Solving Equations with Fractions in Them

Date: 12/06/2004 at 15:12:14
From: Amanda
Subject: How do you solve equations with multiplication


I'm stuck on -5/7 n = 35.  I don't understand how you change a
fraction like this to a whole number.

Date: 12/06/2004 at 22:00:29
From: Doctor Boyd
Subject: Re: How do you solve equations with multiplication

Hi Amanda,

Thanks for writing to Dr. Math.  Let's look at a similar but slightly
easier problem:

   1
  --- n = 35
   7

We know that one seventh of "n" is 35, so now we need to collect
together enough pieces of "n" to make a whole "n".

Let's pretend that "n" is this long:

  +----------------------------------+

Now, I can break it into 7 pieces:

  +----+----+----+----+----+----+----+

And I know that each of these pieces is 35

    35   35   35   35   35   35   35
  +----+----+----+----+----+----+----+

So the total of "n" is

  35 + 35 + 35 + 35 + 35 + 35 + 35 = 245

Now, notice that there are 7 of these, so it could be a multiplication:

  7 * 35 = 245

So, if we look back at our original equation, we see that all we had
to do was take 7 "1/7 n"s and 7 "35"s to find out how much one "n" was
worth. In other words, we just multiply both sides by "7":

             1
            --- n = 35
             7

             1
       7 *  --- n = 7 * 35        -->(Multiply both sides by 7)
             7

             7
            --- n = 7 * 35        -->( 7 * 1/7 = 7/7)
             7

            1 * n = 245           -->(7/7 = 1)

                n = 245

Does that give you a clue of how to solve your question? Please write
back if you'd like some more help with this, or if you have any other
questions.

All the best,

- Doctor Boyd, The Math Forum
  http://mathforum.org/dr.math/