Multiplying Mixed Numbers

My students ALWAYS mess up with multiplying mixed numbers because they just want to multiply across.

It is helpful to EXPLAIN WHY this does NOT work.

First of all, make sure your students understand what the problem 3 1/2 x 1 1/4 is saying.  It is saying that I want ALL of 3 1/2 (hence the 1) and then I want another 1/4 of the 3 1/2.  If I want ALL of 3 1/2 and then I want another piece of it (1/4 of it), is there any way my answer could be 3 1/8 which is SMALLER than 3 1/2?  NO WAY!

Then, remind them of multiplication like in the example below.  In multiplication, you have to multiply with EVERY DIGIT.  The same will be true of fractions.

Sooooo, to apply the same method to mixed numbers, we will have to multiply each part of the problem together and then add it up!

Now, they have to add up all these numbers just like you do at the end of large digit multiplication.

WHEW!  The students will see JUST HOW MUCH WORK THIS IS!  Now, they will see that changing the numbers into improper fractions and then solving is MUCH QUICKER.

I find that explaining all of this to my students is very effective in them comprehending conceptually how multiplying mixed numbers works!  What do you find works in your class for multiplying mixed numbers?  Let me know!