Arithmetic question

[d-gun]

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?

[zwzsg]

you cannot add apples to oranges

Little Johnny went to the market. From Mr William, he bought 5 apples. From Mrs Donnel, he bought 7 eggs. And from Mr Patterson, he bought 3 oranges. How many fruit is there in little Johnny's basket?

[d-gun]

that was tricky but you see we are adding FRUIT, not APPLES and ORANGES.

5 fruit + 3 fruit = 8 fruit.

5 apples + 3 oranges = ???? (appanges?) this does not compute

[smoth]

if you have 6a where a is apple in means you have (a,a,a,a,a,a) you cannot resolve 6a+5o because the a and o represent non-numeric values. If you say wanted to get the combined weight of it you would then find out the weight of apples and oranges(assuming they all weigh the same) and then give a value to a and o. So it would be something like
a = 2
o = 1
which would give you 6(2)+5(1)

Apple and orange represent an abstract item until defined.

for feet/pounds or feet*pounds you would need to find how many feet or pounds. This isn't hard stuff. if you have say 1 square foot of something that weights one pound you can then resolve it.

I am unsure of what your conundrum is

[knorke]

I thought multiplication was repeated addition

it is. the right things must be added together.

if you spam 5 flash for 100 metal each you can not calculate
5 flash + 100 metal = something
but to calculate the total prize you can do "repeated addition"
100 metal +100 metal +100 metal +100 metal +100 metal = 500 metal
->
5 flash * 100 metal = total cost= 500 metal

[zwzsg]

how come you can multiply them?

Multiply apples by oranges? o_O

[smoth]

I thought multiplication was repeated addition

it is. the right things must be added together.

if you spam 5 flash for 100 metal each you can not calculate
5 flash + 100 metal = something
but to calculate the total prize you can do "repeated addition"
100 metal +100 metal +100 metal +100 metal +100 metal = 500 metal
->
5 flash * 100 metal = total cost= 500 metal

Problem statement we have 5 flash, each costs 100 what is the total cost.

Or cost = 100
x = cost

f(x) = 5(x)
f(100) = 500

lets play with apples and oranges.

Problem statement we have 5 flash, each costs 100 apples and 200 oranges. The apples and oranges weigh 50 pounds what is the total weight storage needed for the cost of a flash.

Or weight = 50
a = 100
o = 200

5(50(a+o))

does this help?

If you cannot define apples and oranges as some sort of quantitative unit you will not be able to use them. Apple and orange is abstract so you have to decide on what about the apples and oranges you are trying to evaluate.

[Regret]

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?

You do realize how units work right?

Notice "miles per hour" is your "oranges * (1/apples)".

no need to be mean about it - moderation

[zwzsg]

if you spam 5 flash for 100 metal each

I prefer the wording: a hundred metal per flash. Where "per" is represented by a slash.

''''5 flash x 100 metal / flash

' ' ' ' ' ' ' ' ' ' ' ' ' ' 'metal
= 5 flash x 100 -------
' ' ' ' ' ' ' ' ' ' ' ' ' ' 'flash

' ' ' ' ' ' ' ' ' ' ' ' ' ' 'metal
= 5 flash x 100 -------
' ' ' ' ' ' ' ' ' ' ' ' ' ' 'flash

= 5 x 100 x metal

= 500 metal

But the teacher never allows me to keep units in equations! ;_;

[d-gun]

Ok, lets use a real-world example:

I am loading 100-pound drums on a truck by rolling them up a ramp. The truck bed is 3 feet above the street and the ramp is 6 feet long. How much force must I exert on the drums as I go up the ramp?



3ft x 100lb = 300 ft-lb of work (drums end up with more energy)
6ft x ??? lb = 300 fl-lb? (where ??? = how many pounds of force must be exerted to give 300fl-lb of work)

the answer is 50 lb of force.

If you cannt add feet and pounds, how come you can multiply them?

[Teutooni]

Syst├¿me international d'unit├®s, motherf*****, do you speak it?

[zwzsg]

3ft x 100lb = 300 joules of work

Err, feet and pound are archaic units. They don't give nice joules when multiplied.

The real formula would be:
height x weight x gravity = energy
3 feet x 100 pound * 9.81m/s┬▓ =
0.914 meters * 45.36 kilograms * 9.81m/s┬▓ = 407 joules

[Johannes]

If you cannt add feet and pounds, how come you can multiply them?

x+y=x+y
x*y=xy

[zwzsg]

No!

X x Y = x-y

Where X is foot and Y is pound, that yelds: foot x pound = foot-pound

[d-gun]

3ft x 100lb = 300 joules of work

Err, feet and pound are archaic units. They don't give nice joules when multiplied.

The real formula would be:
height x weight x gravity = energy
3 feet x 100 pound * 9.81m/s┬▓ =
0.914 meters * 45.36 kilograms * 9.81m/s┬▓ = 407 joules

right, it should have been ft-lb not joules, thanks.

The 100-lb drums end up 3 ft higher so they end up with 3ft * 300lb = 300 ft lb more energy

http://en.wikipedia.org/wiki/Foot-pound_(energy)

[knorke]

I am loading 100-pound drums

at this point, thread failed.

also in your barrel example, the length of the ramp does not matter, if there is no friction etc.
only heighth.
its all in the gravity
ie
potential energy = height * mass* g
g= 9,81m/s┬▓ (gravition)

edit
so its already been said.
well, how many red comet games did you play in the meantime!

[d-gun]

at this point, thread failed.

??? nobody cares about your silly french units of measurements. at my supermarket food is measured in lb.

the length of the ramp DOES matter a lot. it is an inclined plane designed to reduce the necessary force required to do a certain amount of work by increaseing the distance through which the force acts.

try unscrewing a bolt with your fingers, then get a wrench and try. levers, block-and-tackle, and compound pulleys work on the same principle.

anyway, you arent answering the question

addition: 1ft + 1lb = ...does not make sense...(there is no real-world thing for this to be a measure of, for example force or torque)

repeated addition: 1ft * 1lb = 1 pound-foot (a work)

i still dont get it...

[Peet]

??? nobody cares about your silly french units of measurements. at my supermarket food is measured in lb.

[knorke]

at my supermarket yo momma always has already eaten all the food when i get there

but yes i didnt read the question correctly. i thought you were messing up required force and work or something, sorry.
The "drums end up with more energy" confused me but you meant something else.

repeated addition: 1ft * 1lb = 1 pound-foot (a force)

i still dont get it...

http://en.wikipedia.org/wiki/Joule
One joule is defined as the amount of work done by a force of one newton moving an object through a distance of one metre
So I think it is just a defined this way.

Actually there are only 7 base units:
length, mass, electric current, temperature, strength of light, time.
Everything else is defined by them, even the "simple" ones we are so used to, ie speed.
Definations do not need to make "sense", there are just defined that way.

[zwzsg]

the length of the ramp does not matter

I think he wanted to calculate the force needed to push a 100-lb drum upward a 30┬░ ramp. But instead he described the ramp as being 6 feet long and ending 3 feet above ground. Then he calculated the potential energy of a drum atop this particular kind of 30┬░ ramp, and equated it to the work needed to push the drum along the ramp, and got the force from there.

Because on earth surface gravitation is nearly constant, any mass units (such as pound) double as a force unit. It's not very rigourous, but people often talk about kilogram-force, or in this case, pound-force. So beside the confusion between imperial and SI energy units that he just edited out, it's not thaaaat wrong.

1 pound-foot (a force)

Nein! A work!

Take care when using the words: work, force, energy, weight, mass. They all have their own meaning. Ok, work and energy are the same dimension, and the weight is a kind of force. But a force multiplied by a length is a work.