If they are not on the same dimension then you cannot do this. They will be different numbers and will not go together.
No, it is not.
Yes they must be in the same units of measurements.
Yes.
When adding or subtracting fractions their denominators must be the same
If they are not on the same dimension then you cannot do this. They will be different numbers and will not go together.
Efficiency is a ratio of the same quantities. Usually, output power / input power. As the numerator and denominator have the same quantities, the dimensions cancel each other out.
No, it is not.
Yes they must be in the same units of measurements.
No
When two physical quantities are added together, they must have the same units in order to be combined. This means that both quantities must be expressed in the same type of measurement, such as meters or kilograms, for the addition to be valid.
Yes.
When adding or subtracting fractions their denominators must be the same
Same direction and equal magnitudes.
No, it is not true.
It is called algebra. When two quantities are related as long as you do the same operation to both (add, subtract, multiply, or divide) you do not change the relation
If you intend 'dimensions' to mean units then whenever the two quantities are to be operated on each other then they must have the 'dimensions', refer to dimensional analysis