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Adding and Subtracting Fractions
by Gail Englert

A response to the question:

What is the best method of teaching how to rename fractions to have common denominators in order to add or subtract?

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The students in my fourth grade class already know how to add and subtract fractions with common denominators. What is the best method of teaching them how to rename fractions to have common denominators in order to add or subtract. How do I make it easier in their terms and words how to teach this? Please help! Thank you.


I have an unusual approach to this for my fifth grade students, and they have had some wonderful successes building number sense...

I have my students use a fraction chart or fraction pieces/bars to list out several equivalent fractions for each of the fractions in the problem. Then, they are free to select one fraction from each "set" to use to solve the problem. Here is how it works:

           1/2   2/4   3/6   4/8   5/10   6/12
         + 3/12  1/4                      3/12

They can choose to add 6/12 and 3/12, or 2/4 and 1/4. Either one will get them the correct answer, and the benefit of using 2/4 and 1/4 is they won't have a fraction that has such large terms...

Here is another example:

       10/12   5/6
      - 5/10   3/6   4/8   2/4   1/2

The way "we" would have solved as this fifth graders would have been to list out the multiples of 12 and 10, and then find the least common multiple... 60... so the new problem would have been

      - 30/60    

which doesn't seem like such a tough problem, but 20/60 is not in lowest terms (though, it isn't hard to simplify)

My students would do 5/6 - 3/6 and get 2/6, which is familiar to them, and they would have little trouble recognizing it is 1/3.

Let me preface all this by saying that my students found equivalent fractions in this same way, using fraction charts and pieces... then looking for similarities in the sets. They "discovered" ways to name equivalent fractions using what they noticed about the fractions in the sets...

When they looked at all the "halves" they noticed that the numerator was always half as large as the denominator... the thirds had a "third as large" relationship, and so on... After some experimenting, they decided they could multiply to find the equivalent fractions, just like we do.

I would encourage you to let them select their equivalent fractions the way I have shown. There is no reason I can think of why they should HAVE to use the least common denominator, when they are demonstrating great fraction sense by finding several options.

-Gail, for the T2T service

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