Formula
\text{Unit Rate} = \frac{a}{b}Used to calculate: The amount of one quantity corresponding to one unit of another quantity.
—
What Is the Unit Rate Formula?
The unit rate formula compares two quantities by dividing one quantity by another so that the second quantity has a value of one. It expresses how much of the first quantity corresponds to each single unit of the second quantity.
—
Formula and Variables
\text{Unit Rate} = \frac{a}{b}| Symbol | Meaning | Unit |
| Unit Rate | Amount of the first quantity per one unit of the second quantity | Units of a per unit of b |
| a | Amount of the first quantity | Depends on the problem |
| b | Amount of the second quantity | Depends on the problem |
—
How to Use the Formula
Identify the two quantities being compared. Place the quantity being measured per unit in the numerator and the quantity that will be reduced to one unit in the denominator. Divide the numerator by the denominator. The result gives the amount of the first quantity for one unit of the second quantity.
—
When Is This Formula Used?
The unit rate formula is used when two quantities need to be compared on a per-one-unit basis.
Common uses:
– Calculating price per item or unit
– Calculating speed or distance per unit of time
– Comparing rates expressed using different quantities
—
Important Notes
– A unit rate has a denominator corresponding to one unit of the second quantity.
– The denominator b cannot equal zero because division by zero is undefined.
– The unit rate generally retains compound units, such as dollars per item or miles per hour.
– A common point of confusion is reversing the quantities. The order of the numerator and denominator determines what the unit rate represents.
—
Alternate Forms
Alternate form:
\text{Unit Rate} = \frac{\text{Quantity}_1}{\text{Quantity}_2}Alternate form:
a = (\text{Unit Rate})b—
Related Formulas