Dividing fractions by fractions is easy.
Keep, invert, multiply. Voila! On the other hand, understanding dividing fractions is a bit of a head-scratcher. Importantly, most modern standards expect students to reason mathematically, not just memorize the algorithm. Fortunately, there are visual models to help clear things up.
There is more than one way to model division of fractions. Maybe we draw stacked bar models and compare. This works for denominators that divide evenly, like fourths and eighths, or thirds and sixths. But what if you need to divide 1/4 by 1/3? In that case, the bar models don’t line up evenly. Sad face.
Fortunately, there are other ways to do it. As you can see above, area models work better. Importantly, they serve their purpose: students see how many times the divisor fits into the dividend. Furthermore, by counting the number of shaded parts, the quotient is revealed. Lastly, it connects to division of whole numbers.
Connect to multiplication.
In the Common Core, dividing fractions with visual models is part of sixth grade math. Standard 6.NS.1 expects student to “Solve word problems involving division of fractions using visual fraction models.” Also, the cluster states “apply and extend previous understandings of multiplication.” Furthermore, visual models of multiplicaton and division are very similar. The two can easily be confused. For these reasons, the graphic organizer has two word problems. First, we look at multiplication of fractions. Then, we consider a division word problem. By addressing both operations, we address the standard and call attention to confusing aspects of the lesson.
If you use this lesson with your class, feel free to share your thoughts in the comments below.