# How to Find Unit Rate Formula – Definition, Examples, FAQs

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## What Is the Unit Rate Formula?

A unit rate is a rate that compares the first quantity to one unit of the second quantity, expressed as a ratio. A unit rate tells us how many units of the first quantity relate to just one unit of the second quantity.

Put simply, a unit rate is when the first quantity is described for one unit of the second quantity. Typically, it is expressed as a fraction or ratio.

How much something costs per unit in relation to another quantity is calculated using the unit rate formula.

When calculating a rate, the denominator represents the independent variable, while the numerator represents the dependent variable. Unit rate is a comparison of quantities with different units, often linking a dependent variable (numerator) to an independent variable (denominator), helping understand their relationship.

It’s a powerful tool for analyzing real-world scenarios involving different measurements. Time usually acts as the independent variable, while money often serves as the dependent variable in rate calculations. For example, miles per hour, dollars per gallon, etc.

## Unit Rate: Definition

Unit rate can be defined as the ratio between two measurements with the second term fixed at 1 unit.

It helps us understand how one quantity changes concerning another quantity when the second quantity is one unit. The unit rate allows for direct comparisons and is expressed in the form of “quantity per one unit.”

## Unit Rate Formula

The formula for finding a unit rate for any two quantities say a and b can be given as,:

Unit Rate = Quantity of Interest ÷ Number of Units $= \frac{a}{b}$

where

Quantity of Interest or a: The quantity or amount you want to find the rate for.

Number of Units or b: The number of units or items associated with the quantity of interest.

Example: Consider the scenario where you need to figure out the unit rate for the daily sales of apples. If 200 apples are sold in 5 days, the unit rate would be:

Unit Rate = 200 apples ÷ 5 days

Unit Rate = 40 apples per day

So, the unit rate in this case is 40 apples per day. It tells you that on average, 40 apples are sold each day.

Remember that the unit rate should have consistent units in both the numerator and the denominator. In the example above, it’s “apples per day.” This ensures that the rate is accurately represented and can be easily compared with other rates.

## How to Calculate the Unit Rate Using the Unit Rate Formula

To calculate the unit rate, divide the measured quantity by the chosen unit. In a unit rate, the second quantity is consistently 1. Determine the unit rate by dividing the top number by the bottom number, making the bottom number equal to 1.

Finding unit rates using the formula is a straightforward process. Let’s understand the steps with an example.

Example 1: Mia purchased 10 pounds of apples for $20. What is the unit rate of the cost per pound of apples? Step 1: Identify the quantities. Quantity of the second item (dependent variable): Cost of apples$= \$20$

Quantity of the first item (independent variable): Weight of apples = 10 pounds

Step 2: Apply the formula and perform the calculation.

Unit rate $= \frac{Quantity\; of\; second\; item}{Quantity\; of \;first\; item}$

Unit rate (cost per pound) $= \frac{\$20}{10}$pounds Unit rate (cost per pound)$= \$2$ per pound

Step 3: Interpret the result.

The unit rate of the cost per pound of apples is $\$2$. This means that each pound of apples costs$2.

Example 2: How to solve unit rates with fractions

Lets walk through an example to understand this.

A car travels $\frac{2}{3}$ of a mile in $\frac{1}{4}$ of an hour. Calculate the unit rate of miles per hour.

Given: Distance traveled $= \frac{2}{3}$ mile, Time taken $= \frac{1}{4}$hour

To find: Miles per hour

Unit rate $= \frac{Distance\; traveled}{Time \;taken} = \frac{\frac{2}{3} mile}{\frac{1}{4} hour}$

To divide fractions, we invert the divisor $(\frac{1}{4})$ and multiply.

Unit rate $= (\frac{2}{3} mile) \times (\frac{4}{1} hour) = \frac{8}{3}$ mile per hour

Therefore, the unit rate is $\frac{8}{3}$ miles per hour.

## Facts about Unit Rate Formula

• Unit rate is frequently used in everyday circumstances where you need to compare different numbers, such as when calculating speed (in miles per hour), cost per unit (in dollars per item), efficiency (in things produced per hour), and many more instances.
• Quantities can be scaled up or down using the unit rate. For instance, if you are aware of the unit price of 2 apples per $1, you can simply determine that 10 apples would cost$5.
• Depending on the situation and preferred format, unit rates can be expressed as either fractions or decimals. Decimals may be more useful and practical in certain circumstances.
• The slope of a line on a graph can be used to depict the unit rate when comparing two quantities graphically. Higher unit rates are associated with steeper lines, and vice versa.
• When two quantities are inversely proportional, their unit rates will vary inversely. For instance, if the number of workers on a project decreases, the unit rate of work completed per worker will increase.

## Conclusion

In this article, we learned about the unit rate formula. Understanding the unit rate formula is essential for various mathematical applications and real-world scenarios, as it simplifies comparisons and enables meaningful interpretations of data involving different quantities. Now, let’s solve some examples and practice problems to understand the concept better.

## Solved Examples on Unit Rate Formula

Example 1: A restaurant serves 180 meals in 3 hours. Calculate the unit rate to find the meals served per hour.

Solution:

Number of meals served = 180

Time taken = 3 hours

To find: Number of meals served per hour

Let a = number of meals served, b = time taken to serve

Unit rate formula: unit rate $= \frac{a}{b}$

Unit rate$= \frac{Meals\; served}{Hours \;taken}$

Unit rate $= \frac{180}{3}$

Unit rate = 60 miles/hour

Therefore, the unit rate is 60 meals per hour.

Example 2: A car travels 360 miles on 12 gallons of fuel. Calculate the unit rate of miles per gallon (MPG).

Solution:

Distance traveled = 360 miles

Fuel used = 12 gallons

To find: Miles per gallon

Let a = distance traveled, b = fuel used

Unit rate formula: unit rate $= \frac{a}{b}$

Unit rate $= \frac{Distance\; traveled}{Fuel\; used}$

Unit rate $= \frac{360 \;miles}{12 \;gallons}$

Unit rate = 30 miles per gallon

Therefore, the unit rate is 30 miles per gallon.

Example 3: A factory produces 10 units of a product per hour. How many units will it produce in 6 hours?

Solution:

Units produced per hour = 10

Time taken = 6 hours

To find: Units produced in 6 hours

Let a = Units produced, b = hours taken

Unit rate $= \frac{a}{b} = \frac{Units \;produced}{Hours\; taken}$

Unit rate $= \frac{10\; units}{1\; hour} = 10$ units per hour

Number of units produced in 6 hours = 10 units per hour × 6 hours = 60 units

Therefore, the factory produces 60 units in 6 hours.

Example 4: A bakery bakes 60 cookies in 2 hours. How many cookies will be baked in 6 hours?

Solution:

Given: Cookies baked per hour = 60

Time taken = 6 hours

To find: Cookies baked in 6 hours

Let a = Cookies baked, b = Hours taken

Unit rate $= \frac{a}{b} = \frac{Cookies\; baked}{Hours\; taken}$

Unit rate$= \frac{60\; cookies}{1\; hour} = 60$ cookies per hour

Number of cookies baked in 6 hours = 60 cookies per hour × 6 hours = 360 cookies

Therefore, the bakery bakes 360 cookies in 6 hours.

Example 5: A store offers a discount on buying 20 T-shirts for $200. Calculate the unit cost of a T-shirt. Solution: Price of 20 T-shirts$= \$200$

To find: Price per T-shirt

Let a = Price of T-shirts, b = Number of T-shirts

Unit rate $= \frac{a}{b} = \frac{Price\; of\; T-shirts}{Number \;of\; T-shirts}$

Unit rate $= \frac{\$20}{20\; T-shirts} = \$10$ per T-shirt

The unit cost of a T-shirt is 10 dollars per T-shirt

## Practice Problems on Unit Rate Formula

1

### What is the definition of a unit rate?

A rate that involves two different units.
A rate with a denominator of one.
A comparison of two similar quantities.
A rate expressed as a fraction.
CorrectIncorrect
Correct answer is: A rate that involves two different units.
A unit rate is a specific type of rate in which the second quantity is expressed in terms of one unit of the first quantity. It allows for easy comparison between different quantities.
2

### In a unit rate, the denominator is always equal to

The numerator.
1
The sum of numerator and denominator.
The difference between numerator and denominator.
CorrectIncorrect
A unit rate is when the first quantity is described for one unit of the second quantity.
3

### When comparing two ratios to find the unit rate, you can use

Subtraction
Cross multiplication
Exponents and roots
CorrectIncorrect
When comparing two ratios to find the unit rate, you can set up a proportion and cross-multiply to find the value of the unknown variable.
4

### Which of the following correctly represents the unit rate of 3 kilograms of apples for $\$6$?$\$2$ per kilogram
$\$6$per kilogram$\$18$ per kilogram
$\$3$per kilogram CorrectIncorrect Correct answer is:$\$2$ per kilogram
The unit rate is calculated by dividing the total cost (\$6) by the quantity of apples (3 kilograms).
5

### If a car travels at a speed of 60 miles per hour, how many miles will it travel in 2.5 hours?

125 miles
150 miles
140 miles
180 miles
CorrectIncorrect
To find the total distance traveled, multiply the unit rate (60 miles/hour) by the time (2.5 hours).
60 miles/hour x 2.5 hours = 150 miles.