Subtracting Mixed Fractions With Borrowing

Date: 01/08/2004 at 20:46:02
From: Ethan
Subject: Subtracting Fractions

Hi Dr. Math -

My name is Ethan and I'm in 7th grade.  I am stumped when it comes
to subtracting (mixed number) fractions.  Then I found this website
and I decided to ask.  Say I have 5 6/8 to be subtracted from 10 3/8.
Do I have to borrow because the 6 is bigger than the 3? I know that
you can't subtract a smaller number from a bigger number. If you do
have to borrow, then how do you do it?

Date: 01/09/2004 at 10:50:52
From: Doctor Ian
Subject: Re: Subtracting Fractions

Hi Ethan,

There are a couple of ways to approach a problem like this.  One way--
which doesn't require borrowing--is to convert the mixed numbers to
improper fractions, and then subtract those:

  10 3/8 - 5 6/8 = 83/8 - 46/8

                 = 37/8

If you're not sure how to do that conversion, take a look at 

  Converting Mixed Numbers to/from Improper Fractions
    http://mathforum.org/library/drmath/view/58876.html 

Another way to proceed is to "borrow" 1 from the larger integer.  That
is, 10 3/8 is the same as 10 + 3/8, right?  So 

  10 3/8 = 10 + 3/8

         = 9 + 1 + 3/8

         = 9 + 8/8 + 3/8

         = 9 + 11/8

And now we have 

  9 11/8 - 5 6/8 = ...

which is easier to do, right?  This is exactly the same thing we're
doing in a subtraction problem, when we borrow from the next column
over, e.g., 

                 . . . . . . . Here we exchanged one ten
                 .             for ten ones.

    84        7 14
  - 26  ->  - 2  6
  ----      ------
              5  8

We just exchanged one of our tens for ten ones, to make subtracting
ones possible.  The same idea works when subtracting times...except
you have to remember that there are 24 (not 10) hours in a day, and
60 (not 100) minutes in an hour, or seconds in a minute:

               . . . . . . . . Here we exchanged one hour
               .               for 60 minutes.
               .
    7:15     6:75
  - 5:41  -> 5:41
  ------     ----
             1:34

Does this help? 

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