Arithmetic question

[d-gun]

this seems to be going off topic, i am not interested in physics at the moment...i was just using it as an example to demonstrate the question.

why cant you add pounds to feet, but you can multiply them?

or better

why cant you add force to distance, but you can multiply them?

force * distance = work

fundamental units of force are f = ma

mass * acceleration * distance = work (energy)
kg * m^2/s^2 * m = kg-m^3 / s^2


i am only confusing myself further

[zwzsg]

I thought multiplication was repeated addition

I want you to explain me i*i in terms of repeated addition.

Oh, and the repeated addition corresponding to 1ft*1lb is not 1ft+1lb, it is 1ft+1ft+1ft+.. (1lbtimes). This may be the conceptual trick you were looking for.

Good luck conceptualising "1lb times" though.

[smoth]

there is a reason I ignored his second example.

[knorke]

[zwzsg]

force x distance is not the repeated addition force + distance.

It is: force + force + force + force (as many times as the distance).

So, you don't add force to distance, you only add force to force, which is allowed. You add force to force "as many times as the distance".

You can think of it as, the force had to be applied on every peeble along the road. Where a peeble represent the dx, the infinitesimal unit of distance over which you integrate along the path.

[knorke]

i still like my flash example because its something we can relate to. not like infinitesimal small pebbles.

[Argh]

why cant you add pounds to feet, but you can multiply them?

or better

why cant you add force to distance, but you can multiply them?

force * distance = work

Well, you can... it's all numbers. It just won't mean anything.

They're expressed in that way because that is how you need to apply them to get a meaningful result. Formulas like that are expressed as formulas for a reason.

To get to your fundamental question, though:

Multiplication is addition of the second item to itself for as many times as the value of the first item. It's iterative addition, with an additional step of multiplication involved if we involve decimals or fractions.

If X * Y, if X is 5, then it's equivalent to Y + Y + Y + Y + Y.

It's just a faster way to write that out, and it provides a simple shorthand for dealing with fractional values and decimals, i.e., if X = 3.5, then it's Y + Y + Y + (Y * 0.5).

We're taught a different way to handle it (memorizing the results of multiplying any two single numbers) when we're kids, so that we know that 8 * 5 = 40, for example... because that's the fastest way for people to process it. We can just memorize those tables and then we're OK with multiplication of fairly small numbers, or large ones if we're careful and check our work a lot.

Computers do it via a binary adder, though, IIRC- the slow way for humans- because of the way binary circuits work.

[d-gun]

force x distance is not the repeated addition force + distance.

It is: force + force + force + force (as many times as the distance).

So, you don't add force to distance, you only add force to force, which is allowed. You add force to force "as many times as the distance".

You can think of it as, the force had to be applied on every peeble along the road. Where a peeble represent the dx, the infinitesimal unit of distance over which you integrate along the path.

this is what i was looking for, thanks.

just to test my understanding:

displacement = velocity * time
1.2m = .1m/s + .1m/s + .1m/s ("time" number of times, where each unit of time is an infintesimal, but in this case we say 12 seconds)

so you add up all the individual displacements over the time period, hence you add iteratively (multiply).

now for the ultimate test of mental fortitude...division (iterative subtraction?):

[maackey]

You've got your units wrong.

1.2 m = .1m + .1m +.1m + ... (12 times -- you are travelling a distance of .1m every second)

the total distance is the sum of all the marginal distances.

.1m/s is the velocity, but distance is velocity * time

.1m * 12 s = 1.2 m s = 1.2m (the seconds cancel out)
__s___________s


you cannot have meters = sum of meters/second
total meters are always equal to the sum of meters

What grade are you in? I ask because a lot of this conceptual stuff really *clicked* once I reached calculus and learned how to do integrals and derivatives.

To reiterate your first question and the answer a lot of people gave already in various ways:

when you multiply apples and oranges, you are adding apples together orange times. it becomes 2 dimensional instead of 1 dimensional

4apples*6oranges = 24apple-oranges -- see? 2 dimensions.

you can think of it like a grid - apples are on the x axis, and oranges are on the y axis. apple-oranges don't really mean a lot, but there are other units that actually mean stuff (like force, energy, etc...) and you can actually find them by plotting them on a graph of the dimensions.

[Hoi]

Apples and oranges are just terms to explain simple math to kids. The "a" and "b" and "x" you use in math are a value, and can be anything. The most important things is that they are a number, and numbers can be multiplied.

You can't compare apples and oranges to like, force and distance. See the post above in the topic :)

[Johannes]

There kinda is nothing stopping you from adding together stuff of different metrics together.
5m + 6N = 5m + 6N
Yes right here I've got some meters and Newtons, and I added them together. But that's the most simple form of displaying it. If you don't consider m (5 + 6kg/s^2) simpler at least.
But there kinda is no sensible use for such equation in physics.

[Panda]

Hi

If you cannot add apples to oranges (or feet to pounds, etc), how come you can multiply them? I thought multiplication was repeated addition

I understand that this provides a new unit through dimensional analysis (ie foot-pounds), but how can this be explained conceptually?

We use a base ten number (a mathematical object used in counting and measuring) system in math, not a base fruit system.

[Das Bruce]

We use a base ten number (a mathematical object used in counting and measuring) system in math, not a base fruit system.

Every base is base 10.

[smoth]

hex is base 16

[fc14159]

Units are only as useful as the equations you use with them. For example, when you multiply pounds by feet, you can get ft-lb as a unit for energy or work. However, you can also get ft-lb as a unit for torque, which measures something completely different. In both cases, the pound part basically means the same thing, while the feet are different. Using the very basic definitions of the units, the energy definition uses the feet to measure how long the object with the given amount of force. In the torque definition, the feet is used to measure the distance from the center of the axis to where the force is applied. Therefore, if you use some sort of torque measurement in some equation for energy, you will get something meaningless, and vice versa.

[luckywaldo7]

As a side note, I think it is about @#$%ing time US switches to metric system. Using lbs and ft is all too real a horror in American engineering.

[MidKnight]

As a side note, I think it is about @#$%ing time US switches to metric system. Using lbs and ft is all too real a horror in American engineering.

T-that's terrible!

[Teutooni]

As a side note, I think it is about @#$%ing time US switches to metric system. Using lbs and ft is all too real a horror in American engineering.

No! The entire world should learn some silly unit system used by a small minority - after all, that's how they measure food at supermarkets in Burma. ~~

[d-gun]

You've got your units wrong.

1.2 m = .1m + .1m +.1m + ... (12 times -- you are travelling a distance of .1m every second)

the total distance is the sum of all the marginal distances.

.1m/s is the velocity, but distance is velocity * time

.1m * 12 s = 1.2 m s = 1.2m (the seconds cancel out)
__s___________s


you cannot have meters = sum of meters/second
total meters are always equal to the sum of meters

What grade are you in? I ask because a lot of this conceptual stuff really *clicked* once I reached calculus and learned how to do integrals and derivatives.

To reiterate your first question and the answer a lot of people gave already in various ways:

when you multiply apples and oranges, you are adding apples together orange times. it becomes 2 dimensional instead of 1 dimensional

4apples*6oranges = 24apple-oranges -- see? 2 dimensions.

you can think of it like a grid - apples are on the x axis, and oranges are on the y axis. apple-oranges don't really mean a lot, but there are other units that actually mean stuff (like force, energy, etc...) and you can actually find them by plotting them on a graph of the dimensions.

you hit the nail on the head man. thanks

i am 2nd year engineering

I have always had good grades in school math classes but most of the time solving the problems was a matter of repetition, didnt matter if I understood concepts because there were hundreds of problems to "mimick" solving from each chapter...i could get 85% on an exam with part marks.

[hoijui]

multiplication is repetition of addition ...
http://www.youtube.com/watch?v=EkkHoM6E00c#t=2m16s
there is not a single implication.