Question

How do you convert a rate to a unit rate?

Answer 1

Hint: In order to convert the rate to a unit, we need to divide the numerator and denominator of the given rate with the denominator of the given rate. The unit rate can be defined as a ratio that compares one unit of a particular quantity to that of different units of some other quantity.

Complete step by step answer:
We know, unit Rate is applied particularly in the metric system where two quantities need to be related.
Some examples of unit rate are Kilometres per hour, miles per hour, cost per item etc.
We can notice from the above examples that in every term, the denominator is in a unit of the quantity. This implies that we are dealing with unit rates.
To convert rate to unit rate, let us discuss how to calculate the rate.
The rate can be defined as the ratio between two related quantities, such that one of the quantities is changing with respect to another. Usually, the rate is calculated per unit time. Thus, the formula to calculate rate is:
$r = \dfrac{d}{{dt}}\left( x \right)$
Thus, the rate is obtained by differentiating any quantity with respect to time.
In the case of unit rate, the quantity in the denominator must be one. Therefore, the ratio of rate must be simplified in such a manner that we get one in the denominator.

Note: The unit rate can also be obtained from the graph. In case of straight-line curves, these are also known as linear curves, the unit rate can be calculated as the slope of the curve. On the other hand, for non-linear curves, that is graphs not having a straight line, unit rate is calculated as the tangent to the curve.