Solve for h

Q:  Solve for h:  5h/7 = 5/14

A:  The dreaded fraction haunts us again, huh?

5h/7 = 5/14

I am trying to get h by itself… Since the h is being divided by a 7, I am going to multiply everything by a 7 to get rid of it:

7*(5h/7) = 7*(5/14)

Now simplify:

35h/7 = 35/14

Reduce fractions:

5h = 5/2

Now, there is a 5 multiplying the h… SO, we need to divide everything by 5.  But wait… Does this will give us 5/2 divided by 5… ACK!  A fraction inside of a fraction.  This is definitely do-able, but not the easiest.  So, instead of dividing by 5, I am going to multiply everything by 1/5 (this is essentially the same thing).  Watch:

5h = 5/2

(1/5)*5h = (1/5)*5/2

Multiply fractions across the top and across the bottom to get:

5/5 * h = 5 / 10

reduce:

h = 1/2

There it is.