How To Calculate Unit Rate in 4 Steps (With Examples)

Let’s say we have a 12-ounce box of pasta, which costs $1.49. The rate is then $1.49 per 12 ounces. If we have a pound of deli meat and the cost is $9.99, our rate would then be $9.99 per pound. Lastly, let’s say we have an 8-pack of 20-ounce bottles of soda and the cost is $5.98. Our rate then is $5.98 per pack.

If we look at this last example a little closer, we’ll see that there is room to break down the rate even further. The example provides the price of an 8-pack, but what if I want to determine the cost of one 20-ounce bottle? The ratio ‘(‘frac{$5.98}{8’text{ bottles}}’) provides that information. This quick calculation tells me that each 20-ounce bottle costs approximately $0.75.

How to Find Unit Rate? In a unit rate, the denominator is always 1. So, to find unit rate, divide the denominator with the numerator in a way that the denominator becomes 1. For example, if 50km is covered in 5.5 hours, the unit rate will be 50km/5.5 hours = 9.09 km/hour.

Unit Rates | Solving Unit Rate Problems

What is a unit rate?

The term “unit rate” refers to the amount of something at a rate of one. This is the smallest comparison between two measurements in integers, or a ratio with a denominator of one. Examples of common unit rates include miles per hour as a speed, miles per gallon for energy usage and megabits per second for internet speeds. Understanding unit rates can help you compare the qualities of different items. For example, if one car can drive up to 60 miles per hour and another can drive 100 miles per hour, you may choose the faster one.

Manufacturers can also use unit rate costs to determine how to price their products. For example, a manufacturer of toys knows it costs them $1.00 to make a toy, and they want to mark it up by 50% to make a profit. Using the unit price, they can determine that the retail price is best at $1.50.

How to calculate unit rate

You can use unit rate to learn more about how much something costs to produce or how long it takes to make. You can also use it to learn more about how quickly teams can process information or manufacturing. Here are the steps you can follow to calculate unit rate:

1. Gather information

The first step to calculating the unit rate for something is gathering information. To determine the unit rate, you can gather information about two different measurements. For example, if you work at a theme park, you may want to calculate the unit rate for how many come through the gates per second, on average. You know that the gate processing hours for the park are between eight in the morning and noon, so you can gather information about how many people come through the gates each day. It may look like this:

Monday = 6,202 guests

Tuesday = 9,248 guests

Wednesday = 9,975 guests

Thursday = 5,895 guests

Friday = 9,744 guests

Saturday = 14,041 guests

Sunday = 11,118 guests

Based on these numbers, you can determine the average amount of visitors who come through the gates each morning is 9,460. You can determine this by adding the number of visitors per day and dividing the sum by the number of days, like this:

6,202 + 9,248 + 9,975 + 5,895 + 9,744 + 14,041 + 11,118 = 66,223

66,223 / 7 = 9,460

2. Write the problem

The next step to help you determine the unit rate is to write the problem out so its easier to understand. When trying to find the unit rate, you often divide the first or top number by the second or bottom number to get to one. This is because any number divided by itself equals one, except zero. So, for example, if you write the amusement park example, it may look like this:

9,460 guests / 4 hours each morning

If you want to specify guests per minute or second, you can alter the equation by multiplying the time by the conversion. This may help to better understand how many guests the park processes on a smaller level. For example, there are 60 minutes in an hour, so to find the average number of guests per minute, you may multiply four by 60. It may look like this:

9,460 guests / 240 minutes each morning

9,460 guests / 14,400 seconds each morning

3. Divide to get one

The final step to finding the unit rate is dividing the numbers. To find the unit rate, divide the top number, or first number, by the bottom or second. For example, in the amusement park example, you can complete the division problem to find the unit rate of guests per hour:

9,460 guests / 4 hours each morning = 2,365 guests per hour

You can further convert to find the rate of guests per minute or second. You can use this to understand that clerks manage 39 guests per minute, or that a guest comes through the gates about every two seconds. It may look like this:

9,460 guests / 240 minutes each morning = 39 guests per minute

9,460 guests / 14,400 seconds each morning = 0.66 guests per second

4. Consider additional information

To make unit rates useful, you may consider additional information. For example, an amusement park manager may want to learn more about how fast each gate attendant can attend to a guest on average. They can use the unit rate of 39 guests per minute, plus the information that the park usually has about five attendants working to understand how quickly attendants can process guests. Heres the equation they can use:

39 guests per minute / 5 attendants = 7.8 guests per minute per attendant

The manager may determine that an attendant can process about seven or eight guests at a time. If the manager knows a weekend event at the park may attract full capacity, or 20,000 guests, the manager may use this information to determine how many attendants to staff that night. They can do this by dividing the total number of guests by the amount of time the gates are open for the event, then by the average rate of guests the attendants can manage. It may look like this:

20,000 expected guests / 120 minutes to process them = 167 guests per minute for the event

167 guests per minute / 7.8 guests per attendant per minute = 21 attendants to maintain the guest processing rate

FAQ

What is the formula for unit rate?

A unit rate is a ratio between two different units with a denominator of 1. To calculate the unit rate, divide the numerator by the denominator. The resulting decimal number is the unit rate.

How do you find rate and unit rate?

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

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