Welcome to my math blog! The purpose of this blog is to help you stay informed about our learning and experiences that have taken place during our math class. I have also included links your child (and you) may want to use in order to supplement math learning in 5th grade.

## Monday, January 19, 2015

### LCM and GCF using Venn Diagrams

Here come the fractions!  In preparation for adding and subtracting fractions, I introduced the concepts of Least Common Multiple and Greatest Common Factor.

I explained that we use LCM whenever we are expected to add and subtract fractions that do not have a common denominator.  However, I used two visual graphics to teach this concept instead of listing all of the factors of each of the given denomiators.  We began by finding the prime factors of both of the given denominators by using a factor tree.  For example:

Then we use our factor trees to place our numbers into a Venn Diagram (placing the common factors in the center).  Once all of the factors from both numbers  have been placed on the Venn, multiply ALL of the numbers together to find the LCM.

Once we had a common denominator, we now had to create equivalent fractions using this new denominator.  Then add the fractions together to determine the answer.

Now, once we had an answer we need to simplify our fraction.  To do this, we need to use the Greatest Common Factor to determine what to divide by.  We began much in the same manner as LCM.  We took the numerator and denominator and created factor trees.  Then we placed our prime factors in a Venn Diagram.  This time, however, you need only multiply the factors that are in the center section of the Venn... the ones both numbers have in common.  This is the number you need to divide the numerator and denominator by to find simplest form of the fraction.