How to Multiply Fractions

Date: 9/6/96 at 16:57:28
From: Anonymous
Subject: How to Multiply Fractions

Dear Dr.Math,

I keep trying to multiply fractions. But every time I do, the 
teacher tells me it's wrong. I am in 7th grade and math is my best
subject so I don't know how I could have forgotten. Please help!

In need of help,
   Kiral 

Date: 10/27/96 at 22:48:9
From: Doctor Lynn
Subject: Re: How to Multiply Fractions

Dear Kiral,

When you multiply fractions you just need to multiply the tops
(the numerators) and the bottoms (the denominators) separately and
then cancel down.

For example:

   2     3     2 * 3      6      3
   -  *  -  =  -----  =  --  =  --
   5     4     5 * 4     20     10


When you add fractions it's harder because you have to change the
fractions so that the bottoms are the same before adding them.
For example:

   2     3      8    15    8+15     23        3
   -  +  -  =  --- + -- =  ----  =  --  =  1 ---
   5     4      20   20     20      20       20

If you don't understand how either of these examples work, I suggest 
that you ask your teacher about it, because that suggests that you 
might need help with cancelling or with making the bottoms of the 
fractions the same, which is hard to explain in e-mail, though we'd be 
happy to try if you want. 

Basically, when you cancel a fraction down, you are trying to find a 
number which "goes into" the top and the bottom of the fraction.  When 
I cancelled

  6          3
 ---   to   ---
  20         10

it was because 2 went into 6 and 20, so I could divide both numbers by 
2. When you try to make the bottoms of two fractions the same, you are 
looking for a number which both of the bottoms go into.  When I turned

   2     3         8    15
   -  +  -  into  --- + --
   5     4         20   20

it was because 5 and 4 both went into 20, so I multiplied the top and 
the bottom of the first fraction by 4 so that the bottom was 20, and 
I multiplied the top and the bottom of the second fraction by 5, so 
that its bottom was 20 too. 

I hope that helps.  If you have any more problems, please write back 
and we'll try to help.

-Doctor Lynn,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/