Multiplying and Adding Fractions

Date: 04/01/97 at 23:31:39
From: Eric Pelfrey
Subject: Multiplying and Adding Fractions

(1/3 + 2/5) * 3/4. I can't find the answer!
Please help me. 

Date: 04/02/97 at 06:26:04
From: Doctor Mitteldorf
Subject: Re: Multiplying and Adding Fractions

Dear Eric,

People spend a lot of time in school studying fractions before they 
take on a problem as tough as this one.

Here's a way you might think about it.  First, you might break up 
the multiplication: the 3/4 multiplies the sum of the other two 
fractions, but you could just as well make it multiply each one 
separately:

1/3 * 3/4   +   2/5 * 3/4

The first part is 1/3 of 3/4.  Well, this is easy, since 1/3 of 3 
anythings is 1 anything.  If you have 3 fourths, you have 1/4, 1/4 
and 1/4.  So a third of that is just 1/4.

The next part is harder.  2/5 of 3/4.  I'd think of my 2/5 as 4/10 to 
start with, if I were you.  Then it's just 3/4 of 4/10 that you want.  
Well, 1/4 of 4 tenths is just 1 tenth - same way we did the other one.  
If 1/4 of 4 tenths is 1 tenth, then 2/4 of it makes 2/10 and 3/4 of it 
makes 3 tenths.  So the answer is 3/10.  

Here's what we've got so far:

 (1/3 + 2/5) *  3/4

  1/3 * 3/4  +  2/5 * 3/4

         1/4 + 3/10

Now what's left is to add 1/4 and 3/10.  I don't know if you've 
studied this yet - there's a trick that they teach you in 6th grade, 
that goes like this:

Think of the  1/4 as so many twentieths.  It's the same as 5/20.
Think of the 3/10 as so many twentieths.  It's the same as 6/20.

Now you can just add them up.

1/4 + 3/10 is the same as 5/20 + 6/20, which is 11/20.  That's the 
answer.

Whew - that had a lot of steps.  Did you get them all?  Anything we 
should go over again?

The one thing I'd be asking if I were you:  How did I know to change 
the 1/4 and 3/10 to twentieths?  Where did I get the number 20?  Are 
there any other numbers I could have used instead of 20?

What do you think?

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