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Yes, two quantities must have the same dimension in order to be added together. This is because addition involves combining like terms, and only quantities with the same dimensional units can be meaningfully combined. For example, you cannot add meters and seconds, as they represent different dimensions.
What else can I help you with?
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
What requirements must be met by two physical quantities when they are added together?
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.
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
For two vector quantities to be equal they must have the same direction and the same?
Same direction and equal magnitudes.
What condition must be met before you can add or subtract?
Before you can add or subtract, the quantities involved must be expressed in the same units or form. For example, if you are adding lengths, both measurements must be in the same unit, such as meters or centimeters. Additionally, when dealing with algebraic expressions, the terms must be like terms, meaning they should share the same variable and exponent. Only then can you combine them appropriately.
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
Is it true that two quantities having the same dimensions must be measured in the same units?
No, it is not true.
