General Math Question (Solved)

Spectral Swallow

Maybe I'm just glitching or something but for some reason I can't get the division to work for me here.

Okay, so take for example you wanted to know what 6 X 10 is. Instead of just saying '60' you could go:

4 X 10 = 40
2 X 10 = 20

And then add up the answers. Basically breaking it down into a simpler problem. But when you try to do something similar in division:

60 ÷ 10 = 6

You can't just go:

60 ÷ 5 = 12
60 ÷ 5 = 12

And then add them. So what exactly am I missing here?

xraydog

It works if you break down the dividends instead of the divisors:

60 / 10 = 6

40 / 10 = 4

20 / 10 = 2

Unknown

This content has been removed.

Spectral Swallow

Yeah but that's doesn't really help where I'm going with it though. An example of what I'd be kinda trying to get to would be:

3x+2y+5

---

3z+14


And then just doing:

3x+2y+5 / 3z
and
3x+2y+5 / 14

You see? What I'm trying to do isn't in the book or anything, I was just curious why it wouldn't work.

oldsak

Remember dividing a number by a number is like multiplying it by 1/(that number).

so for your example the appropriate thing to do would be
60 * 1/20

When you do 60 ÷ 5 you're multiplying the divisor (10 or 1/10) by 2 instead of dividing it by 2.

Unknown

This content has been removed.

Peter Ebel

Because division takes priority over addition. What you'd end up with there is:

(3x/3z+14)+(2y/3z+14)+(5/3z+14)

Unknown

This content has been removed.

Gdiguy

mcdermott wrote: »

Spectral Swallow wrote: »

Yeah but that's doesn't really help where I'm going with it though. An example of what I'd be kinda trying to get to would be:

3x+2y+5

---

3z+14


And then just doing:

3x+2y+5 / 3z
and
3x+2y+5 / 14

You see? What I'm trying to do isn't in the book or anything, I was just curious why it wouldn't work.

It doesn't work because that's not how division works. I'm not sure of the best way to explain it, but basically the easiest way to understand why this won't work is to ignore the idea of "division," and instead thinking of division as multiplication by the inverse (which it is). So instead of dividing by 6, you multiply by 1/6.

Then just realize that 1/(x+y) does not equal 1/x + 1/y...it equals A/x + B/y, where A and B are values to be determined though a fun process known as partial fraction decomposition.

If you're in need of proof that 1/(x+y) != (1/x)+(1/y), then just substitute constants in for x and y to prove it to yourself.

To be more specific, multiplication has the distributive property, which basically states that a * (b + c) = a * b + a * c. So, as above, 10 * (4 + 2) = 10 * 4 + 10 * 2.

Division doesn't have that property, as stated well in the post above

Peter Ebel

Gdiguy wrote: »

mcdermott wrote: »

Spectral Swallow wrote: »

Yeah but that's doesn't really help where I'm going with it though. An example of what I'd be kinda trying to get to would be:

3x+2y+5

---

3z+14


And then just doing:

3x+2y+5 / 3z
and
3x+2y+5 / 14

You see? What I'm trying to do isn't in the book or anything, I was just curious why it wouldn't work.

It doesn't work because that's not how division works. I'm not sure of the best way to explain it, but basically the easiest way to understand why this won't work is to ignore the idea of "division," and instead thinking of division as multiplication by the inverse (which it is). So instead of dividing by 6, you multiply by 1/6.

Then just realize that 1/(x+y) does not equal 1/x + 1/y...it equals A/x + B/y, where A and B are values to be determined though a fun process known as partial fraction decomposition.

If you're in need of proof that 1/(x+y) != (1/x)+(1/y), then just substitute constants in for x and y to prove it to yourself.

To be more specific, multiplication has the distributive property, which basically states that a * (b + c) = a * b + a * c. So, as above, 10 * (4 + 2) = 10 * 4 + 10 * 2.

Division doesn't have that property, as stated well in the post above

Division has distributive property. Example: (4+2)/2 = (4/2)+(2/2) = 2+1 = 3

Unknown

This content has been removed.

musanman

Division distributes just fine, that's not the issue.

If you have

3x+2y+5

---

3z+14

you can break it down, but it's 3x / (3z+14) + 2y / (3z+14) + 5 / (3z+14)

what you need to realize is you're dividing by a quantity 3z+14...and based on the order of ops the parenthesis come before the division

Spectral Swallow

Thanks guys, I understand it a lot better now, it was just one of those things like, 'hmm, it SHOULD work, since it works with multiplication, and division is just multiplying by the recip' but for some reason my mind just wasn't working.

Thanks for the help.