Final answer:
In mathematics, to join values through operations like addition or subtraction, they must have same units or be dimensionally consistent. Both sides of an equation must also maintain these consistent dimensions for the equation to be valid.
Step-by-step explanation:
When joining values together in mathematical operations, such as addition or subtraction, the values must be dimensionally consistent. This means that they must have the same units or be of the same type (e.g., both in dollars, both in meters, etc.). For instance, it is not meaningful to add 3 meters to 4 seconds since these represent different physical quantities. This concept is rooted in the principle that you can't combine unlike terms — similar to how you can't add apples and oranges — because they represent different dimensions of measurement.
Moreover, when working with equations, both sides of the equation must have the same dimensions. This ensures that the equation is balanced and mathematically valid. Without dimensional consistency, the addition or subtraction would result in an undefined or nonsensical value.