit Rates (and Unit Prices)

Many questions involving rates will ask you to compare two different rates and answer questions about them.

The best way to compare two rates is to convert both rates into unit rates so that they can be compared easily.

Example 1) Frazer drives 310 miles in 6 hours. Captain drives 250 miles in 5 hours. Who drove fastest?

Frazer unit rate is 310 ÷ 6 = 51.67 miles in a hour (to 2dp)

Captain unit rate is 250 ÷ 5 = 50 miles in a hour.

Frazer drove the fastest.

Example 2) Sally buys 5 packs of cookies for \$8. Flame buys 3 packs of the same cookies for \$5. Who got the best deal?

Sally's unit price is \$8 ÷ 5 = \$1.60 per pack

Flame's unit price is \$5 ÷ 3 = \$1.67 (rounded to 2dp) per pack

Sally got the best deal.

Example 3) Quadra reads 400 pages of a book in 7 hours. Tyger reads 190 pages of the same book in 4 hours. Who has the faster reading speed?

Quadra's unit rate is 400 ÷ 7 = 57.1 pages per hour (to 1dp)

Tyger's unit rate is 190 ÷ 4 = 47.5 pages per hour (to 1dp)

Example 4) Frazer and Sally go fishing. Frazer catches 16 fish in 3 hours. Sally catches 23 fish in 5 hours. Who had the best hourly rate at catching fish?

Frazer's unit rate is 16 ÷ 3 = 5.3 fish per hour (to 1dp)

Sally's unit rate is 23 ÷ 5 = 4.6 fish per hour (to 1dp)

Frazer has the best hourly rate at catching fish.

Example 5) Gardener George plants 59 hedging plants evenly over a length of 18 yards. Gardener Georgina plants 75 hedging plants evenly over a length of 22 yards. Who plants their hedging plants furthest apart?

Gardener George's unit rate is 59 ÷ 18 = 3.3 yards per plant (to 1dp)

Gardener Georgina's unit rate is 75 ÷ 22 = 3.4 yards per plant (to 1dp)

Gardener Georgina plants her plants furthest apart.

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