Question

Writing an equivalent rate with a term of 1 makes rates much easier. When comparing rates, which term should be equal to 1?

a) Rate of change
b) Multiplying factor
c) Denominator
d) Numerator

Answer 1

To compare rates easily, set the denominator equal to 1. This simplifies the multiplication and makes it easier to cancel out and convert units while ensuring the expression remains an equality.

Step-by-step explanation:

When comparing rates, the term that should be equal to 1 is c) Denominator. By setting the denominator to 1, we create an equivalent rate with a term of 1 which simplifies the comparison of rates. For example, the conversion factor 100 cm per 1 m is used to convert meters to centimeters. This conversion factor is equal to 1 because the same quantity is represented in both the numerator and the denominator, albeit in different units. Thus, when multiplying by this conversion factor, the original unit in the denominator cancels out with the unit in the conversion factor, leaving the desired unit in the numerator. This process ensures that the expression remains an equality and simplifies the comparison of different rates.