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Why is adding subtracting and equating quantities possible only if they have the same dimension?
If they are not on the same dimension then you cannot do this. They will be different numbers and will not go together.
Is adding or subtracting two related quantities by the same number is called scaling?
No, it is not.
Must two quantities have the same dimensions when subtracting them?
Yes they must be in the same units of measurements.
Must two quantities have the same dimensions if you are subtracting them?
Yes.
How are adding fractions different?
When adding or subtracting fractions their denominators must be the same
Why is adding subtracting and equating quantities possible only if they have the same dimension?
If they are not on the same dimension then you cannot do this. They will be different numbers and will not go together.
Why does efficiency have no dimension?
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.
Is adding or subtracting two related quantities by the same number is called scaling?
No, it is not.
Must two quantities have the same dimensions when subtracting them?
Yes they must be in the same units of measurements.
Must two quantities have the same dimensions if you are multiplying them?
No
Must two quantities have the same dimensions if you are subtracting them?
Yes.
How are adding fractions different?
When adding or subtracting fractions their denominators must be the same
What is adding or subtracting two related quantities by the same number called?
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
For two vector quantities to be equal they must have the same direction and the same?
Same direction and equal magnitudes.
Is it true that two quantities having the same dimensions must be measured in the same units?
No, it is not true.
Must two quantities have the same dimensions?
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
What is dimensional consistency?
dimensional consistency says that in any equation the dimensions of the quantities in the rhs and lhs are same. for example force =mass*acceleration force dimensions are MLT-2 : mass dimension M ;acceleration dimension LT-2 togehter the right hand side is also having MLT-2 dimension same as that of force.
