6.3 Multiplying Fractions
Part (d) of the activity on the previous page does not give a surprising result, mathematically speaking. One-third of one-half is indeed one-sixth. To convince yourself, take a piece of notebook paper. Fold it in half along the long side and shade one half of the paper. Then, fold it into thirds along the short side. The paper is now split into six equal pieces, or sixths. If you look at the shaded half, you can see that one out of three parts of this portion represents one out of six parts of the entire paper as shown below.
Mathematically, this is written as .
To multiply two fractions together, you must multiply the numerators together, then multiply the denominators together, and reduce the answer if necessary.
It is often easier to reduce before multiplying out. For example, let’s consider .
Multiplying the numerators together, then multiplying the denominators together gives , but we can cancel out the 2s using division: .
This calculation is equivalent to canceling at the start of the calculation:
The next page summarizes this procedure, followed by an exploration to help you learn how to use your calculator to aid in the multiplication of fractions.