Multiplying Mixed Fractions Using Distribution – Why?

Carole Garfield in a comment asked for help with teaching the multiplication of mixed fractions using the distributive property.  If I just want to teach students how to multiply mixed fractions I would not use distribution as in this example.

Multiply Mixed Fractions - Without Distribution

Multiply Mixed Fractions – Without Distribution

None of these steps are difficult except maybe the long division and things move quickly.

If I had to teach multiplication with distribution, I would use the multiplication square that some of my students seem to like.  This is the same square they may have used to learn two digit multiplication which also uses the distributive property.  An example would go something like this.

Multiply Mixed Fractions - With Distribution

Multiply Mixed Fractions – With Distribution

[I just found this error (4/26/16).  The answer in the second example should be the same as in the first: ten and three fourteenths.]

This method takes more steps and is a bit tedious.

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About jrh794

I am a sixty-five year old math instructor at Southern Oregon University. I taught at the College of the Siskiyous in Weed California for twenty-six years. Prior to that I worked as a computer programmer, carpenter and in various other jobs. I graduated from Rice University in 1967 and have a MS in Operations Research from Stanford. In the past I have hand-built a stone house and taken long solo bicycle tours. Now I ride my mountain bike and play golf for recreation.
This entry was posted in Curriculum, Math Explorations, Pedagogy, Rants, Teaching and tagged . Bookmark the permalink.

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