Q&A #5357

Subtracting fractions with borrowing

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From: Gail (for Teacher2Teacher Service)
Date: Dec 17, 2000 at 07:50:13
Subject: Subtracting fractions with borrowing

Start out with an estimate.    99 1/5 is really just a little bit bigger
than 99, and 66 4/10 is almost 66 1/2, so now you have the problem
99 - 66 1/2.  99 - 66 is 33, so 99 - 66 1/2 must be 32 1/2.

Now that you have a reasonable (ballpark) answer for your problem, you can
work on the actual problem.  I ask my fifth grade students to think about
several different ways they can represent fifths.  Some people call that
"finding equivalent fractions".  My students know that 1/5 can also be called
2/10, 3/15, 4/20, 5/25, 6/30...   (If you look at all those fractions, you
will see there is a pattern).

Now let's look at 4/10.  It can also be called 2/5, (4/10), 6/15, 8/20,
10/25, 12/30...   Do you see the pattern this time?

So, if we compare the two sets of fractions, we can see there are several
different ways to match the two fractions up so that they have the same
denominator (bottom number).  We could use 1/5 and 2/5, 2/10 and 4/10, 3/15
and 6/15, etc.  The pair you choose won't really make any difference, but in
the end, if you want to do the least work possible, you are probably best off
choosing the pair with the smallest denominators, which, in this case, would
be 1/5 and 2/5.

So now you have the problem 99 1/5 - 66 2/5.  What would happen if you could
take one of the wholes away from 99, and change it into fifths?  You would
have one less whole, and 5 more fifths.  Instead of 99 1/5 you would have 98
6/5.  Now your problem is 98 6/5 - 66 2/5.  That is an easier problem to

Don't be discouraged by the number of steps this seems to take.  The more of
them you do, the more you will remember about equivalent fractions, and you
will be able to begin to find shortcuts.  Think of finding your way through a
building or a new city you are not familiar with.  At first, you have to
think about every step you take, and consult a map or directions often.
Then, after a while, you are able to recognize landmarks, and soon you are
navigating without any trouble at all.  That is the way it is with
mathematics.  At first it all seems strange, but after practice, you can do
it!  :-)
 -Gail, for the T2T service

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