How Do You Algebraically Move a Numerator to the Other Side of an Equation?

[Quantum Joe]

I have a formula

H_o / H_i = -S_o / S_i

The question is if I have this:

0.5/H_i = 2.0/8.0

how do I move the 0.5 numerator to the other side of the equation? What is the algebraic property that describes this? I realize this is a simple question but isn't it always the simple ones that get you?

 

[csprof2000]

Multiply both numerators by 2. This gives you

1.0/Hi = 4.0/8.0

That should do it.

 

[Quantum Joe]

I don't see how that solves the problem.. I need remove the fraction on the left side and keep only H_i. Maybe I am approaching this wrong, if so could someone explain why? I know that 1/Hi is the same as H^-1.

 

[Quantum Joe]

I think this belongs in homework help. I will post it there.

 

[HallsofIvy]

I have a formula

H_o / H_i = -S_o / S_i

The question is if I have this:

0.5/H_i = 2.0/8.0

how do I move the 0.5 numerator to the other side of the equation? What is the algebraic property that describes this? I realize this is a simple question but isn't it always the simple ones that get you?

I don't see how that solves the problem.. I need remove the fraction on the left side and keep only H_i. Maybe I am approaching this wrong, if so could someone explain why? I know that 1/Hi is the same as H^-1.

Then you should have said that to begin with and not just "move the 0.5 numerator to the other side of the equation". In fact, it isn't the numerator that is the problem. To get rid of the fractions multiply both sides of the equations by the denominators:
\frac{0.5}{H_i}(8.0H_i)= \frac{2.0}{8.0}(8.0H_i)
On the left the "H_i" terms cancel and on the right the "8.0" terms cancel:
(0.5)(8.0)= 2.0H_i or 4.0= 2.0H_i.

 

[Mentallic]

Use these basic rules of fractions:

Given any numbers (denominator \neq 0) ~ \frac{a}{b} * \frac{x}{y} = \frac{ax}{by}

If there are common factors in both the numerator and denominator, you can cancel them out ~
\frac{a}{b} * \frac{x}{a} = \frac{ax}{ba} = \frac{x}{b}

So, \frac{H_o}{H_1}=\frac{-S_o}{S_1}

If you try to make H₁ the subject of the equation, it needs to come out of the denominator.
So, to cancel it from the denominator, multiply both sides by H₁

\frac{H_o}{H_1}*\frac{H_1}{1}=\frac{-S_o}{S_1}*\frac{H_1}{1}

Simplifying:

\frac{H_o}{1}=\frac{-S_o * H_1}{S_1}

Now that H₁ is in the numerator, simply divide/multiply both sides of the equation by the required variable so as to cancel out those variables on the same side as H₁:
Multiplying by S₁ and dividing by -S_o

\frac{H_o}{1}*\frac{S_1}{-S_o}=\frac{-S_o * H_1}{S_1}*\frac{S_1}{-S_o}

Simplifying by cancelling common factors in numerator and denominator:

\frac{H_o*S_1}{-S_o}=H_1