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Q&A #18923

Teachers' Lounge Discussion: Subtracting fractions

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From: Loyd <Loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2010122116:58:55
Subject: Subtraction fractions

I liked Ralph's explanation.  My experience in teaching algebra
students is that this type problem is one that causes problems.  I
have heard other teachers also say that the teaching of algebra is
hampered because many students are weak in fractions.  So, I will give
another example a little harder.  

Subtract 5 and 2/3 from 10 and 3/7.  Rewrite:

10  3
   ---
    7
5   2
   ---
    3
First thing is to get the least common denominator (LCD) which is 21. 
So we multiply the first fraction by 3/3 and the second fraction by
7/7.  The new problems is"

10  9
   ---
    21
5   14
   ----
    21
-----------

Now we borrow a "whole" as Ralph's said and change it to 21/21 and add
that to  9/21 and then we can subtract as usual.  The new problem is:

9   30   
    ---
    21
5   14
   ----
    21   Now they are "like" fractions so we can subtract.
-----------
4   16
   ---
    21
   

The trick here is that we can always multiply by 1 and not change the
value.  3/3 and 7/7 were used as multipliers and both of them are
equal to 1.  

Make sure students can are proficient in finding the LCD and LCM even
if denominators are not prime. 

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