The fraction of equivalent measurements is 1.
A rate that compares two equivalent measurements is a conversion rate.
A fraction that compares 2 equivalent measurements is often referred to as a conversion factor. It represents the relationship between two different units of measurement for the same quantity. For example, the fraction 1 mile/5280 feet can be used to convert between miles and feet, as there are 5280 feet in one mile.
There is no particular name unless the two measurements are on absolute scales. For example, the fraction 5/41 compares the equivalent temperatures: 5 deg Celsius and 41 deg Fahrenheit. But the equivalent fraction 10/82 does not compare equivalent temperatures since 10 deg C = 50 deg F. So the fraction has no particular meaning and so no name.
a ratio.... of course!!
It may be called the conversion factor.Note, however, that this only works when both measurements are absolute measurements, or equivalently, the measurement is on a ratio scale. For example, a fraction representing equivalent Fahrenheit and Celsius temperatures is not a conversion factor because the two Zero values do not correspond to the same temperature.
There need not be any such fraction: consider temperatures in the Celsius and Fahrenheit scales.
scale
One ratio or fraction compares part of a quantity to the whole quantity. The other ratio is the equivalent percent written as a fraction with a denominator of 100 and they can divide
It is the scale ratio or scale factor
A fraction.
A rate is a fraction that compares two quantities measured in different units. If the denominator of the fraction is 1 unit, the rate is called a unit rate.
A proper fraction.