Unit Rate Formula

A rate is a ratio that compares two different quantities of different units, such as miles per hour or dollars per ounce. The word per gives a clue that we are dealing with a rate. The word per can be further replaced by the symbol "/" in problems. A unit rate is about comparing a quantity to its unit of measure and can be calculated using the unit rate formula. Let us explore more about it.

What is Unit Rate Formula?

A unit rate that has the denominator as 1, compares a quantity to the other, which is its unit of measure. If a person runs three miles in 30 minutes, he runs at a rate of one mile every 10 minutes. The rate of miles per minute gives the distance traveled per unit of time. Unit rate is always expressed as the quantity of 1.

Let's look into some real-time applications of unit rate.

• Time rate: Distance per unit time, average speed (miles/ hour), and interest (simple or compound) rates
• Cost Price: cost/pound, quantity per cost (20 oz of juice/ 4 dollars), or for comparing prices.
• Other examples can be the literacy rate, the population, and other rates which provide specific data

The unit rate formula to calculate the rate for any two quantities say a and b can be given as,

Unit Rate = Ratio between two different quantities with different units

= a:b

= a/b

Unit Rate Definition

Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity. For example, in one minute there are 60 seconds. Therefore, a unit rate can express be like 60 seconds per minute. Here, per minute refers to one minute.

Unit Rate Formula

The unit rate formula to calculate the rate for any two quantities say a and b can be given as,

Unit Rate = Ratio between two different quantities with different units

= a:b

= a/b

Examples Using Unit Rate Formula

Example 1: A farmer harvests 15 acres per day and gets 150 bushels of wheat per acre. Calculate the number of bushels of wheat he needs to harvest in a day using the unit rate formula.

Solution:

Given:

Land harvested = 15 acres

Let a = quantity harvested and b = number of days

To find: Quantity per day

Bushels of wheat harvested per acre = 15 × 150

= 2250 Bushels

Using the unit rate formula: unit rate= a/b,

Bushels of wheat harvested per day = 2250 / 1

= 2250

Therefore, the wheat harvested per day = 2250 Bushels

Example 2: If a shop offers you 15 chocolates for $7.5, what does the unit cost be?

Solution:

Given:

Price of 15 chocolates = $7.5

To find: cost per chocolate

Let a = cost, b = number of chocolates

Using the unit rate formula: unit rate= a/b,

Per unit cost of chocolates = Cost of chocolates/ Number of chocolates

= $ 7.5/15

Therefore, the per-unit cost of chocolates = $0.5

Example 3: If a fruit shop offers a dozen blueberries for $24, calculate the unit rate.

Solution:

Given:

Price of 12 blueberries = $24

Let a = cost and b = dozen

To find: cost per dozen

Using the unit rate formula: unit rate= a/b,

Per unit cost of blueberries = Price of blueberries/Number of blueberries

= 24/12 = $2

Therefore, the per-unit cost of blueberries = $2