the gradient of a scalar function of any quantity is defined as a vector field having magnitude equal to the maximum space rate of change of the quantity and having a direction identical with the direction of displacement along which the rate of change is maximum.

They are not alike, they are different, but they can be identical in value. Example :- 3/4 and 0.75 are different ways of expressing the same quantity and they are not alike at all.

Identical quantities can be added (or subtracted) from each side.

Each side can also be multiplied (or divided) by any quantity.

An equal adjective is an adjective that describes things that are the same or equivalent in some way. For example, "equal" itself is an equal adjective as it signifies things that are identical in value or quantity.

They must have compatible units of measure.

For example, you cannot directly add a quantity measured in meters to a quantity measured in centimeters. If their units of measure are compatible but not identical, one can be converted to the other.

On the other hand, there is no way to add a quantity in feet to a quantity in pounds, as those are incompatible units of measure.

Additionally, if the quantities are fractions, they must also have the same denominators, also called sharing a common denominator.