How are unit rates written?

Question

Nova Allen · Accepted Answer

see explanation

Depends upon which you are applying the unit measurement

For example, consider the following example of a right triangle

#("Amount of up")/("Amount of along")-> 1/2 #

And this is the same as #(1-:2)/(2-:2) = 0.5/1#

The bottom number is the unit (1 off) compared against and the rate is the #0.5#

#color(magenta)("So the unit rate in this instance is "0.5)#

#color(brown)("So unit rate is comparing quantities against a standardised quantity")##color(brown)("of 1 of something else.")#

If you consider the trigonometric ratio of tangent #->tan(theta)#

For the same triangle:

#tan(theta)=("amount of up")/("amount of along")=1/2 = 0.5/1#

So #tan(theta)=0.5#

Everly Taylor · Answer

undefined Unit rates are typically written in the form of a ratio where the denominator represents one unit of the quantity being measured. This means that the denominator is always 1. For example, if you are measuring the speed of a car in miles per hour, the unit rate would be written as "miles per hour" or "mph." Similarly, if you're measuring the cost of an item per unit, such as dollars per pound, the unit rate would be expressed as "dollars per pound" or "$/lb."

In mathematical notation, unit rates are often represented as fractions where the denominator is 1. For instance, if the cost of 3 pounds of apples is $6, the unit rate of cost per pound would be expressed as $ \frac{6}{3} = 2 $ dollars per pound.

Unit rates provide a standardized way to compare different quantities, allowing for easy comparison across various contexts. They are commonly used in everyday life, such as when comparing prices at the grocery store, calculating speed or distance traveled, or determining efficiency in manufacturing processes.