# Mixed Numbers and the Distributive Property. Is That Possible?

Fifth graders have been working diligently on multiplying fractions and mixed numbers.  We began the unit by exploring parks in 2 neighborhoods.  One was using ¾ of a lot for a children’s play area, and designated ⅖ of that area for blacktop for ball games.  The other neighborhood was using ⅖ of a same-sized lot for a play area and designating ¾ of that area for blacktop.  Students were asked to decide if one neighborhood had more blacktop and prove their answer.

The hardest part was definitely in the proving!  They soon realized that a great way to prove was using visual models of the situation.  See below what some groups came up with:

Not only have we been looking at multiplying proper fractions, but also thinking about mixed numbers.  We have worked with a number of scenarios to find area using mixed numbers.  Some students were surprised to realize that we can use the distributive property (which they have been using since 3rd grade for whole number multiplication) and apply it to mixed numbers.  Below is an example of how it works.  We can split up our numbers into the wholes and the parts and then multiply.  This would be a way to multiply 5 2/8 by 2 ⅓.

Once all of the sections of the array have been multiplied, all you need to do is add up the partial products.

After the break, we will have a class test on multiplying and dividing fractions.  It is already posted on School Loop with the topics.

Have a wonderful Spring Break and enjoy any holidays you may be celebrating!