Solving an Equation with Fractions

Date: 1/30/96 at 21:4:44
From: Mongolian Gypsy
Subject: pre algebra

I have spent the last half hour on this problem:
v = 6 - 5/4 v
I don't know if the question is asking 6 minus 1 1/4 or 6 * 1 1/4. 
Please solve for v. I am in seventh grade and these problems are 
starting to haunt me.

Amy Steiner
email: sfduq@scfn.thpl.lib.fl.us

Date: 1/31/96 at 12:7:40
From: Doctor Elise
Subject: Re: pre algebra

Hi!
These problems will haunt you for many years yet to come, too! :-)

What's called the "order of operations" takes a little getting 
used to.  Basically, unless you have parentheses in your equation 
that tell you how to group things, you do all the multiplication 
and division in the problem before any addition and subtraction.  
Here are some examples:

6 - 5/4 v  Here there are no parentheses, so you do multiplication
           and division first.  I'm being told to take 5, divide 
           by 4, multiply the result by v, and subtract the whole 
           thing from 6.
           
(6 - 5/4) v  Here the parentheses tell me to take 5, divide it 
             by 4, subtract the result from 6, and then multiply 
             the whole thing by v.
             
(6 - 5)/4 v  Here I'm being told to subtract 6 from 5, then divide 
             the result by 4, and multiply the whole thing by v. 

Your problem reads:

v = 6 - 5/4 v

If I add parentheses to show what this really means, I have:

v = 6 - ((5/4) * v)

In words, 'v' equals 6, minus 1 1/4 times 'v'

To solve it you have to put all the 'v's on one side and all the 
numbers on the other.  (Actually, that pretty much sums up 
Algebra.  Any more questions? Just kidding!)

To solve it, I can do anything I want to this equation, as long as 
I do the same thing on both sides of the equals sign.  So I'll add 
(5/4) * v to both sides to put all the 'v's on the same side:

v + (5/4)v = 6 - (5/4)v + (5/4)v

v + (5/4)v = 6

(1 + 1 1/4)v = 6

(2 1/4) v = 6

(9/4)v = 6

Now I want to put all the numbers on the other side of the 'v',
so I'll multiply both sides by 4/9:

(4/9) * (9/4) v = 6 * (4/9)

v = 6 * (4/9)

v = (6 * 4) / 9 

v = 24/9

v = 8/3 

v = 2  2/3

Does this help?

-Doctor Elise,  The Math Forum