Very basic numerator problem

Quote:

Originally Posted by Peleus

Hi all,

I've got a very basic question for you all, in fact I feel a bit silly asking it but here we go.

I'm running into a problem with what we do with a numerator when we want to simplify to solve an equation. Perhaps an example would be the best explanation. My understanding of solving equations is we have to do the same on both sides, so in an example it would be...

10 = A + 5 so this obviously can move to -5 on both sides 10 - 5 = A

10 = A / 5 so this is 10*5 = A (swapping / for *)

10 = A * 5 is 10/5 = A (swapping * for /)

etc etc. Basically moving it to the other side of the = and doing the opposite expression.

In this case X is obviously 10, but we're trying to solve that.

100 = 1000/X

Now in this case, can we isolate X in one move or do we always have to go through the two step process of 100*x = 1000 then X = 1000/100??

Whats the 'opposite' expression of the numerator (assuming along the same lines of the 'opposite' expression of the denominator is multiplication)?

Thanks

In this case, you need to have two steps. But there are two methods:

1.)
$\displaystyle 100 = \frac{1000}{x}$
Multiply by $\displaystyle x$ (*)...
$\displaystyle 100x = 1000$
Divide by $\displaystyle 100$ (/)...
$\displaystyle x = \frac{1000}{100} = 10$

2.)
$\displaystyle 100 = \frac{1000}{x}$
This is the same as...
$\displaystyle \frac{100}{1} = \frac{1000}{x}$
You can make it reciprocal (Fliping the fractions, numerator becomes denominator and vice versa)...
$\displaystyle \frac{1}{100} = \frac{x}{1000}$
Multiply by $\displaystyle 1000$ (*)...
$\displaystyle \frac{1000}{100} = x = 10$