Fraction Multiplication

When we multiply a fraction by an integer, the meaning is clear: it means we add that many equal fractions together. For example, 3 times 1/5 means 1/5 + 1/5 + 1/5.

But what about multiplying a fraction by another fraction? What could that mean? When we multiply any number by a fraction, we mean to divide that number into equal parts and taking a specific number of parts. Thus, multiplying a fraction by another simply means taking a fraction of a fraction. We'll illustrate that here.

1. A rectangle has been divided into 6 equal parts in a 2 × 3 grid. Try clicking in the grid and see what happens.

    

   Pick any one cell and make it red. What is the red cell as a fraction of the whole rectangle?

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2. Let's now divide each cell in the above into equal parts:
   Subdivide each cell into parts    

    

   In this finer grid, which cells are from the red cell above? Color them red now. How many small cells did you color red? Enter your answer:  cells. 

   Looking only at the red part. One small red cell is what fraction of the red area?

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3. Count the total number of small cells. Answer the question: What fraction of the whole rectangle is one small red cell?

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4. OK, you know a small red cell is a fraction of the red area. And you know the red area is 1/6 of the whole rectangle. Mathematically, taking a fraction of 1/6 is expressed as the multiplication:

   1   6

   ×

   1

   =

5. Now go back to step 2 and subdivide into 3, 4, or 5 equal parts.