Adding or subtracting numbers with the same units?

Question

"You can multiply or divide numbers that have different units. Is this also true of addition and subtraction? Explain."

I know the answer!! I just don't know the "logical" answer

Answer 1

a unit is not just something you write after a number like 10 kg, you are saying that there are 10 times the value which you call a kilogram. 10 kg means:

10*(1 unit equal to a kilo).

Similarly in dividing you are saying 10 miles per hour instead of 10 times 1 unit equal to a mile, for every hour that has gone by.

Saying there are 10 plus a kilo would have no meaning because you have not related 10 with a multiple ofthe kilo.

Another way of putting it is numbers can be added because they represent a point on a scale and are called scalars. They only have size. A unit has size and

meaning. Size in the sense that we know how far a mile is compared to a millimetre but also meaning in that it tells us we are talking about distance. When they have both these they are not scalars but are called vectors. The meaning is then called a dimension and to add two vectors you must have the dimensions of both parts the same. Therefore even if you are just using a single concept of say distance and multiplying or dividing it, when you add two things if the dimension isn't the same i.e. one side is area and the other length, then it has no meaning.  

Answer 2

no

u need to change them into  the same units,  multiply or divide,addition or subtraction

eg. 3meters and 500cm

first i have to change them into the same units

300cm + 500cm = 800cm

ok here's a more logical definition:

units desribe dimensions u cant add 2 things from different dimensions.  under laws of polynomial u add like terms.

under physical law u cannot  combine different dimensions together.

Answer 3

Give you an eg:

1) Velocity is rate of change of distance..that means distanc it moves in a particular period of time...If u MULTIPLY velocity by time...you end up wid the distance moved in the period of time u specified

2) Adding velocity and distance will be like......adding 2 mangos and 3 cars for example...what do you get?? Makes no sense does it??!!

Thats why we dont add or subtract things with different units...God knows what u'll end up with!!!!!!